## You’re Home Alone. You Can Buy Zillions Of Video Game Cigarettes Or Beat Yourself At Bananagrams

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,9 and you may get a shoutout in next week’s column. If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter.

## Riddler Express

From Gerald Dorrer, I reckon this here’s a math puzzle:

In the video game “Red Dead Redemption 2,” there is a side quest where the main character is supposed to collect 12 sets of cigarette cards, each consisting of 12 unique cards.

Some cards can be found lying around in the open world, but the easiest way to collect the cards is to buy cigarettes at the store and collect the single random card included in each pack. Suppose Arthur is too lazy to look for cards in the open world and tries to complete the set only by buying packs at the store.

At $5 a pack, how much money do we expect Arthur to spend to complete all 12 sets? ## Riddler Classic From Chadwick Matlin, the deputy editor of some website called FiveThirtyEight, a puzzle perfect for the polar vortex: You’re snowed in alone with nothing to do but play a solitaire game of Bananagrams. As you spread its 144 lettered tiles out on the table in front of you, you begin to wonder: What grid of words can you create that uses all of these tiles in the fewest possible words? What grid uses all of the tiles in the most possible words? (To test if a word is allowed, use the ENABLE word list, a variant of which is used in games such as Words With Friends, for the purposes of this problem. The letters in Bananagrams are distributed as shown here.) Extra credit: How many completed grids are there, period, that use all 144 tiles? ## Solution to the last week’s Riddler Express Congratulations to Erin Seligsohn of Atlanta, winner of last week’s Riddler Express! Last week, we found ourselves on an island with a curious property: All of its young people told the truth and all of its old people lied. Specifically, there was an age limit L — a positive integer — and all islanders who were younger than age L only told the truth, while islanders who were at least L years old only told lies. We met five of them, and they had this to say. A: “B is more than 20 years old.” B: “C is more than 18 years old.” C: “D is less than 22 years old.” D: “E is not 17 years old.” E: “A is more than 21 years old.” A: “D is more than 16 years old.” B: “E is less than 20 years old.” C: “A is 19 years old.” D: “B is 20 years old.” E: “C is less than 18 years old.” What was L, and what could we learn about the ages of the islanders? L was 19 years old. Islander A was 19 years old, B was 20, C was 18, D was at most 16 and E was at least 20. The key is to ferret out the liars. Notice first that there are a few direct contradictions in the islanders’ statements: A and D contradict each other over B’s age, B and E contradict each other over C’s age, and E and C contradict each other over A’s age. So at least one member of the three pairs (A, D), (B, E) and (E, C) must be a liar. We also know that D and B aren’t both liars — that would make E both exactly 17 years old and more than 20 years old, which is impossible. Given those facts, we have a few possibilities we can test. Let’s guess that A, B and E are liars and that C and D are truth-tellers, then check the consistency of their statements. There are two statements about each islander, which we can translate into true facts given our guess about the truthfulness of each of their speakers. The statements about A check out: A is less than or equal to 21 and A is 19. That means A is 19. The statements about B also check out: B is less than or equal to 20 and B is 20. That means B is 20. The same goes for C: C is less than or equal to 18 and C is greater than or equal to 18. That means C is 18. And D: D is less than 22 and D is less than or equal to 16. That means D is at most 16 years old. And finally E: E is not 17 and E is greater than or equal to 20. That means E is at least 20. Because all these statements check out, that means our guess worked! Since A, B and E are liars and C and D tell the truth, that means both of our truth-tellers are at most 18 and all of our liars are 19 or older. Therefore, L must equal 19. And we’re done! And I don’t know about you, but I’m ready to get off this island. ## Solution to last week’s Riddler Classic Congratulations to Onufry Wojtaszczyk of Warsaw, Poland, winner of last week’s Riddler Classic! Once we got off that island, we headed straight for some rest and relaxation at the card table, where we sat down to play a game of bridge. The game begins with an auction. There are four players, each sitting across from his or her partner. Simply put, the auction goes like this: Beginning with the dealer and orbiting around the table, players can place a bid or pass. Players who’ve passed can re-enter the bidding later. A bid is comprised of a number (one through seven) and a suit. Every legal bid must be higher than the one that came before, meaning either that its number is higher or that its number is the same and its suit is higher (from high to low, the suits go no-trump, spades, hearts, diamonds, clubs). The auction ends if the other three players pass after a bid, or if all four players pass right away. But the R&R came to an abrupt end with this question: How many different legal bridge auctions are there? There are 1,574,122,160,956,548,404,565, or more than a thousand billion billion, or more than the estimated number of grains of sand on the planet. To get there, let’s start with a much smaller number: 35. A bid is made up of one of seven numbers and one of five “suits” (the four suits plus no-trump); multiplying numbers and suits gives us 35 possible bids, each with a unique rank. From there, let’s build up to our final calculation. We know now that in every auction, the players will make somewhere between one and 35 bids. We will proceed by counting all the auctions with one bid, with two bids, with three bids and so on, and add up all of their possibilities in a big sum. If an auction comprises $$N$$ bids, say, then there are “35 choose $$N$$” choices for what specific bids those could be. And between those bids will be some number of passes. Before the first bid there could be zero, one, two or three passes (four possibilities), and between all subsequent bids there can be zero, one or two passes (three possibilities chosen at $$N-1$$ points in the auction). We can account for passes by multiplying by those numbers of possibilities. That leads us to our final, big sum: \begin{equation*}1+\sum_{N=1}^{35} {35 \choose N}\cdot 4\cdot 3^{N-1}\end{equation*} An online calculator can turn this into our numerical final answer. That lone “1+” at the front of the equation is the possibility that the auction ends immediately with all four players passing. For extra credit, I asked how many different auctions there would be if we incorporated the bridge tactics known as doubling and redoubling. The calculation process is very similar, and the new formula — taking into account that there are now 21 intra-bid combinations of passes, doubles and redoubles, plus seven ways the auction ends with passes, doubles and redoubles — looks like this: \begin{equation*}1+\sum_{N=1}^{35} {35 \choose N}\cdot 4\cdot 21^{N-1}\cdot 7\end{equation*} And the final answer is, of course, bigger. Much, much bigger: 128,745,650,347,030,683,120,231,926,111,609,371,363,122,697,557. But in the grand scale of gnarly game math, the number of possible bridge auctions isn’t all that enormous: It is only about 0.25 percent of the number of possible chess positions. ## Want more riddles? Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now! ## Want to submit a riddle? Email me at [email protected] ## Bryce Harper May Already Be Past His Prime The Philadelphia Phillies and star outfielder Bryce Harper on Thursday reached a record free-agent agreement in terms of total dollars ($330 million) and years (13). After waiting 123 days since the World Series ended, Harper breaks the mark set just days earlier by Manny Machado. The previous open-market record — Alex Rodriguez’s free-agent contract for $275 million deal with the Yankees on Dec. 13, 2007 — stood for 11 years until this winter.1 But Harper’s deal falls short in terms of annual average value ($25.4 million). For instance, Rodriguez’s mega deals signed in 2007 and 2001 each had greater average values, and offseason speculation expected that Harper might command more than $30 million per season.2 There is no opt-out clause in the deal, but there is a no-trade clause. Given the deal’s less-than-expected annual average value and Harper’s far-longer-than-expected wait on the open market, the contract suggests that the baseball industry didn’t quite know what to make of Bryce Harper. The good news for the Phillies is that Harper should help them immediately. Based on 100 simulations run for FiveThirtyEight by Out of the Park Developments, Harper will improve the Phillies from an 80.2-win team in 2019 to an 86.1-win team, though the computer forecasts still had Philadelphia missing the postseason. Harper caps an aggressive offseason for the Phillies, who traded for catcher J.T. Realmuto and shortstop Jean Segura and added notable free agents Andrew McCutchen and David Robertson to a young core led by ace pitcher Aaron Nola and slugger Rhys Hoskins. But what’s troubling for the Phillies, who are now committed to Harper through his age 38 season in 2031, is that there’s a good chance that Harper has already played his best baseball. Harper was on the cover of Sports Illustrated in 2009 at age 16, dubbed the “most exciting prodigy since LeBron.” A year later, he was the No. 1 overall pick in the draft. He debuted as a 19-year-old in 2012 and won rookie of the year. In 2015, he posted a season of 10 wins above replacement and was named as the National League MVP. Since he reached the majors in 2012, he’s 20th in position player WAR, and he owns a .900 OPS (on-base plus slugging). In many ways, he’s lived up to the hype. But seven seasons into his career, we’re not exactly sure what type of player Harper is. While he’s shown stretches of brilliance, volatility in performance has been his most consistent trait. This has led to an unusual career trajectory to date. He’s one of only 15 position players 25 and younger to own a 10-WAR season, according to Baseball-Reference.com. The rare company includes Ted Williams, Mike Trout, Willie Mays, Lou Gehrig and Cal Ripken Jr. But he’s had just the one elite-level season.3 His other campaigns have had a range of outcomes, from 1.1 to 5.1 WAR. Even within seasons, he’s had dramatic peaks and valleys. Last year, for instance, he hit .214 with an .833 OPS in the first half but was a star in the second half when he hit .300 with a .972 OPS. Injuries have played a role in this. Harper has played fewer than 120 games in three of his seven years in the majors, and those partial seasons have also limited his ability to rack up WAR, which is a cumulative stat that rewards just showing up for work. FiveThirtyEight examined all players in MLB history who have had one season of 8 or more WAR — but only one — before turning 26, and then we studied the trajectory of those players’ careers. There are 32 such players in MLB history, including three other than Harper who are still active: Aaron Judge, Matt Chapman (who hasn’t played his age 26 season) and Evan Longoria. Of the 28 players who are no longer active, 17 never produced another 8-plus WAR season after their age 25 season. The historical players studied peaked at age 24 (6.6 WAR) and 25 (6.5 WAR), then they declined steadily. A player’s peak is often earlier than conventional wisdom would expect. Jeff Zimmerman at FanGraphs found that while the average ballplayer peaks at age 27, good players peak at either 25 or 26 years old. While there are exceptions like Adrian Beltre and Henry Aaron, who had some of their best years later in their careers, the best baseball happens early for many excellent players. That doesn’t mean that Harper (or Machado, for that matter) can’t be a star-level player regularly, but history is betting against him becoming a consistent MVP presence like Mike Trout. Baseball may not quite know what Bryce Harper is, but the Phillies are going to find out. Neil Paine contributed research. ## The NFL Is Drafting Quarterbacks All Wrong No position in professional sports is more important or more misunderstood than the quarterback. NFL scouts, coaches and general managers — the world’s foremost experts on football player evaluation — have been notoriously terrible at separating good QB prospects from the bad through the years. No franchise or GM has shown the ability to beat the draft over time, and economists Cade Massey and Richard Thaler have convincingly shown that the league’s lack of consistent draft success is likely due to overconfidence rather than an efficient market. Throw in the fact that young QBs are sometimes placed in schemes that fail to take advantage of their skills,1 that red flags regarding character go unidentified or ignored2 and that prospects often lack stable coaching environments, and there is no shortage of explanations for the recurring evaluation failures. All of this uncertainty makes the NFL draft extremely exciting: You never know for certain who will be good and who will be an absolute bust. Last year, much of the pre-draft speculation surrounded where current Buffalo Bills starting QB Josh Allen — who is tall and can hit an upright from his knees from 50 yards away — would be selected. This year, when Oklahoma’s Kyler Murray decided to forgo a career in baseball for a chance to become a top pick in the 2019 NFL draft, his measurables captured attention in a different way. Murray, listed at 5-foot-10 and 194 pounds, is 7 inches shorter and more than 40 pounds lighter than Allen, and he’s the the smallest top QB prospect in recent memory. While some scouts and NFL decision makers think Murray’s odds for NFL success are long — or have him off their draft boards entirely because of his lack of size — there is strong evidence in the form of metrics and models that he is actually a good bet to succeed. Like the rest of the league, practitioners of analytics have a pretty poor track record at predicting QB success. It wasn’t just Browns fans who were high on Johnny Manziel — many predictive performance metrics liked him as well. If some of the world’s best football talent evaluators are convinced that Murray’s height is at least a minor red flag, how can we be confident that a 5-foot-10 college QB will be productive in the NFL? When it comes to the draft, deep humility is warranted. Still, there are solid reasons to be excited about Murray. Completion percentage is the performance measurable that best translates from college to the NFL. The metric’s shortcomings — players can pad their completion percentage with short, safe passes, for instance — are well-known. But even in its raw form, it’s a useful predictive tool. ##### Completion percentage translates from college to the NFL Share of NFL quarterback performance predicted by college performance in seven measures, 2011-18 share predicted Completion percentage 17.9% Average depth of target 16.7 ESPN’s Total QBR 12.1 Yards per game 9.2 Touchdown rate 8.5 Yards per attempt 7.0 Adjusted yards per attempt 4.2 For players who attempted at least 100 passes in the NFL. “Share predicted” here refers to the amount of variance in the dependent variable explained by the independent variable in a bivariate regression. Source: ESPN Stats & information group Its kissing cousin in the pantheon of stats that translate from college to the pros is average depth of target: Passers who throw short (or deep) in college tend to continue that pattern in the NFL. These two metrics can be combined3 to create an expected completion percentage, which helps correct the deficiencies in raw completion percentage. If you give more credit to players who routinely complete deeper passes — and dock passers who dump off and check down more frequently — you can get a clearer picture of a player’s true accuracy and decision-making. Another important adjustment is to account for the level of competition a player faced. ESPN’s Total Quarterback Rating does this, and we’re doing it, too. For instance, passes in the Big Ten are completed at a lower rate than in the Big 12 and the Pac-12. We should boost players from conferences where it is tougher to complete a pass and ding players whose numbers are generated in conferences where passing is easier. When we make these adjustments, and then subtract expected completion percentage from a QB’s actual completion percentage, we get a new metric: completion percentage over expected, or CPOE. An example: In 2011 at Wisconsin, Russell Wilson had a raw completion percentage of 73 percent. We would expect an average QB in the same conference who attempted the same number of passes at the same depths that Wilson attempted to have a completion percentage of just 57 percent. So Wilson posted an incredible CPOE of +16 percentage points in his last year of college. CPOE translates slightly less to the NFL than either raw completion percentage or average depth of target,4 but it does a substantially better job of predicting on-field production. In stat nerd parlance, we’ve traded a little stability for increased relevance. ##### CPOE best predicts yards per attempt in the NFL Share of an NFL quarterback’s yards per attempt predicted by college performance measures, 2011-18 share predicted Completion percentage over expected 15.5% Completion percentage 13.5 ESPN’s Total QBR 13.2 Yards per attempt 7.0 Average depth of target 0.0 For players who attempted at least 100 passes in the NFL. “Share predicted” here refers to the amount of variance in the dependent variable explained by the independent variable in a bivariate regression. Source: ESPN Stats & Information group The test of a good metric is that it is stable over time (for example from college to the NFL) and that it correlates with something important or valuable. Completion percentage over expected is slightly more stable than other advanced metrics like QBR. CPOE is also the best predictor of NFL yards per attempt. Since yards per attempt correlates well with NFL wins, and winning is both important and valuable, we’ve found a solid metric. It should help us identify NFL prospects likely to be good — so long as they are drafted and see enough playing time to accumulate 100 or more passing attempts.5 But before we stuff the metric into a model and start ranking this year’s quarterback prospects, it’s worth asking why CPOE in college might be a good measure of QB skill. One possible explanation is that it’s measuring not just accuracy but also the signal from other qualities that are crucial to pro success. The ability to consistently find the open receiver and complete a pass to him requires a quarterback first to read a defense and then to throw on time and on target. Throwing with anticipation and football IQ are both crucial to playing in the NFL at a high level, and they are likely both a part of the success signal in the metric. CPOE is also probably capturing the ability to execute a system efficiently. A quarterback who understands how each piece of the offense complements the others and constrains the opposing defense is a huge asset for his team. The term “system QB” has a negative connotation in player evaluation circles that is probably unwarranted. If a quarterback is operating at a high level, he is inseparable from the system he’s being asked to run. It’s also likely the case that the mental and physical abilities to run any system efficiently are traits that translate — even if only imperfectly — to the pro game. CPOE also measures accuracy, of course — which many believe is the most important trait a QB can posses. Some coaches believe accuracy is an innate skill and not something that can be taught once a player has reached college. Others believe that mechanical flaws can be corrected if other traits like arm strength are present. The Bills clearly hold this view or they wouldn’t have drafted Allen, a player with an incredibly live arm but who had a college completion rate 9.2 percentage points below expected. But regardless of whether accuracy can be taught at the NFL level, all evaluators acknowledge its importance. With all this in mind, I built a simple logistic regression model that attempts to identify players who will go on to establish a career mark of at least 7.1 yards per attempt in the NFL — the league average from 2009 to 2018. The model took into account CPOE and six other metrics, all calculated for the player’s college career.6 There are 49 quarterbacks who have entered the NFL since 2012 who have also attempted at least 100 passes — except for small-school QBs for whom advanced college data wasn’t available. I randomly split those players into two sets and used one set to build the model and the second set to test to see if the model is any better than random chance at identifying which prospects will go on to play productive NFL football. Though the model is relatively simple — and it would be wonderful if the sample size were larger — the results are promising. The model correctly identified many players who went on to have NFL success and many more who didn’t. The best estimate for its generalized accuracy is that it will correctly identify a QB prospect as a hit or a bust in around 74 percent of cases.7 The table below shows the results of the model, labeled Predict, and includes players’ college stats. ##### Results from the quarterback prospect model A random sample of the 49 quarterbacks who were drafted since 2012* by model probability, along with college stats including completion percentage over expected (CPOE) College stats name CPOE YPA Avg. depth of target Total QBR Predicted prob.† Career NFL YPA Russell Wilson +16 10.3 10.4 94 >99% 7.9 Johnny Manziel +9 9.1 8.8 89 99 6.5 Jameis Winston +8 9.4 9.6 83 98 7.6 Kellen Moore +10 8.7 7.8 86 97 7.5 Deshaun Watson +5 8.4 8.8 86 93 8.3 Sam Darnold +5 8.5 9.5 80 77 6.9 Matt Barkley +4 8.2 8.1 77 73 7.4 Jared Goff +1 7.8 9.0 74 61 7.7 Kevin Hogan +4 8.5 9.3 80 37 6.1 Marcus Mariota +4 9.3 8.2 90 33 7.2 Kirk Cousins +4 7.9 8.5 58 29 7.6 Paxton Lynch +2 7.4 7.9 59 14 6.2 Geno Smith +3 8.2 7.3 74 5 6.8 Nathan Peterman +1 7.9 8.9 71 4 4.3 Zach Mettenberger +4 8.8 10.5 71 4 6.8 Trevor Siemian 0 6.4 8.2 53 3 6.8 Matt McGloin -2 7.2 8.5 60 2 6.7 Blake Bortles +4 8.5 7.5 78 1 6.7 Lamar Jackson 0 8.3 11.0 82 0 7.1 *And have attempted at least 100 passes in the NFL. †Probability the player will meet or exceed a career yards per passing attempt average of 7.1. Source: ESPN stats & information group Humility is warranted at this moment, so let’s point and laugh at the failures first. After all, all models are universally wrong, but some can be useful. This one was wrong about Johnny Football, as it practically guaranteed Manziel to be an above-average NFL quarterback. What it didn’t know about was Johnny’s love of all-night parties and other off-field shenanigans. Kellen Moore, a lefty passer who had a decorated career at Boise State, is another hiccup for the model. Moore is an interesting case of a player who just barely reached the 100 passing attempt threshold and eclipsed 7.1 yards per attempt for his NFL career but still bounced around the league and never found success or even a starting job. So the model predicted his statistical success in yards per attempt but not his actual success on the field. The problem here is that our success metric — career yards per attempt over 7.1 — doesn’t perfectly discriminate between good and bad NFL QBs. Much like human evaluators, models can sometimes be right for the wrong reasons, and Moore is a prime example.8 The model was also suspiciously bad at predicting Lamar Jackson, ranking him as an almost sure bust as a passer. Jackson’s career yards per attempt — most of those attempts coming in just seven games — is right at the 7.1 threshold, and while he is no one’s idea of Drew Brees, a success probability of zero seems an overly harsh assessment for a player that has clear talent — especially running the ball — and has already helped his team to the playoffs. Still, the good outweighs the bad. The only other false negatives in the bunch are Kirk Cousins and Marcus Mariota, both of whom have career yards per attempt figures above 7.1. Meanwhile the low probabilities assigned to passers like Nate Peterman, Zach Mettenberger, Paxton Lynch, Geno Smith and Blake Bortles all appear reasonably prescient. Looking forward and applying the model to the current draft class, we find a few surprises. Kyler Murray sits comfortably at the top with a 97 percent probability of being an above-average pro quarterback. Murray’s physical and statistical production comps with Russell Wilson are especially striking. Wilson and Murray had roughly the same yards per attempt in college, identical average depth of target and similar Total QBR.9 Both are also under 6 feet tall and played baseball at a high level. As far as comps go for short QBs, you really can’t do any better. Murray isn’t just a scrambler who excels working outside of the pocket and on broken plays, either. According to the ESPN Stats & Information Group, 91 percent of Murray’s 377 pass attempts in 2018 came inside the pocket, and 81.6 percent of those throws were on target and catchable. Murray faced five or more defensive backs on 82 percent of his passing attempts and threw a catchable pass 78.8 percent of the time. Against nickel and dime packages, he was even better when blitzed, with 79.1 percent of his passes charted as catchable when the defense brought pressure. And Murray didn’t just check down to the outlet receiver when the other team sent heat. Kyler pushed the ball downfield at depths of 20 yards or greater 21 percent of the time vs. a blitzing defender. Meanwhile the other consensus first-round talent, Ohio State’s Dwayne Haskins, is viewed as much less of a sure thing by the model. While his CPOE is identical to Murray’s and his QBR is similar, the model rates his yards per attempt and low average depth of target as red flags that drag down his probability of success. Nickel is the base defense in the NFL, so a quarterback’s performance against it is important, and Haskins faced five or more defensive backs far less often than Murray, dropping back against nickel or dime on just 63 percent of his pass attempts. And when Haskins was blitzed out of those looks, he was not as adept at delivering on-target passes, with 76.4 percent charted as catchable despite only 6.6 percent traveling 20 yards or more in the air. ##### Kyler Murray’s accuracy and rushing put him atop his class College quarterbacks invited to the 2019 NFL combine by their career statistics and predicted probability of success* College stats Player CPOE YPA Avg. depth of target Total QBR Predicted Prob.† Kyler Murray +9% 10.4 10.4 92 97% Will Grier +6 9.0 10.2 78 90 Ryan Finley +4 7.6 8.5 76 78 Jordan Ta’amu +6 9.5 10.1 72 72 Dwayne Haskins +9 9.1 7.8 87 63 Brett Rypien +5 8.4 9.9 67 39 Jake Browning +3 8.3 8.8 73 38 Clayton Thorson 0 6.3 7.9 61 29 Trace McSorley +3 8.1 9.7 73 22 Daniel Jones -2 6.4 7.7 62 17 Gardner Minshew +2 7.1 6.8 70 4 Jarrett Stidham +3 8.5 8.3 69 3 Kyle Shurmur -3 7.0 9.0 59 1 Drew Lock -1 7.9 10.3 66 <1 Tyree Jackson -2 7.3 10.4 59 <1 Nick Fitzgerald -4 6.6 10.2 72 <1 *Excluding Easton Stick because of lack of data †Probability the player will meet or exceed a career average of 7.1 yards per passing attempt Source: ESPN Stats & Information Group Other surprises from the consensus top-four prospects are the rankings of Duke’s Daniel Jones and Missouri’s Drew Lock — both of whom completed fewer passes than we would expect, and both of whom were assigned a low probability of NFL success. Teams should probably be very wary of both players. Since 2011, college QB prospects with completion percentages under expected — a list that includes Brock Osweiler, Trevor Siemian, Mike Glennon, Matt McGloin and Jacoby Brissett — have all failed to post career yards per attempt above the league average of 7.1. Meanwhile West Virginia’s Will Grier — a player few experts have mocked to go in the first round — looks to be the second-best QB prospect of the class. With his excellent college production and nearly prototypical size at 6-foot-3 and 217 pounds, Grier is a player whose stock could rise with a good performance on and off the field at the combine. There are many weeks of interviews, testing and evaluation left to come for each of these prospects, and analytics are just one piece of the process. Models are certainly not a player’s destiny. Murray might end up profiling as a selfish diva who can’t play well with others. Lock could somehow morph into Patrick Mahomes. But ultimately the model and the metrics agree with Arizona Cardinals coach Kliff Kingsbury’s assessment that Murray is worthy of the top overall pick in the draft. Ship him off to a team with an early pick and a creative play-caller, and enjoy the air raid fever dream that follows. ## Legendary Quarterback John Elway Can’t Figure Out Quarterbacks John Elway sees a Hall of Fame quarterback every time he looks in the mirror. So you can imagine the frustration of the Denver Broncos’ general manager that he hasn’t been able to spot a new franchise QB since Peyton Manning left town three years ago. When the Broncos open the 2019 season, Joe Flacco is expected to be the fifth player to get a crack at the position since the 2015 campaign that culminated in a Super Bowl victory. Flacco’s signing came as a shock to Case Keenum, the team’s starting quarterback last year. But it should hardly have been a surprise given that, in Elway’s eight years in charge of the team’s roster, he has already cycled through seven different starting QBs.1 Flacco hardly seems a long-term answer entering his age-34 season — or an answer at all given that he’s 39th out of 42 qualifying starters in yards per pass attempt over the past three seasons, according to ESPN’s Stats & Information Group. The Broncos are 29th out of the 32 teams in Total Quarterback Rating2 since the start of the 2016 season. And the teams behind them — the Jets, Cardinals and Browns — drafted quarterbacks in 2018 with top-10 picks. ##### Denver is throwing nowhere fast NFL teams ranked by Total Quarterback Rating, 2016-2018 Rank Team Passer Rating Total QB Rating 32 Cleveland Browns 75.9 39.0 31 Arizona Cardinals 76.9 41.7 30 New York Jets 75.3 42.7 29 Denver Broncos 79.7 43.0 28 Miami Dolphins 88.2 43.9 27 Jacksonville Jaguars 80.9 47.3 26 Chicago Bears 85.5 47.5 25 New York Giants 86.1 48.0 24 St. Louis/L.A. Rams 89.6 49.0 23 San Francisco 49ers 83.1 49.3 22 Cincinnati Bengals 88.4 49.7 21 Carolina Panthers 82.7 50.0 20 Baltimore Ravens 82.7 50.2 19 Oakland Raiders 91.5 51.1 18 Buffalo Bills 76.9 51.2 17 Tennessee Titans 86.8 55.1 16 Washington Redskins 90.3 56.2 15 Houston Texans 85.6 57.7 14 Tampa Bay Buccaneers 90.6 60.2 13 Indianapolis Colts 91.7 60.5 12 Philadelphia Eagles 92.4 60.9 11 Seattle Seahawks 98.6 61.4 10 Detroit Lions 93.4 61.6 9 Minnesota Vikings 98.8 62.2 8 Green Bay Packers 93.0 62.3 7 San Diego/L.A. Chargers 95.5 62.5 6 Pittsburgh Steelers 94.6 65.4 5 Dallas Cowboys 95.3 67.6 4 Kansas City Chiefs 102.8 69.3 3 New Orleans Saints 105.9 69.7 2 Atlanta Falcons 105.9 71.7 1 New England Patriots 103.2 72.5 Source: Espn Stats & Information Group It’s difficult to make the case that Flacco is any more likely to reverse the team’s fortunes at quarterback than Keenum was. So the Broncos’ search for a quarterback probably isn’t over. Elway admitted after the season that the team needed to find a long-term solution. But they’re not the only team in the NFL with that problem. Washington, Miami and Jacksonville are reportedly looking for new quarterbacks, probably vying with Denver to add one via the draft. And the Giants are widely expected to draft a quarterback after general manager Dave Gettleman refused to commit to Eli Manning as the team’s 2019 starter. Usually, endless quarterback searches correlate with losing. The best example since Elway joined the Broncos’ front office in 2011 is the Browns, who have won just 24.6 percent of their contests while seeing 10 quarterbacks start at least five games. But Denver has managed to win 62.6 percent of its games in that time — the highest winning percentage of any team with at least five different quarterbacks who started at least five games. Most of Denver’s success in this time frame came with Manning under center. He delivered consistency and success (45-12 regular-season record) to a franchise that hasn’t seen the same quarterback start five seasons in a row since Elway did it himself. So a more impressive showing may belong to the Houston Texans, who somehow posted a 51.2 winning percentage despite starting eight different quarterbacks. The Texans finally seem to have found their long-term answer: Deshaun Watson, for whom they traded up from the 25th slot in the 2017 draft. The Broncos had a higher selection to trade that year (20th) but held it to select tackle Garett Bolles. One of Elway’s problems is that even without Manning, the Broncos have not been bad enough to be in position to draft a top quarterback. This year, they’re slated to pick 10th — behind both the Giants and Jaguars. But with a 20-28 record over the past three seasons, they’re not overcoming bad QB play, either. If Flacco does take over as signal-caller, this would be the second year in a row that the Broncos will have looked to another team for its starting QB. That’s an unconventional path to finding a signal caller given that last year, with Keenum, Denver was one of just four teams3 to have a passing leader by attempts who had ever played with another club. Elway has tried drafting quarterbacks, too, selecting presumed Manning replacement Brock Osweiler in the second round of the 2012 draft, Trevor Siemian in the seventh round in 2015 and 26th-overall selection Paxton Lynch — Elway’s one first-round quarterback pick — a year later. Despite the opportunity to learn tips and tricks from Elway, who mastered the position at a Hall of Fame level, none of those players is currently on Denver’s roster. Elway had a chance last year to spend a premium pick on a quarterback but passed on Josh Allen and Josh Rosen. That was after being beaten to the punch by the Jets for the quarterback he was rumored to prefer among all others in 2018, Sam Darnold.4 When he took the job, Elway expected that a consensus franchise quarterback would have to be acquired with a top-five-overall pick. He also believed that one could be developed with the right supporting cast, including the coaching staff. But he did not sound like someone who knew what to look for. “You look for those traits that you see in each quarterback that you believe can translate into a franchise guy,” Elway told the Denver Post in 2011. “There’s the stuff you can see on film, but there’s so much more that you can’t see on film.” Flacco has a reputation for being big-armed like Elway, who was famed for imprinting the “Elway Cross” into the chests of his receivers with the velocity of his perfect spirals. But that element to Flacco’s game has faded in recent years: Since 2016, he ranks 37th out of 41 quarterbacks in Raw QBR on passes 20-plus yards from the line of scrimmage. Yet Elway seems content to bet on Flacco’s reversing the team’s fortunes at least in the short term. Does Elway see something in Flacco that few others can, given how widely the transaction has been panned? Or is it possible that one of the greatest quarterbacks in NFL history just can’t judge or develop quarterbacks? Cognitive scientist Sian Beilock, the president of Barnard College, wrote in Psychology Today that there’s little chance that former athletes can remember what made them great. In fact, those athletes probably couldn’t have communicated it even when they were playing. “When your performance flows largely outside of your conscious awareness, your memories of what you’ve done are just not that good,” Beilock wrote. “This makes it hard to teach what you know to someone else. … As you get better and better at what you do, your ability to communicate your understanding or to help others learn that skill often gets worse and worse.” The same presumably holds true for knowing what to look for in a player at the position you played. So it just may be that the worst person to pick the new Elway for the Broncos is Elway himself. Neil Paine contributed research. ## Relievers Have Broken Baseball. We Have A Plan To Fix It. Earlier this month, Major League Baseball said it was considering a rule change to require pitchers to face at least three batters per appearance — or finish an inning — as part of a series of initiatives to improve the pace of play. I don’t hate this; I’ve always been a fan of relief pitchers working longer outings. But I think the MLB proposal misses the real problem. The issue isn’t really with relievers who face just one hitter at a time. In fact, LOOGYs — Left-handed One-Out Guys — are already fading in popularity as teams realize that if a pitcher isn’t good enough to face multiple hitters in a row, he may not belong in the bullpen pecking order at all. Instead, the problem concerns teams that use a parade of relievers who enter the game from the sixth inning onward and throw the hell out of the ball, knowing they’ll probably max out at one inning at a time. (The Yankee bullpen is a prime example.) You might call these pitchers OMGs: One-inning Max-effort Guys. They can be incredibly, game-changingly effective, but they aren’t necessarily all that skilled. In fact, the whole problem is that OMGs are a renewable resource, with no real constraints on supply. Teams can take failed starters with two decent pitches and, after some weeding out, turn them into OMGs who will strike out 25 or 30 percent of the batters they face, provided they only have to throw one inning every second or third day. It also yields rosters that are grossly imbalanced relative to the amount of value that these relievers generate. According to FanGraphs, relief pitchers accounted for only about 9 percent of the value (in wins above replacement) that all position players and pitchers created last year. And yet, they occupy about 25 percent of roster slots. And to a larger degree than you probably realize, these OMGs bear responsibility for the ever-increasing rate of strikeouts in baseball — something that was easier to shrug off until MLB attendance started to decline. ## More relievers means more strikeouts Strikeouts have been increasing for more or less the entirety of baseball history. Here’s the trajectory from 190811 up until last year — when, for the first time, more plate appearances ended with strikeouts than with base hits. There are a couple of peaks marking the end of the Deadball Era in the late 1910s and then another pitchers’ era in the mid-to-late 1960s, but overall the trend is very steady. Over this period, the correlation between the year and the strikeout rate is 0.91. One other baseball trend has been equally if not more relentless, however: As time has passed, teams have relied more and more on their bullpens. As a result, both starting pitchers and relievers have seen increasingly shorter stints. Thus, the number of pitchers per team per game has steadily increased, from 1.4 in 1908 to around 4.4 now. The correlation is stronger still if you look at the number of pitchers used relative to the number of plate appearances in a typical game.12 For instance, if you take the number of pitchers used per 38 plate appearances13 — over the long run, MLB teams average about 38 plate appearances per game — you get this: That looks a lot like the previous graph showing the strikeout rate — the correlation is 0.96 — including a dip in both pitchers used and strikeouts at the end of the Deadball Era in the late 1910s and again at the end of the Second Deadball Era in the early 1970s, and then an especially steep acceleration in both strikeouts and pitchers used over the past few years. It’s not just a coincidence that relief pitcher usage and strikeout rate are correlated in this way. When you take a starter and use him in relief — especially in a short stint that typically lasts only an inning or so — his strikeout rate will be usually be higher, and sometimes a lot higher. You can also expect him to throw harder and to use a more dangerous repertoire consisting of more fastballs and sliders. Here’s the tale of the tape. Using data from FanGraphs, I looked at all pitchers who worked both as starters and relievers between 2016 and 2018, providing for a direct, head-to-head comparison of how the pitchers performed in each role. These pitchers’ strikeout rates were about 12 percent higher when they came on in relief than when they started. They also threw about a mile per hour harder in relief.14 ##### Starters supercharge their K rate when working in relief Statistics for MLB pitchers who worked as both starters and relievers, 2016-18 As starter As reliever Strikeout rate 18.4% 20.6% Fastball velocity 91.6 mph 92.5 mph Share fastballs 54.1% 55.1% Share sliders 13.9% 15.0% Observations are weighted by the lesser of the number of batters a pitcher faced as a starter and in relief from 2016 to 2018. For example, a pitcher who threw to 500 batters as a starter and 200 batters as a reliever would receive a weight of 200. Pitchers who averaged fewer than 15 batters faced per start, i.e. who served as “openers” or tandem starters, are excluded from the analysis. Source: Fangraphs Those are meaningful gains, but the really big differences come when you use pitchers in short stints that are roughly one inning long. In the next table, I’ve assigned the pitchers who worked both as starters and relievers into three groups: first, those who averaged five or fewer batters faced per relief appearance (these are guys who usually threw just one inning at a time — the OMGs); second, those who averaged more than five but fewer than eight batters faced (a mix of one-inning and multi-inning appearances); and third, those who averaged eight or more batters faced (mostly multi-inning appearances). ##### It’s much easier to throw an inning at a time Statistics for MLB pitchers who worked as both starters and relievers, 2016-18, by how many batters faced per relief appearance Five or fewer batters As starter As reliever Strikeout rate 19.9% 23.9% Fastball velocity 91.7 mph 93.6 mph Share fastballs 53.6% 56.9% Share sliders 17.7% 19.4% Between five and eight batters As starter As reliever Strikeout rate 18.7% 20.6% Fastball velocity 91.5 mph 92.3 mph Share fastballs 53.6% 54.0% Share sliders 12.6% 13.6% Eight or more batters As starter As reliever Strikeout rate 16.7% 17.7% Fastball velocity 91.6 mph 92.2 mph Share fastballs 55.6% 55.8% Share sliders 13.4% 13.9% Observations are weighted by the lesser of the number of batters a pitcher faced as a starter and in relief from 2016 to 2018. For example, a pitcher who threw to 500 batters as a starter and 200 batters as a reliever would receive a weight of 200. Pitchers who averaged fewer than 15 batters faced per start, i.e. who served as “openers” or tandem starters, are excluded from the analysis. Source: Fangraphs The first group — the OMGs — got a massive, 20 percent boost to their strikeout rate as relievers. They also gained about 2 mph worth of fastball velocity. And they were able to throw fastballs or sliders — the pitches that seem to be at the core of increasing K rates — 76 percent of the time in relief as compared with 71 percent of the time as starters. Conversely, the third group — the long relievers who routinely worked multi-inning stints — got only a 6 percent gain in their strikeout rates relative to the ones they had as starters, and they added only 0.6 mph to their fastballs. ## LOOGYs aren’t really the problem The MLB proposal would effectively kill off the LOOGY, along with its much rarer companion, the ROOGY. So it’s worth asking: If relief pitchers are especially effective when they’re limited to only one inning of work, does it follow that they do even better when limited to just one or two hitters? That is to say, could MLB’s proposal to require that pitchers face at least three batters cause an especially large reduction in strikeout rates? The answer is: not really. If you further break down our sample of pitchers and look at those who threw very short stints in relief,15 they actually had fewer strikeouts than those who averaged around an inning per appearance.16 A lot of this is selection bias: Guys who are brought in to face only one or two hitters at a time are usually mediocre pitchers with big platoon splits. Left-handers who became LOOGYs are generally worse as starting pitchers than the rest of the sample; indeed, they’re quite a bit better in relief than in their starting roles. Nonetheless, they’re not all that effective in relief — much less effective than the OMGs — and because they throw so few innings, they don’t affect the bottom line that much in terms of baseball’s strikeout rate. And because LOOGYs are fading in popularity, they don’t necessarily contribute all that much to slowing down the game. Of the roughly 16,000 pitching changes in 2018, only about 5,000 occured in the middle of the inning, according to data provided to FiveThirtyEight by David Smith of Retrosheet. These midinning changes are indeed time-consuming — adding about 3 minutes and 15 seconds worth of game time, Smith estimates. (Pitching changes between innings add only about 15 seconds, by contrast.) But they aren’t all that common. ## How to bring balance back to bullpens There’s a better idea than the MLB minimum batters proposal, one that would also speed up the game but that would yield more interesting strategy and — most importantly, from my point of view — cut down on the number of strikeouts, perhaps substantially. The core of my proposal is simple: Each team should be limited to carrying 10 pitchers on its 25-man active roster, plus an Emergency Pitcher. Like it? Hate it? Well, let me give you some of the details first: • What’s an Emergency Pitcher? He’s a pitcher who could be signed either on a game-by-game basis — in the way that emergency goalies are used in the NHL — or for any length of time up to a full season. The Emergency Pitcher couldn’t be a member of a team’s 40-man roster, although — just for fun — he could be a member of a team’s coaching staff.17 Emergency Pitchers could enter the game only under certain circumstances: 1. If the starting pitcher left the game because of injury; 2. If one team led by at least 10 runs; 3. If it were the 11th inning or later; or 4. If it were the second game of a doubleheader. • Position players could still pitch, but they wouldn’t be allowed to pitch to a greater number of batters than the number of plate appearances they’d recorded so far on the season as hitters. A backup catcher with 100 plate appearances could face up to 100 batters as a pitcher, for instance (which works out to roughly 20 or 25 innings). With this rule, teams could use position players to pitch on an emergency basis basically whenever they wanted, but they couldn’t designate pitchers as position players just to circumvent the 10-pitcher requirement. Brooks Kieschnick types would need to have their innings and plate appearances monitored carefully.18 • After the roster expanded to 40 players in September, minor league call-ups who were not on the 10-pitcher list could start games, subject to a requirement that they threw at least 60 pitches or five innings or — a mercy rule — gave up at least five runs. They could not appear in relief, however. • Relief pitchers, especially the OMGs, aren’t going to like this, so the restrictions could be phased in over several years. For instance, you could start with a 12-pitcher limit beginning in 2020, then ratchet it down to 11 pitchers in 2022 and 10 pitchers in 2024 as teams adapted to the new requirements. As you can see, the goal here is to be fairly strict: While we want to provide for a bit of flexibility, we mostly want to force teams to stick to the 10 players they designate as pitchers as much as possible. For that matter, we’d probably also want to tighten rules surrounding the injured list and minor-league call-ups, which teams regularly use and abuse to add de facto roster slots — but that’s not a part of this proposal per se. ## Toward a new equilibrium So how would teams use their pitching staffs under these rules? That’s anyone’s guess, and part of the fun would be in seeing the different strategies that teams adopted. But my guess is that the average team would do something like this to fill the roughly 1,450 innings that major league teams pitch in each regular season: ##### What a 10-man pitching staff might look like Role Games Pitched Games Started Innings Pitched Ace starter 34 34 230 No. 2 starter 33 33 210 No. 3 starter 33 33 195 No. 4 starter 32 32 180 No. 5 starter 30 22 150 Long reliever/spot starter 40 3 100 Durable middle reliever 55 0 90 RH set-up 60 0 85 LH set-up 70 0 75 Closer 60 0 80 Role Games Pitched Games Started Innings Pitched Emergency Pitchers 10 0 20 September call-up starters 5 5 25 Position players 5 0 10 Games Pitched Games Started Innings Pitched Total 467 162 1,450 This strategy envisions that starting pitchers would throw 6.0 innings per start, up from 5.4 innings per start in 2018 but a bit less than the 6.2 innings per start that pitchers averaged in the 1980s. Relievers would average around 1.6 innings per appearance, meanwhile — considerably up from 2018 (1.1 inning per appearance) and about the same as in the 1980s. Overall, this plan would entail using 2.9 pitchers per team per game, which is close to where baseball was in the late 1980s. But we could balance out the workload more effectively than teams did back then. As you can see in the table, we could get the necessary innings from a 10-man staff without having to ask starters to throw 270 or 280 innings, as ace starters sometimes did in the 1980s, and without having to ask closers to throw 140 innings a year, as sometimes happened too. Starters would have to work through the third time in the order a bit more often, but there would still be plenty of room for discretion on the part of the manager. The most consequential change would be that we’d cut down on the number of OMG innings. There would still be plenty of them, to be sure. But if you went overboard, it would come with a lot of trade-offs. If a team tried to employ five relievers who each worked 70 appearances of one inning each, for instance, its five starters would have to average about 6.5 innings per start, so they’d be working through the third time in the lineup a lot more often. And if you did want to use a pitcher to face only one or two batters, you could still do it, but it would be more costly still — with a 10-man pitching staff, someone else is always going to have to pick up the slack. This would also relieve (pun somewhat intended) the monotony of the OMGs. We wouldn’t be removing any spots from the 25-man roster. (In fact, we’d essentially be adding one for the Emergency Pitcher.) But we’d be requiring at least 15 of them to be used on position players. Pinch runners, pinch hitters, platoon players, defensive replacements and third catchers — all of whom have become endangered species as teams use every marginal roster slot on an OMG — would begin to roam the baseball field freely again. I’m reluctant to estimate the overall amount by which my rule change would reduce strikeouts or improve pace of play. That’s because baseball strategy is a dynamic system, and our goal is to change teams’ overall attitudes toward pitcher usage. Pitching to contact might become more common again, for instance, as starters would need to throw longer outings. Keep in mind that if starters are only expected to work through the order two or two-and-a-half times, tossing perhaps five or six innings, they can also throw at relatively high effort. So we wouldn’t just be reducing strikeouts by exchanging some OMGs for multi-inning relievers; starters would also have to pace themselves more, too. But if relief-pitcher usage has as close a relationship with strikeout rates as I think it does, the net effects could be substantial. This rule would essentially roll relief-pitcher usage back to what it was in the late 1980s or early 1990s and could bring strikeouts back toward what they were back then too, when pitchers struck out about 15 percent of the batters they faced instead of the 22 percent they do now. That’s probably too optimistic; at least some of the increase in strikeout rate undoubtedly has to do with pitchers being bigger and stronger and throwing harder than ever before.19 But some kind of intervention is needed. The OMG-dominated equilibrium of today may be ruthlessly efficient, but it isn’t making for an aesthetically or strategically rewarding form of baseball. ## The Pac-12 Is In Shambles Immediately after the Pac-12 football championship game in late November, an on-screen interview with commissioner Larry Scott at Levi’s Stadium was interrupted by a chorus of boos. Attendees, it seemed, weren’t too fond of the leadership of the “Conference of Champions.”1 For nearly six decades, the Pac-12 managed to emulate its ostentatious slogan across the collegiate sports landscape. The Pac-12 has finished an academic year with the most total national championships of any conference in 52 out of the past 58 years, including the past 13 years. The conference has no shortage of star power on the women’s side: Sabrina Ionescu is piling up unprecedented stat lines on the court with the Oregon Ducks; Ella Eastin is breaking records in the pool for the Stanford Cardinal; and Katelyn Ohashi of the UCLA Bruins recently stole the collective heart of the country on the mat. Last year, women collected nine of the conference’s 12 national titles. The Pac-12 women have already won two titles this year, in volleyball and cross-country, with the men claiming only water polo. But when it comes to the two high-profile men’s sports of football and basketball, the Pac-12 is falling short. Months removed from Scott’s boo-inducing interview, as the college basketball season winds into its final stretch, the conference’s vertiginous fall in the top two revenue-generating sports is unmistakable. While the Pac-12’s performance in football has been steadily declining since the College Football Playoff was introduced, the conference’s decline in men’s basketball seems more abrupt. Two years ago, the Pac-12 featured three 30-win teams for the first time. Three teams reached the Sweet 16, and Oregon punched the conference’s first ticket to the Final Four in nearly a decade. The abundance of talent was confirmed when the conference produced three lottery picks in the NBA draft — including Markelle Fultz and Lonzo Ball, the top two overall selections. The Pac-12 saw the top overall pick in the NBA draft again last season, in Arizona’s Deandre Ayton. But the conference face-planted at the NCAA tournament. Each of the three teams to reach the tourney failed to get out of the first round, including Ayton’s Arizona.2 Not since the Big 12 was formed in 1996-97 had one of the six major conferences3 failed to send a team to the second round of the tournament. No Pac-12 team finished inside the top 25 of KenPom’s adjusted efficiency margin metric, either. Of course, this came after three UCLA Bruins were arrested for shoplifting on international soil in the days preceding a game meant to showcase the conference, and the FBI’s investigation of corruption in college basketball led to the arrests of assistant coaches from USC and Arizona4 before the season even tipped. But that didn’t curtail the enthusiasm of the commissioner heading into this season. “Really excited about what our teams look like,” Scott said at the Pac-12 media day. “Feel like we’ve got a very, very strong conference.” On paper, he wasn’t wrong. The conference accounted for seven of the top 40 recruiting classes, with UCLA and Oregon pulling in two of the top five. Three teams were ranked in the preseason Associated Press Top 25 poll. But as the calendar year came to a close, the Pac-12 was mired in the worst December by a major conference in 20 years. By January, UCLA had fired head coach Steve Alford, and Oregon had lost Bol Bol, the conference’s most marketable player and the crown jewel of the 2018 recruiting class, for the year to a foot injury. Dana Altman’s Ducks, which checked in at No. 14 in the preseason poll and were considered an early favorite to reach the Final Four, are now longshots to even reach the tournament. Cal is one of the worst teams in any conference and in the midst of its worst season in program history. Washington is the highest-ranking team in the conference by KenPom’s adjusted efficiency margin metric and checks in at No. 35. No other Pac-12 team ranks in the top 50. The conference has hardly proved itself against top-notch opponents. In any Quad 1 games,5 the Pac-12 is 11-51. The ACC, Big East, Big Ten, Big 12 and SEC each have at least three times as many wins over that caliber of opponent. Conference record in Quad 1 games, 2018-19 Conference Games Win % Big Ten 164 .372 ACC 135 .326 SEC 134 .313 Big 12 104 .365 Big East 95 .379 Pac-12 62 .177 Quad 1 games are home games against teams 1-30 in NET ranking, neutral games against teams 1-50 and away games against teams 1-75. Source: BartTorvik.com As it currently stands, the conference would be lucky to receive two bids to the tournament, with the Huskies projected to be a No. 9 seed and Arizona State possibly squeaking in as a 12 seed. It’s been a quarter-century since a major conference produced a one-bid campaign. According to Sports-Reference.com’s Simple Rating System, the Pac-12 collectively is just 7.31 points better than an average Division I team this season. That’s on track to be the conference’s worst single-season mark since the 2011-12 campaign and the third worst in the past three decades. The last time a major conference produced a worse SRS was 1997-98, when the Big 12 put up a 7.17 in its second season of existence. You have to go back at least 30 years to find a worse mark produced by the Big East, Big Ten or SEC. If recent history serves, next month’s tournament will reinforce what many already know: The Pac-12, which hasn’t won a national title since Arizona cut down the nets in 1997, has fallen off considerably in terms of prestige. Over the past decade, the Pac-12 has made two Final Four appearances and failed to reach a national championship game. Every other major conference has been to at least twice as many Final Fours and made at least two title game appearances. The Big East has won more national titles in the previous eight years than the Pac-12 has in the past 45. In particular, the performance of the Pac-12 in the 2016 tournament, relative to seeding, was the second worst performance by any conference since at least 2000. And over the past three years, no conference has underperformed more than the Pac-12 when it matters most. The Pac-12 is also struggling in college football. Over the past two seasons, the conference is a combined 4-12 in bowl games, with three wins coming by a combined 4 points. If this feels like a sudden drop, it’s because it is. The Pac-12 has won a single national title in the past 20 years, but you only have to go back three years to find an ESPN segment debating whether it was the best conference in college football. Since the playoff was introduced, the Pac-12 has made two appearances — going 1-2 — and failed to appear in three of the five seasons. In total, the conference was 3.53 points better than the average FBS team in 2018-19, the lowest mark by a Power Five conference6 in six years. Since 2010, the conference has produced three of the seven worst seasons, two of which came in the past two seasons. Oregon State has arguably been the worst Power Five football team for two consecutive years, and programs like Oregon, Stanford and USC, which traditionally have been competitive on a national level, have fallen off considerably. Washington’s good-but-not-good-enough seasonal cadence seems to have run its course, too. This offseason, perhaps the conference’s biggest story was that Kliff Kingsbury almost became an assistant coach at USC. Arizona State is the lone Pac-12 school with a Division I hockey team,7 and there’s a reasonable chance it will end up ranked higher at season’s end than any team the conference fielded in football or men’s basketball. Living up to the standard established by John Wooden, who won 10 national championships over 12 years at UCLA, would be impossible. But falling to the bottom of the major-conference barrel in the two sports most scrutinized is a disastrous turn for a conference literally branded around dominance. To some, the Conference of Champions® has transformed into the Circle of Suck. This may be the bleakest moment in the illustrious history of the Pac-12, as the conference continues its stroll away from relevancy. CORRECTION (Feb. 22, 2019, 12:30 p.m.): An earlier version of this article said the Pac-12 had no football teams ranked in the Associated Press Top 25 at the end of the 2018 season. Two teams were ranked: No. 10 Washington State and No. 13 Washington. ## Don’t Trust Anyone Older Than L Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,8 and you may get a shoutout in next week’s column. If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter. ## Riddler Express From Dominic van der Zypen, a shipwreck demands deduction: We are marooned on an island that has the following curious property: Everyone over a certain age lies all the time. More specifically, there is an age limit L — a positive integer — and all islanders who are younger than age L only tell the truth, while islanders who are at least L years old only tell lies. We are greeted by five islanders who make the following statements: A: “B is more than 20 years old.” B: “C is more than 18 years old.” C: “D is less than 22 years old.” D: “E is not 17 years old.” E: “A is more than 21 years old.” A: “D is more than 16 years old.” B: “E is less than 20 years old.” C: “A is 19 years old.” D: “B is 20 years old.” E: “C is less than 18 years old.” What is L? And what did we just learn about the ages of the islanders? ## Riddler Classic From Mark Whelan, shuffle up and deal. And count very, very high: Bridge, that venerable card game, begins with an auction. There are four players around a table, each sitting across from his or her partner. At its simplest, the auction goes like this: Beginning with the dealer and orbiting around the table, players can place a bid or pass. Players who’ve passed can re-enter the bidding later. A bid is comprised of a number (one through seven) and a suit. Every legal bid must be higher than the one that came before, meaning either that its number is higher or that its number is the same and its suit is higher (from high to low, the suits go no-trump, spades, hearts, diamonds, clubs). The auction ends if the other three players pass after a bid, or if all four players pass right away. How many different legal bridge auctions are there? Extra credit for you bridge nerds out there: What if we incorporate the possibility of doubling into this accounting exercise? Specifically, if the last bid was made by one of the opposing partners, a player may, while bidding, also double, which increases the stakes for the hand. If a player has been doubled before, they may redouble. Including these variations on bids, how many legal bridge auctions are there now? ## Solution to the last week’s Riddler Express Congratulations to Alana Christie of Dallas, winner of last week’s Riddler Express! Last week brought another maze that the enemies of Riddler Nation had crafted to entrap you. It looked like this: Your goal was to get to the star in the middle, and you could start your journey in any square around the perimeter. You then moved through the squares — up, down, left or right — by following the squares’ arrows. If a square had a two-headed arrow, you could choose whichever of its directions that you liked. If you arrived in a square containing a number, you could exit in any direction you liked, but you had to add that number to your score. Your challenge was to solve the maze with the lowest possible score, which was the total of all numbered squares you crossed. What was the score? The lowest possible score was 1. You can achieve it by entering via the green square on the middle of the maze’s right-hand edge, traveling left, then up to a “0,” then left some more, then up, left to another “0,” left, down, left through a “1,” left, down, and you’re there! That path looks like this, as illustrated by solver Matthew Modlin: You could solve this maze simply by playing around a bit — by “following your nose,” as my high school calculus teacher used to say. (My nose, as it turned out, wasn’t especially good at calculus.) Or you could work backward, starting at the star and working toward the perimeter. Or you could employ the computational services of an algorithm. Solver Laurent Lessard, for example, used something called the Bellman-Ford algorithm, which calculates the shortest route and is used in applications such as routing data. His solution looks like this: ## Solution to last week’s Riddler Classic Congratulations to Shailesh Ingale of Chicago, winner of last week’s Riddler Classic! Last week you came on down to play a game on “The Price Is Right” called Cover Up. You were trying to win a car by guessing its five-digit price. You had two numbers to choose from for the first digit, three numbers for the second digit, and so on, ending with six options for the fifth and final digit. To begin, you locked in a guess at the entire price of the car. If you got at least one digit correct on the first guess, the correct digit(s) were highlighted and you got to replace incorrect digits on a second guess. That process continued on subsequent guesses until the price was guessed correctly. However, if none of the new numbers you swapped in were correct, you lost. You could conceivably have won the car on the first guess or with up to five guesses. What were the chances you won the car if all of your guesses were random selections, not based on any knowledge of cars? They were 231/720, or about 32.1 percent. Why? In total, the car could have any one of 2*3*4*5*6 = 720 different prices, each of which is equally likely, as far as you’re concerned. There are also 720 guessing “paths” you could take, each of which is equally likely. The bulk of the solving comes in figuring out which of these paths lead you to driving home in a new car and which do not. To figure that out, let’s denote your guess as ABCDE — or abCDe or ABcde, etc. — where the letters are capitalized if that particular digit is correct and lowercase if it is incorrect. There is only one way to guess all the digits correctly on the first try: ABCDE. There are five ways to go from four correct digits and one incorrect digit to winning the car: ABCDe → ABCDE, ABCdE → ABCDE, ABcDE → ABCDE, AbCDE → ABCDE, aBCDE → ABCDE. And so on. Once we’ve counted up all these paths — solver Ryan Lafitte wrote a handy list of them — we arrive at a total of 231. We divide that by the total number of paths, 720, and we’re done! Now suppose that you knew a little something about cars. Specifically, you knew the ten-thousands place of the car’s price for sure, therefore guaranteeing you at least one correct guess. How much does that knowledge improve your chances of winning the car? Not much, it turns out. Locking in the first digit means you have half as many possible prices and half as many routes for getting to the right price, so your chances of winning in this case are 116/360, or only about 32.2 percent. A little knowledge goes a little way. ## Want more riddles? Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now! ## Want to submit a riddle? Email me at [email protected] ## Trump’s National Emergency Policy Is Unpopular, But Not Really Unpopular Welcome to Pollapalooza, our weekly polling roundup. ## Poll(s) of the week President Trump’s decision to declare a national emergency in order to build more physical barriers on the U.S.-Mexico border was generally unpopular, but polls suggest the move has very high support among Republicans. That dynamic could be important as Trump seeks to overcome challenges to his new policy both on Capitol Hill and in the courts. Two polls conducted entirely after the emergency declaration show a majority of Americans don’t like it: An NPR/PBS Newshour/Marist poll that came out Tuesday showed a 61-36 split against Trump’s policy, and a Morning Consult/Politico poll released on Wednesday found 39 percent in support, 51 percent opposed. A HuffPost/YouGov survey conducted the day before and the day of the emergency declaration found similar results — 37 percent of Americans said they approved of the move, compared with 55 percent who disapproved. These numbers don’t surprise me — they generally mirror Trump’s overall job approval ratings. For much of the past two years, around 40 percent of Americans have approved of the president’s performance, while a clear majority has disapproved. Similarly, overall support for the national emergency declaration is in the upper 30s in the polls we have so far. That’s because Republicans have lined up solidly behind it, according to both polls conducted after the declaration was made — the NPR poll found 85 percent support within the GOP, and the Morning Consult survey found 77 percent support. The HuffPost/YouGov poll found that 84 percent of Trump voters supported the declaration, although that poll was already underway when the declaration was made, so some respondents were asked about the move before it became official while others were asked after the announcement. It’s not surprising that large numbers of Republicans supported Trump’s decision to declare a national emergency — GOP voters overwhelmingly approve of him. But high party support for a Trump policy is not always a given. For example, the policy of separating immigrant children from their parents at the U.S.-Mexico border was significantly more unpopular within the party than the emergency declaration is — a FiveThirtyEight average of polls found that only about half of Republicans were on board with the separations. And while a majority of Republicans supported both the failed 2017 health care bill meant to replace Obamacare (67 percent) and the GOP tax plan passed the same year (64 percent), they did so at rates 10 to 20 points lower than we’re seeing on the national emergency policy. Being backed only by Republican voters still isn’t great for the president. His base alone likely won’t be sufficient to win re-election. But in terms of policy, Trump tends to reverse himself only if there is a breadth of opposition that encompasses more than just Democrats and independents. That kind of opposition tends to create a feedback loop that’s hard to ignore — so, for example, the media criticizes something Trump does or says, establishment Republicans join in, and then the media prominently features those GOP critics in its coverage. Some Republican elected officials were initially wary of Trump declaring a national emergency, but I wonder if they will reconsider that posture after seeing these polls. And with few prominent Republicans willing to cast the national emergency policy as an “extraordinary violation of constitutional norms,” as The New York Times described it last week, I suspect the media will feel pressured to cover this debate as a traditional partisan dispute and so will back off from sharper condemnations of Trump. Like the media, the courts are sometimes hesitant to take strong stands on partisan disputes. So they may be more reluctant to strike down Trump’s policy than they would be if it had gotten more of a mixed reaction from both sides of the aisle. But the biggest reason these polls matter is they can affect what happens on Capitol Hill. House Speaker Nancy Pelosi announced this week that the House will likely hold a vote to overturn the emergency declaration. If such a measure passed both houses of Congress but was vetoed by Trump, Congress would need a two-thirds majority of both chambers to override the veto. That would require 53 Republicans in the House and 20 in the Senate to break with the president. I thought that was unlikely even before these polls came out. Now, seeing almost universal support for Trump’s declaration among Republican voters, it’s even harder to imagine a large bloc of Republicans in Congress breaking with the president, which means this policy is likely to survive. ## Other polling nuggets • Former Vice President Joe Biden, who has not announced whether he will enter the 2020 Democratic presidential race, leads in South Carolina with 36 percent of the vote, according to a new Change Research survey that was provided to the Palmetto State-based Post and Courier newspaper. Also in double digits were Bernie Sanders (14 percent), Kamala Harris (13 percent) and Cory Booker (10 percent). Twelve other Democrats who either have officially entered the race or are rumored to be considering presidential runs were in single digits. • Biden is also ahead in New Hampshire, with 28 percent of the vote, according to a University of Massachusetts, Amherst, poll. Sanders is in second place with 20 percent, and Harris is in third with 14 percent. Seven other Democrats that were included in the survey are in single digits. • An average of 54 percent of white Democrats identified as politically “liberal” during the six-year period from 2013 to 2018, according to data released by Gallup this week. That compares with 38 percent of Latino Democrats and 33 percent of black Democrats. There was also variation by education level — Democrats with postgraduate degrees were the most likely to describe themselves as liberal (65 percent), followed by Democrats with undergraduate degrees (58 percent), those who attended college but don’t have degrees (45 percent) and those with high school educations or less (32 percent). • The same Gallup survey found major differences among liberal and conservative Democrats on a few issues: 81 percent of liberal Democrats think marijuana should be legal, for example, compared with 44 percent of conservative Democrats. Sixty-four percent of liberal Democrats oppose the death penalty for people convicted of murder, compared with 39 percent of conservative Democrats. • 45 percent of Democrats said they would be somewhat or very unhappy if their son or daughter married a supporter of the Republican Party, according to a PPRI/Atlantic survey released this week. Thirty-five percent of Republicans said they would be unhappy if their child married a Democrat. Higher shares of Republicans were concerned about their child marrying someone of the same gender (58 percent unhappy) or someone who identified as transgender (70 percent). • More than 60 percent of Americans said that the government should pursue policies to reduce the wealth gap and that they support a 2 percent tax on wealth above$50 million, according to a survey conducted by SurveyMonkey that was published by The New York Times this week. Opinion is more divided (51 percent support, 45 percent oppose) on a marginal tax rate of 70 percent on income above \$10 million a year.
• Just 17 percent of Virginians said they approved of the job performance of the state’s embattled governor, Ralph Northam (who has denied that he was in a racist photo on his page in his medical school yearbook but has admitted to wearing blackface in the 1980s), according to an Ipsos/University of Virginia Center for Politics survey released this week. Thirty-four percent said they disapproved of Northam, while 44 percent said they neither approved nor disapproved. The good news for Northam is that only 31 percent of Virginians said they think he should resign, compared with 43 percent who said they don’t think he should resign. Lt. Gov. Justin Fairfax, who has been accused by two women of sexual assault, has a slightly worse standing — 35 percent of Virginia residents said they think he should resign, while 25 percent said that he shouldn’t. (The other 40 percent are in neither camp.)
• A new Quinnipiac University survey of Virginia voters found better job approval numbers for Northam (39 percent approve, 44 percent disapprove). And in this poll too, a plurality (48 percent) of Virginians said he shouldn’t resign.

## Trump approval

According to FiveThirtyEight’s presidential approval tracker, 42.5 percent approve of the job Trump is doing as president, while 53.2 percent disapprove (a net approval rating of -10.7 points). At this time last week, 41.5 percent approved and 54.1 percent disapproved (for a net approval rating of -12.6 points). One month ago, Trump had an approval rating of 40.0 percent and a disapproval rating of 55.3 percent, for a net approval rating of -15.3 points.

From ABC News:

## How Bernie’s 2020 Map Might Change Without The #NeverHillary Vote

Bernie Sanders picked up support in some unusual places during his 2016 campaign to be the Democratic presidential nominee. The self-described democratic socialist won states such as Oklahoma and Nebraska that are typically associated with right-of-center policy views. He also did surprisingly well with self-described conservative voters — granted, a small-ish part9 of the Democratic primary electorate — picking up almost a third of their votes. Perhaps less surprisingly given that Sanders isn’t technically a Democrat, he performed really well with independent voters, winning them by roughly a 2:1 margin over Hillary Clinton.

So as Sanders launches his 2020 campaign as a candidate with both formidable strengths and serious challenges, his biggest problem might seem to be that there’s more competition for his base this time around, with Massachusetts Sen. Elizabeth Warren and others also competing for the leftmost part of the Democratic electorate. An equally big problem for Sanders, however, is that voters this time around have more alternatives to Hillary Clinton — left, right and center — to choose from.

Roughly one-quarter of Sanders’s support in Democratic primaries and caucuses in 2016 came from #NeverHillary voters: people who didn’t vote for Clinton in the 2016 general election and who had no intention of doing so. (The #NeverHillary label is a little snarky, but it’s also quite literal: These are people who never voted for Clinton despite being given two opportunities to do so, in the primary and the general election.) This finding comes from the Cooperative Congressional Election Study, a poll of more than 50,000 voters conducted by YouGov in conjunction with Harvard University. The CCES asked voters who they voted for in both the primaries and the general election; it also asked voters who didn’t vote in the general election who they would have chosen if they had voted. Here’s the overall breakdown of what Sanders primary voters did in November 2016.10

##### What Bernie Sanders primary voters did in November 2016
Voted for Hillary Clinton 74.3%
Voted for Donald Trump 12.0
Voted for Gary Johnson 3.2
Voted for Jill Stein 4.5
Voted for other candidates or voted but didn’t recall 2.5
Didn’t vote but said they would have voted for Clinton 1.6
Didn’t vote and didn’t say they would have voted Clinton 1.9

Voters in shaded categories are #NeverHillary voters.

Source: COOPERATIVE CONGRESSIONAL ELECTION STUDY

About 74 percent of Sanders’s primary voters also voted for Clinton in November 2016. Another 2 percent didn’t vote but said on the CCES that they would have voted for Clinton if they had voted; it doesn’t seem fair to consider them anti-Clinton voters, so we won’t include them in the #NeverHillary camp. The remaining 24 percent of Sanders voters were #NeverHillary in the general election, however. Of these, about half voted for Trump, while the remaining half voted for Gary Johnson, Jill Stein, another third-party candidate or didn’t vote.11

Overall, Sanders won 43 percent of the popular vote in Democratic primaries and caucuses in 2016. If 24 percent of that 43 percent were #NeverHillary voters, that means Sanders’s real base was more like 33 percent of the overall Democratic electorate. That isn’t nothing — it could easily carry the plurality in a divided field — and there were plenty of Clinton voters who liked Sanders, so he could pick up some of their votes too. But it does jibe with polls showing that Sanders and Warren together have around 30 percent of the Democratic primary electorate in 2020 and not the 43 percent that Sanders got in 2016.

You might be tempted to think that these #NeverHillary voters are leftists who thought Clinton was too much of pro-corporate, warmongering centrist. But relatively few of them were. Less than a fifth of them voted for Stein, for example. Instead, these voters were disproportionately likely to describe themselves as moderate or conservative. Among the 31 percent of self-described conservatives who voted for Sanders in the Democratic primaries, more than half were #NeverHillary voters, for example. A large minority of the independents and Republicans who supported Sanders were #NeverHillary voters as well.

##### #NeverHillary voters were conservative, not super liberal

The ideological and partisan breakdown of #NeverHillary voters in the 2016 Democratic primaries

Sanders Voters
Group Clinton Sanders Pro-Sanders** #NeverHillary
Very liberal 45.2% 54.6% 46.9% 7.7%
Liberal 55.6 43.7 39.4 4.3
Somewhat liberal 59.4 40.2 32.7 7.5
Conservative* 66.5 31.3 14.9 16.4
Sanders Voters
Group Clinton Sanders Pro-Sanders #NeverHillary
Democrats 66.2% 32.9% 28.8% 4.1%
Independents and Republicans 33.6 65.0 37.9 27.1

* Includes voters who described themselves as “conservative,” “somewhat conservative” or “very conservative.“
** Sanders voters who voted for Clinton in the general election or didn’t vote but said they would have voted for Clinton.

Source: COOPERATIVE CONGRESSIONAL ELECTION STUDY

A more complicated way to characterize the #NeverHillary vote is via regression analysis. Using the CCES — which permits fairly intricate regression model designs because of its large sample size — I took all of Sanders’s primary voters in 2016 and evaluated a host of variables to see what predicted whether they were #NeverHillary in the general election.

The most significant variables were, first, whether the voter was a Democrat, and second and third, two policy questions that have proven to be highly predictive of voter preferences in the past: whether the voter thinks that white people benefit from their race and whether the voter wanted to repeal the Affordable Care Act. Non-Democrats, voters who didn’t think whites benefited from their race, and voters who wanted to repeal the ACA were much more likely to be #NeverHillary voters. Voters who were rural, poor, who lived in the South or the Northeast, who were born-again Christians, who were conservatives, and who were military veterans were also somewhat more likely to be #NeverHillary, other factors held equal. Black people, Hispanics, women, liberals, millennials, union members and voters with four-year college degrees were less likely to be #NeverHillary voters.

In addition, some factors related to the primary calendar affected the #NeverHillary vote. After Trump won the Indiana primary, effectively wrapping up the Republican nomination, more anti-Clinton voters filtered into the Democratic primaries. And the #NeverHillary vote was lower in states where an open Republican primary or caucus was held on the same date as the Democratic one. This implies that a fair number of #NeverHillary voters would actually have prefered to vote in the Republican primary. But if they couldn’t, because the Republican primary was closed or wasn’t held on the same date, they voted in the Democratic primary (for Sanders or another Democrat and against Clinton) instead.

We can also evaluate the geographic breakdown of the #NeverHillary vote. In each state, we can estimate the anti-Clinton vote in two ways, either by directly measuring it (e.g., 19 percent of Sanders voters the CCES surveyed in Illinois were #NeverHillary) or through the regression technique that I used above (which is similar to an MRP analysis). Without getting too much into the weeds, I used a blend of the two methods in each state based on the sample size of Sanders voters there; the direct measurement is more reliable in states with a large sample, while the regression method is better in states with a smaller one. The table below shows where the largest share of Sanders voters (as well as voters who chose another Democratic candidate apart from Clinton and Sanders12) were anti-Clinton voters:

##### Sanders benefited from #NeverHillary voters in red states

The breakdown of Sanders and #NeverHillary voters in the 2016 Democratic primaries

#NeverHillary
State Sanders’s Share of pop. vote share of Sanders voters who were #NeverHillary voted sanders Other Total
Alaska 79.6% 49.8% 39.7% 0.1% 39.7%
W.Va. 51.4 45.2 23.2 7.1 30.4
Okla. 51.9 42.3 21.9 3.7 25.6
Vt. 86.0 28.3 24.3 0.2 24.5
Idaho 78.0 30.4 23.8 0.4 24.2
Neb. 57.1 42.0 24.0 0.0 24.0
Utah 79.2 29.6 23.4 0.3 23.7
Ky. 46.3 37.9 17.6 3.9 21.4
Ore. 56.2 32.1 18.1 1.0 19.0
R.I. 54.7 32.1 17.6 1.2 18.8
Mont. 51.6 31.8 16.4 2.4 18.8
N.D. 64.2 19.6 12.6 5.7 18.3
Hawaii 69.8 25.9 18.1 0.1 18.2
Maine 64.3 28.0 18.0 0.1 18.1
Kan. 67.7 26.4 17.9 0.0 17.9
N.H. 60.1 27.5 16.6 1.2 17.8
S.D. 49.0 34.8 17.1 0.0 17.1
Nev. 47.3 35.1 16.6 0.0 16.6
Del. 39.2 36.8 14.4 0.6 15.0
Wash. 72.7 19.3 14.0 0.1 14.1
Mo. 49.4 25.8 12.7 0.6 13.3
Md. 33.8 31.4 10.6 2.0 12.7
Mass. 48.5 24.4 11.8 0.9 12.7
La. 23.2 40.8 9.4 3.2 12.6
Calif. 46.0 24.2 11.1 0.5 11.6
Ind. 52.5 22.2 11.6 0.0 11.6
Mich. 49.7 21.1 10.5 1.2 11.6
Pa. 43.5 25.1 10.9 0.5 11.4
Ariz. 41.4 24.2 10.0 1.3 11.3
N.C. 40.9 20.9 8.5 2.6 11.1
Minn. 61.7 17.5 10.8 0.0 10.8
Wis. 56.6 18.6 10.5 0.2 10.7
Conn. 46.4 20.8 9.6 1.0 10.6
N.Y. 42.0 25.1 10.5 0.0 10.5
N.M. 48.5 20.8 10.1 0.0 10.1
Ark. 30.0 23.9 7.2 2.2 9.4
Ill. 48.6 18.4 8.9 0.5 9.4
Fla. 33.3 23.8 7.9 1.3 9.2
N.J. 36.6 24.2 8.8 0.1 9.0
Ohio 43.1 19.5 8.4 0.4 8.8
Tenn. 32.5 22.7 7.4 0.8 8.2
Iowa 49.6 15.4 7.6 0.3 8.0
S.C. 26.0 28.8 7.5 0.3 7.8
Va. 35.2 21.3 7.5 0.3 7.8
Colo. 59.0 11.7 6.9 0.4 7.3
Texas 33.2 19.0 6.3 0.9 7.2
Ala. 19.2 25.5 4.9 1.7 6.5
D.C. 20.8 28.0 5.8 0.4 6.2
Ga. 28.2 19.4 5.5 0.3 5.7
Wyo. 56.7 9.3 5.3 0.1 5.4
Miss. 16.6 14.8 2.5 0.5 3.0

Source: COOPERATIVE CONGRESSIONAL ELECTION STUDY

The largest number of #NeverHillary voters, as a share of the Democratic primary electorate, were in Alaska, West Virginia, Oklahoma, Vermont, Idaho, Nebraska, Utah and Kentucky. Other than in Vermont, where extreme loyalty to Sanders generated a large number of write-in votes for Sanders and other candidates in the general election, those are obviously really red and largely rural states. Apart from Kentucky, they were also all states won by Sanders in the primaries.

Although there may have been something of a market for a populist candidate in these states, it’s also likely that Sanders benefited from being the only alternative to Clinton. In fact, there are several states where the #NeverHillary vote pushed Sanders over the top and where the pro-Sanders vote alone wouldn’t have been enough for him to win. These are Indiana, Michigan, Montana, Nebraska, Oklahoma, Oregon, Rhode Island and West Virginia.

The good news for Sanders is that the states where he benefited the most from the #NeverHillary vote — especially in Appalachia and in the Interior West — have relatively low delegate tallies. So they’re places that he can potentially afford to lose. It does mean, however, that Sanders will have to hit his mark in his other strong regions, including New England (where Warren will provide fierce competition), the Upper Midwest (where Sen. Amy Klobuchar of Minnesota could create problems in her home state and Wisconsin) and the Pacific Northwest (where Sanders would prefer that candidates like Washington Gov. Jay Inslee and former Colorado Gov. John Hickenlooper not enter the race).

It also means that Sanders won’t just be competing against other progressives but also against relatively moderate candidates. If #NeverHillary voters from 2016 are again looking for an anti-establishment candidate, Sanders could still fit the bill. If they want a moderate instead, however, they’ll have a lot more choices than they did in 2016 in the form of candidates like Klobuchar and (if they enter the race) Joe Biden and Beto O’Rourke. It’s also possible that #NeverHillary voters were mostly motivated by sexism, in which case any of the male candidates could stand to benefit.

None of this dooms Sanders by any means. On balance, he probably benefits from a divided field, in fact, wherein his extremely loyal base gives him a high floor of support. But a multi-way race is way different than a two-way one, so Sanders’s coalition may not be all that similar to what we saw in 2016.

From ABC News:

## Everything Went Right For The 2018 Red Sox. Are The Champs Destined To Regress?

It’s hard to imagine things going more right for the Boston Red Sox than they did last season. Boston jumped out to a scorching 17-2 start, was 38 games over .500 by the All-Star break, posted the most regular-season wins (108) by an MLB team in 17 years, and then steamrolled through the playoffs with an 11-3 postseason record en route to a World Series title. Statistically, it was probably the most impressive performance any major team had in 2018.4

But now the calendar has flipped to 2019, and as spring training warms up for the Sox in Fort Myers, Florida, Boston must focus on defending its crown — and staving off the inevitable regression that comes in the wake of a season as charmed as the one the Red Sox just enjoyed.

As a rule, clubs that win a crazy number of ballgames in one season tend to come back down to earth quickly in the next. Of the 32 teams that cracked the century mark in wins (per 162 games)5 since 1990, 28 had an inferior record the next year,6 and 24 failed to return to the 100-win club. (Thirteen failed to break even 95 wins.) On average, these 32 triple-digit winners declined by 9.6 wins the following season.

Teams that won substantially more than 100 games have tended to regress even harder. The 2002 Mariners, for example, won “only” 93 games after the 2001 squad tied a major league record with 116 wins; the 1999 Yankees won 98 a year after the team took home 114. The inescapable truth is that few major league teams actually have 100 wins of “true talent” on their rosters, much less 108. Most of these huge winners were aided by some not-insignificant amount of luck along the way.

And it’s hard to argue that the Red Sox weren’t one of the luckier teams in baseball last season. According to the Pythagorean expectation, a team with Boston’s runs scored and allowed should have won four games fewer than it actually did. Furthermore, a team with Boston’s particular statistical profile (its singles, doubles, walks, etc. — both for and against) should have had a Pythagorean record five games worse than it actually did. Add up those two categories, and the Red Sox benefited from an MLB-high 10 extra wins of luck, whether through prevailing in the relative toss-ups of close games or through stringing hits together (or stranding opposing runners) in an unusually favorable manner.

On top of all that, there’s another way a team can have everything go right for it, and that’s at the player level: Did everyone outperform their expected levels of performance at once? Injuries can often play a role here — though the Red Sox were in the middle of the pack in terms of man-games lost to the injured list. More pertinently, Boston also saw a number of players post career-best seasons last year, from American League MVP Mookie Betts (10.6 wins above replacement)7 to blockbuster free-agent signing J.D. Martinez (6.1), plus young up-and-comers such as Andrew Benintendi (4.1) and even longtime puzzles such as Eduardo Rodriguez (2.7).

Altogether, 12 of Boston’s 21 regulars (those who played at least 2 percent of the team’s available playing time)8 exceeded their established level of WAR, with only Jackie Bradley Jr., Eduardo Nunez and the catching tandem of Sandy Leon and Christian Vazquez significantly undershooting their previous production levels during the 2018 regular season.9

And this is to say nothing of the unexpected performances the team received in the postseason from the likes of Steve Pearce — a fizzled-out former prospect who arrived in Boston via a midseason trade and ultimately won World Series MVP — or Nathan Eovaldi, another castoff who had a 1.61 ERA in 22 1/3 postseason innings. (Or, in general, the amazingly fortuitous splits the team had in crucial playoff situations.)

All of those different ingredients explain how a team that won 93 games in 2017 suddenly exploded for 108 and won the championship a year later. But again, the pull of baseball’s gravity is strong. Based on data since 1990, we’d expect a team that improved by 15 games between seasons to give back about 5.2 wins the next season. It’s just another data point to toss onto the heap of statistical indicators that foretell a decline for the Red Sox heading into 2019.

The good news for Boston is that if your starting point is a 108-win team, you have a ton of room to regress and still be one of the best teams in baseball. Even if the Sox didn’t truly have 108 wins of talent on the roster last year, they still played like a 98-win team according to their underlying statistics, and almost all of that team will be back this season (with the notable exception of closer Craig Kimbrel). According to an early preseason version of our 2019 MLB projections,10 we rate Boston as the third-best team in baseball, with a 95-67 projected record and a 10 percent chance of repeating as champs, which is also tied for third-best in MLB.

Trouble is, that might make the Red Sox only the second-best team in their own division. Our simulations consider the archrival New York Yankees just as likely as Boston to win the World Series and actually think that New York is ever-so-slightly better talent-wise. Although the Sox got the better of the Yankees last season, winning 13 of 23 games (including an August sweep and a four-game division series victory), for all intents and purposes, our projections have the two teams in an absolute dead heat as we look ahead to 2019:

##### The Red Sox still have a Yankees problem on their hands

How our preliminary Elo ratings are forecasting the 2019 AL East race

Avg. Simulated Season Chance to…
Team Elo Rating Wins Losses Run Diff. Make Playoffs Win Division Win World Series
Yankees 1566 95 67 +137 74% 41% 10%
Red Sox 1564 95 67 +136 74 41 10
Rays 1527 86 76 +50 42 15 3
Blue Jays 1483 75 87 -52 13 3 1
Orioles 1421 60 102 -198 1 <1 <1

Based on 100,000 simulations of the 2019 MLB season

Sources: Baseball prospectus, Fangraphs, Clay Davenport, Caesar’s Palace

And the Red Sox could be running out of time to make the most of their current core. By 2021, Betts, Bradley, Chris Sale, Xander Bogaerts and Rick Porcello (plus potentially Martinez, who has an opt-out clause) will have all hit free agency. And team president Dave Dombrowski built 2018’s champion in part by bucking MLB’s prospect-hoarding trend and emptying out the farm system’s next generation in favor of short-term wins, so reinforcements aren’t exactly on the way.

The result of Dombrowski’s moves was a championship, and one of baseball’s all-time great single season performances, so I’m pretty sure it was worth it. The question now is how steep the drop-off will be in 2019 — and beyond. In many ways, Boston caught lightning in a bottle last season, enjoying the kind of magical year that comes along only once every decade or so. But if history is any guide, the follow-up will have trouble coming close to matching the original.