Batters Are Getting Plunked At Historic Rates. But Why?

It’s never been more dangerous to be a major league hitter. Through Thursday’s games, batters had been plunked by pitchers 457 times, struck with a fast-moving projectile made of cowhide and densely wound yarn. Considering that MLB pitchers are throwing harder than at any time in recorded history, it’s safe to assume that getting hit by a baseball has never stung worse.

The current rate of 0.41 batters hit by a pitch per team game is the highest since 1900, the same year that the Brooklyn Superbas led by Wee Willie Keeler won the Chronicle-Telegraph Cup. (There was no American League yet and thus no World Series.)

This level of plunkings has given us some interesting results — and inevitable dust-ups. On Monday, four Reds were hit by pitches — in one inning, tying a record set in 1893. Mets batters were hit seven times on the hands just through April. Presumably in retaliation, reliever Jacob Rhame threw at the head of Rhys Hoskins, who retaliated himself with the slowest home-run trot since 2015. Rhame was suspended two games.

While the rate of HBPs has fluctuated across the game’s history, it was just 0.34 per team game three seasons ago, which is more in line with where it was for most of the 1990s and 2000s. So what is causing the recent spike? It’s a bit of a mystery.

There’s one simple explanation: There are more opportunities to hit someone now because hitters are extending counts and pitchers are throwing more pitches. The past two full seasons saw the highest number of total pitches (721,282 in 2018 and 721,279 in 2017, according to Baseball-Reference.com) on record.2 But even though the raw counts are higher, the share of total pitches that hit a batter last season is also going up: 0.266 percent of all pitches in 2018 hit a batter, the second-highest share on record. Through Thursday, this season has seen a share of 0.274 percent — which would be the highest that we’ve seen.

Some speculate that pitchers are just wilder than ever because of a focus on throwing hard in lieu of command. Walks per game (3.44) are well above the average since 1900 (3.19), but pitchers are throwing only fractionally more balls as a percentage of pitches this year (36.7) than the 2009-to-2018 average (36.6).

Of course, one specific reason for an HBP is that the pitcher meant to do it. Retaliation is as old as the game itself. And nothing gets a pitcher more snippy than giving up a homer. Balls are flying out of ballparks more than ever before, giving pitchers more opportunities to throw at the offending players. But it’s not just the act of hitting a home run, it’s what can come next: Don’t flip your bat or stand too long watching it or lollygag around the bases or trash talk the opposition in mid-trot. This year, Tim Anderson was beaned for flipping the bat too aggressively at his own dugout.

Furthermore, with home runs all the rage, pitchers may seek to expand the strike zone by moving batters farther away from home plate, effectively making the outside part of the plate more out of reach. Miss just a little in to a hitter in midlean over the plate and … kerplunk.

While we can’t measure the pitchers’ intent, we can measure where pitches are being located. According to data from Baseball Savant, more pitches than ever before are being thrown on the inside third of the plate and off the plate to the inside.

Through Tuesday’s games, more than 32 percent of pitches were inside, which is the highest rate since pitch location was first tracked in 2008. This rate is up more than 3 percentage points from 2008, which may not seem like much on first blush but would equate roughly to an increase of more than 30,000 inside pitches.

With more pitches directed inside, more batters are bound to get hit. But how much of that is on the batters themselves? Even as far back as 1997, players were bemoaning how hitters could treat the batter’s box like they owned it.

”Today’s game, you see guys digging a little trench in there,” Hall of Famer Tony Gwynn told The New York Times. “I just get flashbacks and wonder if they would do that if [Bob] Gibson or [Steve] Carlton or [Nolan] Ryan or [Tom] Seaver were out there. You can’t let a hitter go up there and think he controls both halves of the plate. If you bust a guy in, keep him honest, get him off the plate, you might be able to get him out away.”

Gibson, a Hall of Famer and the man largely responsible for the lowering of the mound, was viewed as a tiger on the field. He once dusted Reggie Jackson at an old-timer’s game. (Jackson had homered off of Gibson in a similar game the previous year.) After his close friend and teammate Bill White was traded, “Hoot” immediately plastered him on the elbow. And slugger Dick Allen said, “Gibson would knock you down and then meet you at the plate to see if you wanted to make something out of it.”

But Gibson hit “just” 102 batters in 3,884.3 career innings, or 0.24 per nine frames. That ranks 359th out of the 471 pitchers who threw at least 1,000 innings and hit at least 50 batters, according to Baseball-Reference.com. So the guy whose Hall of Fame bio says he “may well have been the most intimidating pitcher in MLB history” hit batters at a rate well below the hurlers of today’s game.

The pitcher today placing opposing trainers on the highest alert is Charlie Morton of the Tampa Bay Rays, who has led his league in hit batsmen four times in the past six years — despite never pitching more than 170 innings in any of those years. Morton nails 0.78 batters per nine innings, a career rate last exceeded by Ed Doheny (0.90), who retired in 1903. Morton’s ERA this year currently stands at a career-best 2.64. And in 2018, with the Astros, his .833 winning percentage led all of baseball: His 15 wins were one fewer than the number of batters he tattooed.

Neil Paine contributed research.

Check out our latest MLB predictions.

Did The Rockets Miss Their Chance?

gfoster (Geoff Foster, sports editor): After a lopsided and — let’s face it — largely uninteresting first round, the second round of the NBA playoffs is delivering on its promise. We have only one team that’s already punched its ticket (Milwaukee). Philadelphia and Portland were each able to force a Game 7 last night with clutch wins at home, but let’s start with the Golden State-Houston series, which resumes with Game 6 in Houston tonight. The extent of the Kevin Durant injury is not totally known, but we do know he is out for the remainder of this series. This possibly devastating news was likely a little bit easier to swallow for Golden State fans considering that many people (including myself) looked at that noncontact injury Wednesday and assumed he injured his Achilles.

Does this give Houston a legitimate shot to take this series? Or did they blow a crucial opportunity by not stealing Game 5 when KD went down?

chris.herring (Chris Herring, senior sportswriter): Both.

If they lose the series, they’re going to kick themselves for what happened in Game 5. But that said, they still have a decent shot to pull the upset. The margin for error is so much less now without KD there. They have to play well enough on offense while hoping that either Steph Curry or Klay Thompson are simply ineffective for a game or two. Steph reached down deep and remembered who he was in that fourth quarter, but it’s not inconceivable to me that Houston takes advantage of this.

natesilver (Nate Silver, editor in chief): It absolutely gives them a shot. Golden State was basically the equivalent of half a star player better than the rest of the top tier (Houston, Milwaukee, Toronto). Take that player away, and they’re probably a half-step behind instead. Without KD, they’re underdogs in a neutral-court series against all of those teams. HOWEVER, the Warriors only need to win one of the two remaining games to close out against Houston, and one of those games is at home, so they’re still overall favorites (64 percent favorites, more precisely) to win the series.

neil (Neil Paine, senior sportswriter): The elephant in the room is how eerily similar to last year this is playing out. The Warriors were in the same spot Houston is, down 3-2, with the opponent suffering a key injury. (That time it was Chris Paul who was out, and Golden State stormed back, obviously.)

chris.herring: Right.

natesilver: At the same time, although Harden disappeared down the stretch run for Game 5 and that wasn’t great, I think Houston gets a little bit too much grief. Beating the KD-less Warriors is still a big feat — remember, they won 73 games without KD! — especially at Oracle Arena.

chris.herring: It’s just that Houston had erased a 20-point Warriors lead and taken the lead on the road, with KD out of the picture, and Steph struggling. If you win that game, you’re up 3-2 with a chance to close it at home. They can still do it, but now they have to come back instead of merely going in for the kill.

neil: We often talk about the seeming inevitability of Golden State winning these past few years. But if they win again, that fourth quarter will be looked back at as a turning point of sorts, I think. A place where they made their stand as the season could have begun slipping away. Curry even started to get things rolling in that fourth quarter, after a brutal series for the most part.

natesilver: I don’t know — the whole game felt like Golden State’s to lose. The first half in particular was wide-open and sloppy, which you’d think was the Warriors’ jam more than Houston’s.

chris.herring: Just a couple of really clear things that killed the Rockets. Paul has never shot that poorly in a playoff game. Kevon Looney basically became PJ Tucker for a night, with all the offensive rebounds. The bizarre, fluke play at the end of the game.

natesilver: Sometimes I wonder if these analytics-heavy teams don’t emphasize offensive rebounding enough. Of course, they’ve spent way more time looking at the data than I have. But certain types of situations increase offensive rebound percentage more than others, and it can be a hidden source of value.

chris.herring: Maybe it was just GSW’s game to take unless the Rockets took it from the Warriors, which goes to Nate’s point about the game having been in Oakland.

I’m just really stuck on the “What if?” of that outcome. What if that was the last game at Oracle, potentially, and the Rockets could close this out tonight at home? The hype surrounding tonight would be insane.

I guess similar to last year, when Houston had a 3-2 lead but without Paul.

neil: It’s worth noting that with KD on the court in the series, the Warriors are +8.8 per 100 possessions; without him, they’re -6.2. So this injury really does add a huge late wrinkle to what was already a mega-interesting series.

chris.herring: I know the Warriors have won championships without KD and have even played stretches without him since he joined the team. But I do think it’s interesting that they’d gotten so used to relying on him this postseason.

He’d led them in scoring for eight straight games.

neil: He also completely changes HOW they play. They run so many more isolations with KD.

chris.herring: Even for Steph and Klay, going from that to having to do it all themselves again is a shift.

gfoster: Obviously, Curry and Thompson will need to step up on the offensive side to make up for that lost production — and both have been pretty so-so if not bad. But without DeMarcus Cousins and with a thin bench, I wonder how this affects them defensively. How do you think both teams adjust?

chris.herring: I would assume the Warriors are going to start Looney without Durant there.

You don’t have a ton of options, really.

But the Rockets can shade their defense a lot differently without Durant in the mix.

natesilver: I guess the one thing about Golden State is that with both KD and Steph out there — and Klay! — there are probably some diminishing returns in terms of being able to get good looks. Meaning, KD won’t hurt quite as much as if they didn’t have another super-high-usage player (Curry) and another super-efficient player (Thompson). Maybe there’s less margin of error against Houston’s defense, though.

neil: If the Warriors’ lack of depth was ever going to finally catch up to them, it’s now.

natesilver: Yeah, what I really worry about for GSW is the bench units. Curry still doesn’t look exactly right, and if you’re playing him 42 minutes, or whatever, that probably isn’t great.

But also not great if you’re playing him 38 minutes and have 10 minutes of a pretty terrible lineup.

gfoster: Likewise, Draymond Green gets into foul trouble again, and it’s even more complicated.

chris.herring: It’s pretty wild to consider how inevitably we talk of the Warriors winning it all again when an injury like this — one that keeps him out the remainder of the series, but not for the entire playoffs — is so consequential.

neil: The flip side, though, is how they still have a good chance to win without a top-five player. Any other team loses a player of KD’s stature and it’s sorta over.

natesilver: For the past several seasons, our model has usually had Golden State at about 50 percent to win the championship when the playoffs begin. Sometimes a little higher, sometimes a little lower. Either way, though, that’s a long way from 100 percent.

chris.herring: I’m interested to see how Paul responds tonight. And to see whether Tucker is a pest again the way he was in Game 4.

He’s not a big-time offensive player, but Tucker not having to guard KD all game long could open things up for him, too.

neil: Tucker, Paul and (weirdly) Austin Rivers seem to be the bellwethers for Houston. When they play well, the Rockets have won. Harden, on the other hand, has been pretty even in production between wins and losses this series.

natesilver: Which is usually how it works, Neil. 😉 But I agree. This is one of those series where I think basically every game was the deserved outcome, notwithstanding some of the foul controversies in Game 1.

neil: Well, my point is that it hasn’t exactly been Harden abnormally taking over games to will Houston to their wins. (To the extent that 35 points per game is just normal for him, haha.)

natesilver: I agree, it’s been the entire game plan working. And I don’t think the game plan really worked in Game 5.

gfoster: The Trail Blazers and Nuggets will play Game 7 in Denver. Game 7s in the NBA playoffs strongly favor the home team: Nearly 80 percent of them have gone to the home side. How are Portland’s chances of being in that 20 percent group?

neil: You would think that number would be even higher in Denver’s favor because the Nuggets have such a strong home-court advantage.

natesilver: We actually have Denver at “only” 76 percent, so a bit lower than the historical norm, and we account for the fact that teams at altitude have a bigger home court-advantage. But the home team in Game 7 is by definition the higher seed, and the thing about the Nuggets is that they aren’t as strong as a typical highly seeded team.

chris.herring: The Blazers’ chances are wonderful if they can get one more game of bench production like the one they just got in Game 6.

neil: Rodney Hood! He knows a new contract is coming. Averaging 16.2 PPG in this series.

It was also big for Dame Lillard to get hot from three again like he was against OKC.

chris.herring: This tweet blew me the hell away:

neil: LOL

chris.herring: Not just Hood, either. Zach Collins played his butt off, too, in Game 6 and stepped up in a way I didn’t expect.

All this while the Nuggets’ bench did almost nothing on the night.

That’s kind of been the story of the entire series, really.

natesilver: If Zach Collins and Enes Kanter and Rodney Hood are having breakout games … maybe that just means that Denver isn’t very good?

chris.herring: The Nuggets haven’t been able to take Nikola Jokic off the court at all.

gfoster: I wonder how much fatigue will begin to play a factor, which we have obviously seen in these long series. Dame looks a little gassed no?

natesilver: Jokic has also looked gassed at times, except that’s how he always looks so it’s hard to read too much into it.

chris.herring: Dame hit some ridiculous shots yesterday — both of the “he’s in a different area code” sort of way, and one where he was falling over and just threw something up and got it go down anyway.

natesilver: Did we discuss the four-overtime game? I thought some of the player usage decisions were pretty ridiculous, in terms of teams not incorporating their benches more.

neil: Yeah, there were some wild minute totals being recorded in that game. Jokic played 65 minutes!

natesilver: Most ever in a playoff game.

chris.herring: Yeah. Mike Malone said he needs to trust his bench a bit more.

gfoster: C.J. McCollum played 60. Dame played a relatively breezy 58.

chris.herring: It’s been tough. Denver’s backup point guard, Monte Morris, who in my opinion was one of the two or three most consistent bench players in the league, has scored 4, 3, 0, 2, 6 and 0 in this series.

And trusting a bench that is consistently giving you negative returns whenever Jokic takes a breather … there isn’t time to watch negative returns roll in!

It’s the playoffs. Every minute is huge.

natesilver: Random aside, but it does seem like teams that are dependent on a PG or a C can have more problems with their depth than a look at their roster might imply. If your star is a SG or SF or maybe a PF, you can slide guys around a lot more and give the team different looks. It’s hard to replace a guy like Jokic, though, in way that’s fluid with your overall gameplan.

neil: Yeah, there’s a lot more benefit to versatility in the middle of basketball’s “defensive spectrum” (or whatever we’re calling it).

chris.herring: 100 percent, Nate.

neil: Both ends call for more specific skills that aren’t as easily replicated when your star needs a breather.

natesilver: This is also sort of an interesting problem with on/off statistics. If certain types of players make roster construction harder, and lead to worse lineups when they’re off the floor, a lot of the +/- stats will mistakenly give them credit for that.

chris.herring: There was that game to start the playoffs that Denver lost, where Jokic took only nine shots. I was close to writing an entire story about that notion.

They’ve done a much better job making sure he’s constantly involved in everything since then. They just have a limited bench.

I still wouldn’t like their chances in the next round. But if KD takes a while to come back, at least they’d be playing another thin team in GSW, assuming the Warriors find a way to get one of the next two.

gfoster: Moving to the East, Philly staved off elimination and will go back to Canada for Game 7 — and they didn’t get booed (that much) by their home fans, so that’s big. Obviously, this was a big game for Ben Simmons and Jimmy Butler, but Joel Embiid posting a +40 in 36 minutes while only scoring 17 is absurd.

neil: Philly’s Big 3 were amazing in Game 6. They finally got it all together at once.

chris.herring: I thought Simmons was the story of the night.

natesilver: While Embiid’s +40 stood out in Game 6, I noticed that Simmons has had a positive rating in every Philly win so far in the playoffs and a negative one in every Philly loss.

chris.herring: Exactly

natesilver:

chris.herring: Simmons had 21 points in Game 6, but had only managed 33 TOTAL in Games 2-5.

natesilver: I guess that isn’t hugely surprising, but still — Simmons is one of the ultimate “can’t live with him, can’t live without him” players.

neil: And one narrative of these playoffs has been about whether Simmons truly fits into Philly’s group, especially long-term. He’s been under a LOT of scrutiny and criticism.

chris.herring: I think it’s somewhat unlikely that he has a repeat performance in Game 7 on the road. But even if they can get 15 or so from him on halfway efficient shooting, it’s massive.

We know what he is for now.

natesilver: I was sorta-kinda persuaded by the argument that his natural position is as a stretch center.

chris.herring: But I think that’s part of what works against him in these playoffs: If you keep him and Philly out of transition, he’s going to struggle to score, and he’s going to clog the paint in that dunker’s spot

I really loved that story, too, Nate — and was going to find a reason to post it in here.

neil: “A bigger and more athletic version of Draymond Green with more scoring ability”

chris.herring: And in a way, that’s what he did yesterday.

natesilver: I think he’s become a bit underrated at this point. Like, even if you concede the argument that he and Embiid are a bad fit together, if I’m one of the 29 other GMs, I’d be looking for a way to buy low on Simmons.

chris.herring: He scored off a couple putbacks. And he scored on fastbreaks. Your challenge is that you can game-plan him during the playoffs as an opposing defense.

The fact that he isn’t a jump-shooting threat whatsoever — like, we KNOW he’s not going to shoot — makes him different in that sense than a Draymond, or a Giannis Antetokounmpo. It puts more pressure on the other guys to find ways to score while playing defenses that take advantage of that.

But he’s still really, really good.

natesilver: If Simmons shot a Giannis number of threes, could he shoot at Giannis’s percentage? It’s not that high a bar to clear.

chris.herring: Nah, I’ve watched him warm up several times before. Whereas most NBA players, at any position, can knock down a handful of threes without much trouble, it doesn’t come natural for Simmons at all.

natesilver: Haha

chris.herring: You’re more likely to see him miss five or six triples in a row than you are to see him hit three or four out of 10 when he’s warming up wide-open.

natesilver: Do you buy the theory that he’s shooting with the wrong hand?

chris.herring: I think it’s a real possibility, yes. When you watch him shoot with his right hand, it looks more natural than with his left.

And I said it on Twitter recently: I think Giannis will be a league-average shooter from three next year.

neil: Is perimeter shooting a skill that a player can learn to at least be competent at with enough work? I guess Giannis is a weird comparison point because his best 3-point percentage in a season was still the 34.7 percent he hit as a 19-year-old rookie.

natesilver: Historically, lots and lots of players have learned to shoot the three, especially recently.

neil: Yeah, especially big men, I suppose.

chris.herring: I legitimately can’t believe Jason Kidd is still in consideration for jobs when he convinced Giannis (and Jabari Parker) not to shoot threes anymore

natesilver: But with Simmons, his free-throw percentage is pretty bad, and he’s bad on long twos, so that does suggest there might be something structurally wrong with his shot.

chris.herring: Anyway, I think the Raptors should be fine at home. The series has showcased a number of swings in either direction. If they keep Simmons out of transition, Kyle Lowry doesn’t lay an offensive egg at home, and Kawhi Leonard is himself, I think they’ll be OK

gfoster: Kristaps Porzingis aside, was there a bigger trade deadline move than Toronto getting Marc Gasol? I suppose we could point back to Rodney Hood.

chris.herring: Gasol was tailor-made for this series, and the matchup with Embiid. He’s not nearly as talented, but he can hold his own with a player who otherwise would have had a chance to break this series open.

(Although it’s fair to point out that Embiid has also had, like, three different illnesses this series, somehow.)

natesilver: It’s a pretty high-leverage Game 7 in that whichever team loses isn’t going to feel at all good about its season. Not like, say, Portland, which to be honest can be pretty happy even if they get blown out in Denver.

chris.herring: That’s certainly true.

neil: And this is the point where both teams’ seasons ended last year, too. So they couldn’t even point to a second-round berth as progress.

gfoster: Does Brett Brown keep his job if Philadelphia loses?

natesilver: I don’t think so.

chris.herring: I’d like to think he *should* be safe with a loss, since the series made it seven games. But the owner has been pretty clear in saying that he wanted to see progress with how all-in the Sixers just went. And losing in the second round again, technically, wouldn’t be progress.

natesilver: I know Philly has a bunch of weird fits, but Occam’s razor is that a team with Embiid, Simmons, Butler, Tobias Harris and JJ Redick ought to be VERY good, even with no bench.

chris.herring: We talked about it before, but I don’t know if I could blame Brown for not getting more out of a group that hasn’t spent that much time together. Especially with Embiid being less than healthy this series. But I’m also not the one making multimillion-dollar decisions in these trades, hirings and firings.

neil: Yeah, even though it wouldn’t surprise me at all if they went in a new direction, it would feel a little unfair given the fit and the lack of cohesion.

natesilver: I do sort of wonder if they trade Simmons if they lose.

gfoster: Does Butler return if they lose?

chris.herring: The city of Philadelphia will riot if they don’t bring Butler back.

neil: 🔔

chris.herring: He’s been fantastic at times, and it’s clear how much he cares about winning. I think the better question is whether they’ll bring Harris back — and if so, at what money.

Butler is fascinating because of the mileage he has on his body. But the fans will legitimately be furious if they don’t bring him back.

neil: I’m always shocked at how young Butler is. He feels like he’s been around forever.

natesilver: Who they would trade Simmons for is a tricky question, because his salary is still pretty low next year. On Twitter the other day, I suggested that an interesting trade might be Simmons straight up for the No. 2 or 3 overall pick, and everyone semed to hate that.

chris.herring: A Simmons trade could immediately improve the playoff outlook of the team, but he’s also so young to where it’s very easy to see how and where he could improve. But it’s part of the reason why I’d at least like to see him experimenting with a jumper during games. You really can’t go entire postseasons without so much as even attempting a shot outside the paint. And playing center on a team with Embiid won’t work long-term.

natesilver: Because he’s only making like $8 million next year, though, it’s hard to trade him for a veteran talent without having to package him with someone else and messing up your books. So if you could trade him for a young point guard, and actually use Butler as your primary ball handler in a lot of lineups, that might be interesting.

chris.herring: It’s easy to say in hindsight, but having Landry Shamet still would have been massive for this team. You also have the question of what to do with a player like Redick — one of your few floor-spacers — once his deal ends this summer.

gfoster: Speaking of next season’s plans, I wanted to touch on Boston quickly, who was knocked out this week by Milwaukee (who we haven’t even mentioned). What is going to happen with that team? Does Kyrie Irving stay?

neil: What a miserable end to the series (and probably his Celtics career) for Kyrie.

chris.herring: I just want to reiterate here: I think Milwaukee can, and probably will, win the whole thing this year.

The Bucks haven’t gotten quite enough credit for taking care of business. We wrote the piece about the Celtics having shut down Giannis in Game 1 — and then didn’t mention them again. The Bucks have been impressive as hell.

neil: If the Rockets hold court at home in Game 6, the Bucks will be the only team to advance in less than seven games. (And they did it in five.) Although idk how much that says about the Celtics.

chris.herring: But Kyrie … who knows with this guy?

natesilver: Good news, New York: Kyrie Irving is now officially enough of a headcase to play for the Knicks!

neil: LOL, Nate.

chris.herring: I don’t think you can go as far as to say that Kyrie burned bridges with the Celtics. But there were so many odd moments where he seemed to be talking about his teammates and what all they needed to do when it wasn’t clear that Kyrie had the stature to say those things.

What I mean by that: If you aren’t all the way in, and you waffle on the idea of being somewhere long-term, it looks weird if you readily critique your younger teammates, who probably feel just as invested, if not more invested, as you are. So it was interesting to see Terry Rozier say that he felt he dealt with BS all season. It was interesting to see Jaylen Brown’s many faces on the bench as their season was winding down.

natesilver: It’s still hard to see him coming back. I mean, he hasn’t been that subtle about conveying his intentions. Which doesn’t mean he couldn’t change his mind later.

chris.herring: It was interesting to hear Al Horford admit that the Bucks reminded him of his 60-win Hawks team, but with a legitimate superstar. And it was interesting to watch Kyrie have a horrible shooting series in which he said he should just take more shots to shoot himself out of the slump.

Yeah. I think he’s gone. Knick fans had to be ecstatic at how that all played out.

natesilver: It’s also not clear how much Boston wants him back. Certainly the fans have turned on him. His teammates don’t love him. He doesn’t provide that much value relative to the max contract. I’m pretty bullish on Kyrie, but he’s not a huge bargain.

chris.herring: Aside from wanting to make up for whatever this season was, I don’t know why Kyrie would return to Boston at this point if he feels over the whole situation.

gfoster: I think Kyrie’s status in Boston is contingent on whether the Celtics pursue Anthony Davis, right? Wouldn’t he stay in that scenario?

chris.herring: I never understood why he committed to staying as the season was starting. But the fact that he did, if he doesn’t actually want to be there, doesn’t mean he should still follow through with it. I think they’ll likely pursue Davis regardless of Irving.

natesilver: Mayyybee not, Geoff? A lot of the other teams that Kyrie might go to could also put together a decent offer for AD.

chris.herring: The challenge there is if Irving is gone/leaving, you would have a pretty bare cupboard to entice Davis to stay. Because he’ll be a free agent pretty soon, too.

natesilver: By this point next week, we’ll know who has the No. 1 overall pick, too.

chris.herring: That was the risk the Celtics waged by trading for Irving in the first place. (They gave up a banged-up Isaiah Thomas, so it wasn’t a huge risk. But still.)

This risk would likely involve Jayson Tatum and other important pieces. You’d have to make sure Davis wanted to be there before pulling that trigger, I’d think.

natesilver: If push comes absolutely to shove, the Celtics still have Tatum and Brown on cheap deals, a ton of extra draft picks and a good coaching/scouting/analytics staff.

So that’s a fair bit of assets to fall back on. It might make you a little more risk-averse, even though Danny Ainge has a reputation as a gambler.

gfoster: So under the new lottery rules, the Knicks, Cavs and Suns each have a 14 percent chance at landing Zion Williamson. The Bulls are 12.5 percent, Atlanta 10 percent, Wizards 9 percent.

natesilver: Which is the most annoying scenario? That he ends up in Cleveland, maybe?

gfoster: Yes. Has to be.

neil: Yet ANOTHER Cavs No. 1 pick would be hilarious.

gfoster: It’s like when the Edmonton Oilers won the lottery in four out of six years. (hockey reference!!)

chris.herring: Maybe I’m too much of a purist? The idea of them winning a fourth lotto in such a tight window would be insane (and maybe depressing on some level, because it feels like incompetent ownership would be gifted with a star yet again). But I also think it would make the Cavs interesting. That said: If he goes to the Hawks, that would be kind of fascinating — perhaps the most interesting fit of the teams with a realistic chance.

neil: Trae Young + Zion, let’s GOOOOOO.

chris.herring: If he goes to the Knicks, the hype will be like something I’ve never seen in my lifetime. Especially with the KD/Kyrie rumors having been out there, too.

gfoster: I do like the idea of Ja Morant on the Knicks.

natesilver: Would you trade him for Anthony Davis, though?

chris.herring: Will give a lot of voice to the idea of the Knicks swapping the No. 1 pick for a Davis package or something

natesilver: WOULD YOU DO IT, CHRIS, IF YOU’RE THE KNICKS?!?

gfoster: All-caps questions need answers.

chris.herring: LOL.

neil: Yeah, I feel like the bottom part of this chat has just been Nate angling to get AD, KD and Kyrie on the Knicks.

chris.herring: If I had a really strong sense that I was going to get Durant and/or Kyrie, I would be fine with that. If it was just Davis, and no pieces around him, no. I don’t trust the Knicks enough to truly build it from the ground up, with a single star player in place.

Hopefully that makes sense and won’t get me stoned by the Knick fans who read this.

natesilver: I’m reading Knicks message boards where people are like “Mitchell Robinson is too good to trade for Anthony Davis.”

chris.herring: He’s not. But man, it would be great to hold on to him if you could.

Especially if you’re giving them Zion/the first pick. Kevin Knox and Frank Ntilikina, you’d feel more comfortable giving away.

natesilver: Yeah, I think Zion for Davis is at least fair value for New Orleans, considering that he really just has one year left on the contract. So if the Knicks are giving up a bunch of other stuff too, I start to not like the trade.

gfoster: All right, the lottery is Tuesday, so next week we will have more developments to discuss in this weekly 2018-19 Playoffs/Wild Knicks Speculation chat. Enjoy the conclusion of the second round!

Check out our latest NBA predictions.

Can The Riddler Bros. Beat Joe DiMaggio’s Hitting Streak?

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,5 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 Scott O’Neil, unriddle this sequence:

What number comes next?

2
6
10
3
8
9
4
7
?

Submit your answer

Riddler Classic

From Steven Pratt, where have you gone, Joe DiMaggio? To Riddler Nation, perhaps:

Five brothers join the Riddler Baseball Independent Society, or RBIs. Each of them enjoys a lengthy career of 20 seasons, with 160 games per season and four plate appearances per game. (To make this simple, assume each plate appearance results in a hit or an out, so there are no sac flies or walks to complicate this math.)

Given that their batting averages are .200, .250, .300, .350 and .400, what are each brother’s chances of beating DiMaggio’s 56-game hitting streak at some point in his career? (Streaks can span across seasons.)

By the way, their cousin has a .500 average, but he will get tossed from the league after his 10th season when he tests positive for performance enhancers. What are his chances of beating the streak?

Submit your answer

Solution to last week’s Riddler Express

Congratulations to 🎖 Alex Murray 🎖 of Philadelphia, winner of last week’s Riddler Express and the new Median Marquess of Riddler Nation!

Last week brought two interactive challenges. In the first, you submitted a whole number between 1 and 1 billion, and whoever submitted the number closest to 2/3 of the mean of all the submitted numbers won.

I received over 2,500 submissions. The mean of all the valid submissions was 163,918,246. Two-thirds of that is 109,278,831, or nearly 11 percent of the maximum submission. Our winner, Alex Murray, submitted 109,185,185 — off by less than 100,000. That particular number was chosen because, as Alex rather cryptically explained, it was “163,777,777 times two-thirds.” In any case, that worked! Well chosen, Alex.

Here is the distribution of all of the numbers submitted by the Nation, in bins of 10 million. Five of you said you just guessed your phone numbers.

I see you, people who submitted 1 billion. You had no chance of winning, but you did have an effect on everyone else. One such submitter, Zane from Pittsburgh, explained: “I seek chaos.” Another, Will Heath, said that he “just wants to watch the world burn.” Yet another, Emma Cooper, wrote, “I do not intend to be right but I intend to make other people wrong.”

As the benevolent leader of this column I am shocked and appalled. Shocked and appalled, I say!

This challenge is well known in game theory and it is called — also shockingly — guess 2/3 of the average. In this game, there is a unique (pure strategy) Nash equilibrium, meaning a set of actions for all the players from which no player would want to deviate. We … did not achieve it.

To achieve equilibrium, each player would submit the lowest possible number, and everyone would then share in the prize. Why? You can arrive at this result through a process known as the iterated elimination of weakly dominated strategies. For example, no player would want to submit a number above 666,666,666, because that’s 2/3 of the highest possible submission, which means 2/3 of the average submission cannot possibly be higher than that. Given that, no player would want to submit a number above 444,444,444 (2/3 of 666,666,666), and then no number above 296,296,296, and so on. Eventually, by this iterative logic, the only submission that makes any strategic sense is 1.

Therefore, I’m proud to share our new slogan. Riddler Nation: Out of Equilibrium Since 2015.

Solution to last week’s Riddler Classic

Congratulations to 👑 Vince Vatter 👑 of Gainesville, Florida, winner of last week’s Riddler Classic and the reigning king of Riddler Nation!

Last week also brought the third installment of the Riddler Nation Battle Royale. These were the rules: In a distant, war-torn land there were 10 castles. There were two warlords: you and your archenemy. Each castle had its own strategic value for a would-be conqueror. Specifically, the castles were worth 1, 2, 3, …, 9 and 10 victory points. You and your enemy each had 100 soldiers to distribute, in any way you like, to fight at any of the 10 castles. Whoever sent more soldiers to a given castle conquered that castle and won its victory points. (If you each sent the same number of troops, you split the points.) You didn’t know the distribution of the enemy forces until the battles began. Whoever won the most points won the war.

You submitted a plan distributing your 100 soldiers among the 10 castles. I took all these battle plans and adjudicated all the possible one-on-one matchups.

I received nearly 1,500 battle plans, nearly 1,200 of which were valid — i.e., they only used 100 soldiers and only whole numbers of soldiers and so forth. And without further ado, here were the top performers:

Riddler Nation’s top 5 warlords
Castle Record
Name 1 2 3 4 5 6 7 8 9 10 W T L
Vince Vatter 0 0 12 1 1 23 3 3 33 24 846 21 293
Nate Bailey 0 0 12 1 2 23 3 3 33 23 843 9 308
Iggy Chiang 0 0 12 0 0 22 0 0 34 32 837 6 317
Alex Quick 3 0 6 8 15 22 4 3 31 8 819 24 317
Chad Burge 5 6 6 8 13 22 27 4 4 5 814 19 327

The top warlords relied heavily on the data from the first two such battles. And, amazingly, this is Vince’s second consecutive Riddler warlord victory! He explained that he “used a genetic algorithm (the same as in the last competition) to explore distributions that would be good against the second-round distributions and the first- and second-round distributions combined. Then I used the same algorithm to optimize against those and the first- and second-round distributions simultaneously.”

Our runner-up, Nate, explained: “I used k-medoid clustering to find median strategies that represent the most common strategies, then found an allocation of soldiers that beat the eight most common strategies. I then used that as an initial input to Robbie Ostrow’s simulated annealing code from Part 2, which spat out the above.” Well spat, Nate.

And our fourth-place finisher, Alex, explained simply: “A computer told me to.” Fair enough.

Most successful strategies, broadly speaking, devoted more troops to the high-value castles and ignored the low-value castles, sometimes entirely — none of which is too surprising. But that relationship is not perfect, and the win-loss record of any given strategy is highly sensitive to specific deployments. Our top performers tended to fight hard for Castles 3 and 6, for example. (Note also the tight similarity between the first- and second-place strategies above.)

Here is how the average soldier deployments broke down last week compared to the previous battles:

Troop deployment strategies

How Riddler Nation distributed its forces in each battle royale

Average number of soldiers sent to castle …
Battle 1 2 3 4 5 6 7 8 9 10
May 2019 2 3 4 7 9 12 13 17 17 16
May 2017 3 4 6 8 10 12 15 17 14 12
Feb. 2017 3 3 4 7 9 13 16 19 16 11

On the whole, this third edition of the battle royale saw a dramatic increase in soldiers sent to the highest-value castles — Castles 9 and 10 — with three and four more soldiers sent there on average. This additional firepower was, on average, siphoned mostly from the battles for Castles 3 and 7, where two fewer troops were sent.

This challenge is also well known in game theory, where it is called the Colonel Blotto game. However, unlike the 2/3-of-the-average game, there is no simple equilibrium — the analysis involves gnarly mixed strategies and often relies heavily on computation. It was analyzed as early as 1950 by researchers at the RAND Corporation, and it has applications in military strategy and political competition — including in yours truly’s doctoral thesis.

Though it is all quite easy, apparently, if your name is Vince Vatter.

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]

The Loudest Places You Can’t Hear

Where is the loudest place in America? You might think New York City, or a major airport hub, or a concert you have suddenly become too old to appreciate.

But that depends on what kind of noise you’re measuring. Sound is actually a physical thing. What we perceive as noise is the result of air molecules bumping into one another, like a Newton’s cradle toy. That movement eventually reaches our eardrums, which turn that tiny wiggle into an audible signal. But human ears can’t convert all molecular motion to sound. Sometimes the particles are jostling one another too fast. Sometimes they’re too slow. Sometimes, the motion is just happening in the wrong medium — through the Earth, say, instead of through the air.

And when you start listening for the sounds we can’t hear, the loudest place in America can end up being right under your feet.

Scientists have tools that can detect these “silent” waves, and they’ve found a lot of noise happening all over the U.S. Those noises are made by the cracking of rocks deep in the Earth along natural fault lines and the splashing of whitecaps on the ocean. But they’re also made by our factories, power plants, mines and military.

“Any kind of mechanical process is going to generate energetic waves, said Omar Marcillo, staff scientist at Los Alamos National Laboratory. “Some of that goes through the atmosphere as acoustic waves, and some goes through the ground as seismic waves.” Marcillo’s work focuses on the seismic.

When researchers track seismic activity, they’re sensing the waves that make the Earth roll and rumble, of course. But those waves aren’t that much different than what we hear as sound. Some kinds of waves produced by earthquakes have even been known to generate sounds that people can hear before the ground starts to shake beneath them. And, along the way, their instruments also pick up the relatively small vibrations of very loud machines, including the spinning blades of wind turbines and hydroelectric dams.

Marcillo is trying to map these sources of small seismic signals in order to help other scientists track very small earthquakes that could help predict big, dangerous natural disasters. Right now, it’s hard to tell what’s a baby quake and what’s people being loud. “If you can understand the background noise, then you can better detect a signal,” he said.

To do that, Marcillo and his team used data collected over a decade by the U.S. National Seismic Network — 100 stations that track the movement of the ground all over the country. They combined that data with information about nearby industries to start figuring out which noises were likely human-made. “We’d have operational data telling me a wind farm started up, and I could see a signal emerging in the data within a couple months,” he said.

The result is a map that shows some big regional differences in seismic noise, with the wind-heavy Plains states showing up as “loudest.”

_But if what you’re measuring is infrasound, it’s Nevada causing a racket. Infrasound travels through the air, just like the stuff we can hear does, but in this case, the molecular jiggles and vibrations are happening too slowly for our eardrums to convert them into information our brains understand. Infrasound can travel long distances and is often the unheard ripples set off by an audible sound that happened far, far away.

Back in 2011, Scripps Institution of Oceanography researchers Catherine De Groot-Hedlin and Michael Hedlin, who are married, mapped infrasound across the country by adding infrasound sensors to 400 existing seismic detection stations that are part of the USArray, a continent-wide seismic observatory. Their analysis spotted mining blasts, rocket launches and other sharp spikes in infrasound activity. They weren’t able to pick up the constant hum of a wind farm, De Groot-Hedlin said, but they could see daily upticks that coincided with working hours at mines. “You can see lunchtime [in the data],” she said.

In their data, it’s Western states like Nevada, Utah and Idaho that turn up loudest, probably the result of nearby military facilities.

Like Marcillo’s map, the map created by deGroot-Hedlin and her husband is meant as a jumping off point for further research: a sort of catalog of sound. The idea is that other scientists can refer back to their research later, to figure out why they’re getting a weird reading, to better understand atmospheric phenomena that also affect how infrasound travels, or to better understand how infrasound itself might affect things like bird migration.

In both cases, the map is less about where the loudest place is and more about how it got that way — i.e., people and the stuff we do. Turns out, to understand the world around us, we sometimes have to tune ourselves out first.

Marc Gasol Is Joel Embiid’s Kryptonite

Joel Embiid has described himself as the “most unstoppable player in the league” — and for good reason. When he’s at his best, like in Game 3 of the Eastern Conference semifinals, he can make defenders look downright foolish as he pump-fakes his way into windmill dunks. But so far in Philadelphia’s series against Toronto, Game 3 has been the exception. The Raptors have all but shut Embiid down on the offensive end, thanks in large part to Marc Gasol — the man who has perfected the art of stopping the league’s most unstoppable player.

Through five games of the series — which the Raptors lead 3-2 — Gasol has matched up with Embiid on 201 possessions, holding him to just 21 points per 100 possessions. That’s a significant dip from Embiid’s season average of 37 points per 100 possessions.

If you think those numbers are obscured by Embiid’s recent upper respiratory problem, consider this: Over the past two seasons (which is as far back as the NBA’s matchup data goes), Gasol has played against Embiid on nine separate occasions (including the regular season and this year’s playoffs). During that stretch, the two have matched up on a total of 379 possessions. Embiid averages just 19 points per 100 possessions when Gasol is his primary defender, by far his lowest average against anyone who has guarded him on at least 100 possessions.

To put it another way: Against average competition, Embiid rivals Stephen Curry, Giannis Antetokounmpo and James Harden as the most prolific scorer in basketball in terms of points per 100 possessions. But when he’s guarded by Gasol, he essentially turns into Dewayne Dedmon.

At 7 feet tall and 250 pounds, Embiid can usually bully smaller defenders and tactically position himself in the post. But Gasol is too big to be pushed around, and it’s forcing Embiid out of his sweet spots. Throughout the series, Gasol has refused to cede ground to Embiid, denying the entry pass into the post and forcing Embiid to catch the ball outside of the paint. During the regular season, Embiid averaged 7.4 touches in the paint per game. Against Gasol and Toronto in the playoffs, Embiid is averaging just 4.2 touches in the paint per game.

Another factor contributing to Embiid’s lack of paint touches is the crowd that’s been forming right around the basket. Fellow Sixer Ben Simmons can’t shoot outside of 10 feet and so positions himself near the rim, which brings his defender to effectively provide help defense when Embiid is in the post. That’s a problem especially when the help defender is Kawhi Leonard, the player who has guarded Simmons most of the series.

To make up for his lack of paint touches, Embiid has had to rely on his jump shot to generate points. But that’s not his strong suit. In the regular season, Embiid shot 34 percent on jumpers. In this series, he’s just 10 for 37 (27 percent) on those shots. Gasol is forcing Embiid to do what he does least well, and it’s working to the Raptors’ advantage.

The fact that Gasol has given Embiid trouble shouldn’t be all that surprising. Even at 34 years old, Gasol can still play like the defensive player of the year he once was. Just ask Nikola Vucevic: Gasol neutralized the All-Star center during the Raptors’ first-round series against the Magic. Vucevic scored just 17 points per 100 possessions when Gasol was the primary defender — a far cry from Vucevic’s season average of 32 points per 100 possessions.

When Gasol was brought to Toronto in a midseason trade, it was reasonable to wonder whether the big Spaniard had enough in the tank to make a difference on a contending team. Those doubts have been put to rest, in part because Gasol has chiseled out a perfect role for himself. In Toronto, Gasol doesn’t need to anchor a defense while also serving as a primary scorer, like he was forced to do in Memphis. Instead, he’s able to focus on what he does best, which is lock down the opposing team’s best big man.

In all fairness to Embiid, he’s reportedly battled through injury on top of illness during the playoffs. And if we’ve learned anything from his monster Game 3, it’s that a healthy Embiid can live up to his self-proclaimed title. The only question is whether he can do it consistently against an elite defensive stopper like Gasol.

Check out our latest NBA predictions.

The Warriors Are Leaning Into The Death Lineup — And It’s Not Working

For a long time now, the Golden State Warriors have owned the NBA’s ace in the hole: the Death Lineup. First deployed at the suggestion of assistant coach Nick U’Ren during the 2015 NBA Finals, the lineup quickly became the most dangerous in the league. And it got even scarier when the Warriors swapped out the weakest member of the first iteration of the Death Lineup — Harrison Barnes — for Kevin Durant before the 2016-17 season.

Since Durant signed with Golden State, the lineup of him, Stephen Curry, Klay Thompson, Andre Iguodala and Draymond Green has played 529 minutes during their regular-season run, outscoring opponents by a total of 268 points — and 20.5 points per 100 possessions. Prior to their series-evening Game 4 loss against the Houston Rockets, the group had shared the floor for 317 playoff minutes, outscoring opponents by 121 total points and 16.7 points per 100 possessions.

In this year’s playoffs, though, the NBA’s most feared lineup has begun to show signs of vulnerability — and the Houston Rockets have taken advantage. In Game 4, Houston outscored that unit by 11 points across 22 minutes — and that figure includes the 14-8 run with which the Warriors closed the game over the final 5:45. Such a performance for the Death Lineup is — to put it mildly — highly unusual.

That unit has now seen the floor together in 32 of the 48 playoff games that encompass the Durant era,1 and it has been outscored in just seven of those 32 games. When the lineup has shared the floor for at least five minutes, it has been outscored just four out of 23 times. And when that group has played 10-plus minutes together, they’ve been outscored only twice in 13 games.

Take a look at the list of seven playoff games in which the Death Lineup has been outscored, though, and see if you notice anything.

The Death Lineup is killing the wrong team

Since acquiring Kevin Durant, the playoff games in which Golden State’s “Death Lineup” has been outscored, 2017-2019

Game Opponent Minutes +/- Win
2018: conference finals, Game 2 Rockets 22 -18
2019: Round 2, Game 4 Rockets 22 -11
2019: Round 1, Game 5 Clippers 9 -8
2017: Round 2, Game 4 Jazz 2 -8
2017: Round 1, Game 1 Trail Blazers 6 -7
2019: Round 1, Game 3 Clippers 2 -5
2019: Round 1, Game 2 Clippers 4 -4

Source: Basketball-Reference.com

First, and most obviously, the two worst games that group has played have come against the Rockets. Last year, they were blasted by 18 points in Game 2 of the Western Conference finals, and Monday night, they were outscored by 11. But you might also notice that of the seven games, four of them are from this year’s playoff run, which right now is only 10 games old.2

Part of this may be a product of Steve Kerr and the Warriors leaning too much on the Death Lineup. Before this series, the Death Lineup had never been used for more than 22 minutes in a single playoff game. It has now played 22 or more in all four games against the Rockets, including an all-time playoff high of 34 in Game 3, and the Warriors still managed to lose two of those four games. Those losses dropped their playoff record when the group shares the floor for 20-plus minutes to just 2-3, with all of those games coming against the Rockets.3

That the Warriors have had to use their best lineup more often against Houston than anybody else is perhaps not surprising. The Rockets were fairly open last season about having constructed their team specifically to defeat the Warriors — so open that general manager Daryl Morey declared prior to the start of last season that the organization was “obsessed with ‘How do we beat the Warriors?’”

They nearly pulled it off during last year’s Western Conference finals, falling in seven games after taking a 3-2 lead but seeing Chris Paul get injured in the final moments of Game 5. Houston was criticized in some circles for its offseason maneuvers, namely letting Trevor Ariza walk for a deal with the Phoenix Suns. The crowing got even louder when Houston started the season poorly,4 but here they are again in position to send the Warriors home early. The Rockets don’t have home-court advantage this time around, but perhaps they have another advantage: their bench.

Houston’s in-season pickups of Austin Rivers and Iman Shumpert fleshed out their wing depth, and that duo has provided strong minutes during this series. Rivers missed Game 1 with an illness, but the Rockets are plus-17 in his 85 minutes over the past three games. Similarly, they’re plus-15 in 65 minutes with Shumpert on the floor during the series. Nene has been used only sparingly as the Rockets have leaned into small-ball lineups with P.J. Tucker at center when Clint Capela rests, but Houston is nevertheless plus-18 with Nene in the game.

The Warriors’ bench, meanwhile, has been a disaster. All five players who have come off the bench for at least 10 minutes during these four games have seen the Warriors get outscored during their time on the floor. It’s getting to the point where Kerr seemingly cannot trust any of them — including previously reliable role players like Shaun Livingston.

Playoff games in which Golden State has used the bench for 50 or fewer minutes, 2017-2019

Game OPPONENT Bench Min.
2019: Round 2, Game 3 Rockets 39
2019: Round 2, Game 1 Rockets 44
2019: Round 2, Game 4 Rockets 47
2018: conference finals, Game 4 Rockets 48
2019: Round 2, Game 2 Rockets 50

Source: Basketball-Reference.com

Kerr gave his bench guys only 47 combined minutes in Game 4, the third-fewest minutes he has ever given them in 48 playoff games since the team signed Durant. Only five times has he given out 50 bench minutes or fewer, and four of them have come during this series, which is only four games old.

With his bench foundering and the Death Lineup no longer delivering its standard kill shot, Kerr is going to have to hope things take a different turn as the series returns to Oracle Arena for Game 5. Maybe that’s Curry busting out of his series-long shooting slump in an even bigger way than he did on Monday night or Klay Thompson finally exploding for the first time in what seems like forever. Maybe it’s figuring out a way to force James Harden into a subpar performance. Maybe it’s something else. But something has to change for them, or else they’re going to be heading home for the summer unexpectedly early.


We used math to help LeBron cast 'Space Jam 2'


Check out our latest NBA predictions.

Kawhi Leonard Is The Terminator

Even though they held a one-point lead with just more than a minute left in Game 4, Kawhi Leonard and the Toronto Raptors found themselves with their backs against the wall on Sunday in Philadelphia.

The Sixers and their raucous home crowd at Wells Fargo Center could almost taste a victory, one that would have given them an enormous 3-1 series advantage over Toronto heading into Game 5. And they would be accomplishing that despite getting a poor scoring effort from Joel Embiid, who was under the weather for the second time during the series.

But as the clock ticked down to that final minute, Leonard, who’d gotten almost everything he’d wanted Sunday, had other plans. He used a screen from teammate Marc Gasol, and four dribbles to his right, but both of Philly’s pick-and-roll defenders — Embiid and Ben Simmons — opted to follow Leonard to the right wing. Where another player might have passed the ball, Kawhi chose to elevate, lofting a rainbow 3-pointer over the outstretched left arm of the 7-foot-2 Embiid.

Aside from all but assuring that Toronto would knot the best-of-seven series at two games apiece, the shot punctuated yet another virtuoso performance by Leonard, who logged 39 points on 13-of-20 shooting and 14 rebounds, and is so far having one of the most efficient postseason runs we’ve ever seen from an NBA player, let alone a wing player specifically.

In this series against Philly, Leonard is somehow averaging 38 points on 62 percent shooting, with a perfect-looking shot chart. He’s drained an unthinkable 21 of his 24 uncontested shot attempts through the four games, including hitting 6-for-6 on Sunday.

Leonard did all this while continuing to have an impact on the defensive end, where he held Simmons in check during the first half before sliding over during the third period and heavily limiting swingman Jimmy Butler, who had scored efficiently up until that switch occurred.

Leonard wasn’t solely responsible for Toronto’s win Sunday. Gasol — who’d been held to eight points or fewer in Games 1-3 — was more aggressive and finished with 16 in Game 4. Similarly, Kyle Lowry looked for his shot early and finished with 14 points after having just seven in Game 3. Danny Green was a perfect 8-for-8 from the line. All of these contributions were helpful in light of Pascal Siakam, arguably Toronto’s second-best player, shooting 2-of-10 from the floor while playing through a calf injury, and Serge Ibaka being the only Raptor to score off the bench.

But make no mistake: Kawhi has played as if he were content to do this all by himself if need be. And in many ways, that spectacle is still noteworthy considering how far a cry it is from what Leonard was earlier in his career, before he became a clear-cut franchise player.

During this postseason, just 33 percent of Leonard’s baskets have been assisted, according to NBA Advanced Stats, while the other two-thirds have been self-created. Snapshots over time illustrate how that’s flipped almost entirely, as he’s become more of a 1-on-1 player. During the 2012-13 regular season, for instance, 65 percent of Kawhi’s makes were assisted. That share of assisted baskets dropped to 54 percent during 2014-15, and to just under 48 percent in 2016-17 before dwindling to just a third during these playoffs.

The question to raise here, of course, is whether it’s possible for Leonard to keep this up. He can’t keep shooting 70 percent from midrange when he was a 46-percent shooter from there during the regular season, right?

On some level, the answer to that may depend on whether the Sixers are willing to be more aggressive about forcing the ball out of Leonard’s hands. We’ve written before about what makes Leonard so different from the other stars in the NBA (aside from how mysteriously quiet he seems to be): He does just about everything at an above-average level, while defending and scoring better than almost anyone. But if there’s one area to test, it’s his playmaking, which generally pales in comparison to LeBron James’s or even Kevin Durant’s. (Both contemporaries regularly enjoy 2-to-1 assist-to-turnover ratios, while Leonard has yet to post such a season.) Leonard, who had five assists and seven turnovers Sunday, has closer to a 1-to-1 ratio this postseason, with 31 assists and 29 turnovers so far.

Going one level deeper, Kawhi was the NBA’s least efficient wing player5 this past regular season when opposing defenses either blitzed or trapped him in pick-and-rolls, with the Raptors scoring just 0.46 points per chance in such situations, according to data from Second Spectrum.

So while Philadelphia hasn’t been able to stop The Terminator-like Kawhi yet, the Sixers at least have something they can try in hopes of slowing him down as the series moves back to Toronto.

Which Numbers Will Help You Find The Kentucky Derby Winner?

It’s almost time for the 145th running of the Kentucky Derby, so even if you won’t be in the grandstand, throw on the most flamboyant ensemble in your armoire, grab your floppiest hat and make yourself a mint julep. Take part in the event that makes kings of horses and donkeys of humans.4

Unlike say, golf, in which the field is effectively always the safer bet than any particular player, favorites win about a third of the time on the horse track. But for years, Churchill Downs was the exception. The 20-horse field,5 the biggest faced by the 3-year-old thoroughbreds involved, has fueled unpredictability as contending horses have gotten lost in traffic. As a result, two decades went by without a favorite winning. But that trend has taken a 180-degree turn lately. Starting with Orb in 2013 and followed by California Chrome, American Pharoah, Nyquist, Always Dreaming and Justify, favorites have won six consecutive Kentucky Derby, a never-before-seen sequence that, frankly, is upsetting older scribes and proponents of the underdog. Depending on the sportsbook, had you placed a $1 bet on each respective winner since 2013, you’d have walked away from the Run for the Roses with a whopping $25, good for a few cups of burgoo.

This year’s favorite, Omaha Beach, was scratched because of an entrapped epiglottis, leaving the most wide-open field in recent memory. And while there have been sport-rattling upsets in the past decade and a half, like Mine That Bird in 2009 (50-1) and Giacomo in 2005 (50.3-1), the average winner since 2000 checked in at roughly 12-1 — even with those longshots included. But since there technically has to be a favorite, let’s focus on the five thoroughbreds — three of which are trained by Hall of Famer Bob Baffert — with morning-line odds shorter than 12-1: Game Winner (5-1), Improbable (6-1), Roadster (6-1), Maximum Security (10-1) and Tacitus (10-1).

Pre-Derby performance

Every winner since the turn of the century came to horse racing’s crucible on scorching hot streaks, if not outright victories. Since Animal Kingdom in 2011, every winner at Churchill Downs won its final prep race. Of the past 19 winners, only Giacomo and Mine That Bird, two horses tied for the second-biggest upset in the race’s history, failed to place either first or second in the race preceding the Kentucky Derby. A whopping 13 won their previous race.

Winners win at the Derby

How each Kentucky Derby winner did in its final prep race, 2000-18

Year Horse Race FINISH
2018 Justify Santa Anita Derby 1
2017 Always Dreaming Florida Derby 1
2016 Nyquist Florida Derby 1
2015 American Pharoah Arkansas Derby 1
2014 California Chrome Santa Anita Derby 1
2013 Orb Florida Derby 1
2012 I’ll Have Another Santa Anita Derby 1
2011 Animal Kingdom Spiral 1
2010 Super Saver Arkansas Derby 2
2009 Mine That Bird Sunland Derby 4
2008 Big Brown Florida Derby 1
2007 Street Sense Blue Grass Stakes 2
2006 Barbaro Florida Derby 1
2005 Giacomo Santa Anita Derby 4
2004 Smarty Jones Arkansas Derby 1
2003 Funny Cide Wood Memorial 2
2002 War Emblem Illinois Derby 1
2001 Monarchos* Wood Memorial 2
2000 Fusaichi Pegasus Wood Memorial 1

* Monarchos also ran the Florida Derby in 2001 and won

Source: Horse Racing Nation

Unsurprisingly, the favorites this time around are accomplished on the track, each having won at least 60 percent of his career starts. Each of the five favorites at least showed in its most recent outing. Maximum Security and Roadster are coming off consecutive wins.6

While not as long as the mammoth test in the Belmont Stakes, the Derby rewards stamina in ways few races can match. It’s critical, then, for a horse to showcase beforehand that it has the legs to survive the pace, which every year grinds challengers to dust before the final furlong. As Neil Greenberg of The Washington Post noted, the past 68 winners raced at the next-longest distance — 1⅛ miles — before attempting the 1¼ test at Churchill Downs. Each of this year’s top five contenders has gone that distance before.

The contenders can largely be distilled from four races: the Wood Memorial at New York’s Aqueduct Racetrack, the Florida Derby, the Arkansas Derby and Southern California’s Santa Anita Derby. Nearly three-quarters of Derby winners since 2000 have finished one of these four races in either first or second.

Lately, however, winners of the Wood Memorial, which was recently downgraded to a Grade 2 stakes race, have gone cold on horse racing’s biggest stage. Each of the past three winners7 has finished no better than ninth in Louisville, while no horse that even ran at Aqueduct’s crown jewel has gone on to win the Derby since the gelding Funny Cide in 2003.8 If that streak holds, this year’s Wood winner, Tacitus, is doomed — as is Wood runner-up Tax, who has also drawn some betting attention at 20-to-1.

Meanwhile, the winners of the Florida Derby and the Santa Anita Derby — which were claimed this spring by Maximum Security and Roadster, respectively — have dominated on the first Saturday in May, providing six of the past seven winners.

There are only 20 posts available at the Kentucky Derby. Those spots are now filled by fairly green thoroughbreds — largely because of a qualification change that first went into effect during the 2013 Derby, along with the ever-present injury risk that would negate the cartoonishly lucrative breeding opportunities for retired horses. Last year, for example, Justify became the first horse in 135 years to win the Derby without having raced as a 2-year-old. Upon dominating six events over a 112-day career, he promptly retired and was sold for $60 million. Many front-runners enter with no more than five races under their hooves.

Of this year’s top contenders, only Game Winner has more than five starts. Improbable enters with five, and Roadster, Maximum Security and Tacitus each enter with just four.

Speed ratings

More than a quarter-century ago, Andrew Beyer invented the Beyer Speed Figure, in what would later be recognized as a watershed moment for the horse racing industry. His metric takes into account a number of variables — including time, distance and track bias — to parse the speed of a thoroughbred.

And Beyer’s rating system has been awfully predictive at Churchill Downs.

Including Justify’s win last year, 25 of the 27 Derby winners since Beyer’s metric was introduced have clocked a speed rating of at least 95 before the Derby. All of the favorites this year have also done so.

Typically, horses find their stride in the leadup to the event, posting gaudy speed ratings before they hit Louisville. Game Winner enters having averaged a speed rating of 98.8 in his previous four races, which ranks fastest among this year’s entrants. Only three of the past six Derby winners averaged a faster time: Justify, American Pharoah and California Chrome, who all averaged triple digits in their races immediately preceding their Derby wins.

The need for speed

How the past six Kentucky Derby winners compare with this year’s field based on their speed ratings in the four races leading up to the Derby

speed ratings
Horse Most recent Race 2 Race 3 Race 4 Average
Justify (2018) 114 104 100 N/A 106.0
American Pharoah (2015) 102 99 99 103 100.8
California Chrome (2014) 106 102 94 101 100.8
Game Winner 97 98 103 97 98.8
Improbable 98 97 100 99 98.5
Nyquist (2016) 97 103 97 96 98.3
Maximum Security 102 100 96 94 98.0
Tax 101 102 103 84 97.5
Vekoma 101 92 101 96 97.5
Roadster 98 96 95 96 96.3
Win Win Win 97 92 101 95 96.3
Tacitus 103 95 85 93 94.0
Code of Honor 95 95 91 95 94.0
Orb (2013) 97 102 89 86 93.5
War of Will 89 96 94 94 93.3
Country House 92 95 93 91 92.8
Always Dreaming (2017) 102 84 89 96 92.8
Cutting Humor 99 84 94 93 92.5
Spinoff 102 93 89 82 91.5
Bodexpress 98 97 80 90 91.3
Long Range Toddy 83 97 91 92 90.8
By My Standards 102 90 80 83 88.8
Gray Magician 93 84 85 90 88.0
Plus Que Parfait 72 87 94 88 85.3

No speed ratings available for Japanese horse Master Fencer

Source: 365horses

The Run for the Roses will bring tens of thousands of horse racing fans to the eternal cathedral in Louisville. Nineteen 3-year-old colts will be guided past the twin spires in search of history in the greatest two minutes in sport. Three of them — Game Winner, Roadster and Improbable — are trained by Baffert, who is in search of his sixth win, which would tie Ben Jones for the most all-time wins at the Derby. With this weekend’s biggest star and a Hall of Fame jockey on the sidelines, and a track increasingly dominated by favorites, this could be his moment. It’s best not to bet against the guy with two Triple Crowns in the past four years.

From ABC News:
2019 Kentucky Derby preview

Biden Is Way Out In Front. Second Place Is Anyone’s Guess.

Last week, when he launched his presidential campaign, I made the case for why Joe Biden is the front-runner for the Democratic nomination. This week, with the release of several new polls, that case has become clearer.

Four national polls released on Tuesday all showed Biden’s support significantly higher than it was in previous editions of the same surveys. CNN’s poll found Biden at 39 percent — up 11 points from 28 percent in their previous poll in March — and well ahead of Bernie Sanders, who was at 15 percent. Quinnipiac University had Biden at a similar 38 percent, but with Elizabeth Warren nominally in second place at 12 percent of the vote, compared with 11 percent for Sanders and 10 percent for Pete Buttigieg.


Biden leading FiveThirtyEight's endorsement tracker


Morning Consult also released its weekly tracking poll, and it showed Biden at 36 percent, up from 30 percent last week — an impressive result, especially considering that about half the poll was conducted before Biden officially launched his campaign. In interviews conducted after Biden’s announcement, he was polling closer to 39 percent. A HarrisX poll for ScottRasmussen.com found the smallest bounce, with Biden at 33 percent, up from 29 percent in its poll last month.1 The Morning Consult and HarrisX polls still had Sanders fairly clearly in second place.

New national polls show Biden clearly in front

Democratic primary polls released on April 30, 2019

CNN HarrisX Morning Consult Quinnipiac
Candidate Latest Change Latest Change Latest Change Latest Change
Biden 39% +11 33% +4 36% +6 38% +9
Sanders 15 -4 16 -2 22 -2 11 -8
Warren 8 +1 6 +1 9 +2 12 +8
Buttigieg 7 +6 5 +2 8 -1 10 +6
Harris 5 -7 5 -1 7 -1 8 0
O’Rourke 6 -7 5 -1 5 -1 5 -7
Booker 2 0 3 -1 3 -1 2 0
Klobuchar 2 -1 1 -1 2 0 1 -1
Castro 1 +1 1 0 1 0 1 0
Yang 1 N/A 0 -1 2 0 1 +1
Gabbard 2 +2 1 +1 1 0 0 0
Gravel N/A 1 N/A N/A N/A
Gillibrand 1 0 1 0 1 0 0 0
Hickenlooper 0 0 2 +2 1 0 0 -1
Delaney 0 0 1 0 1 +1 0 0
Inslee 1 0 0 0 1 0 1 +1
Williamson 1 N/A 0 -1 N/A 0 0
Swalwell 1 N/A 1 N/A N/A 0 N/A
Ryan 0 N/A 0 N/A 1 0 0 N/A
Moulton 0 N/A 1 N/A 0 N/A 0 N/A
Messam 0 N/A 0 N/A N/A 0 N/A

Source: polls

On average between the four national polls, Biden has gained 8 percentage points. Where did he take that support from? It came from all over the place. Sanders is down 4 points, on average, as is Beto O’Rourke. Kamala Harris is down 2 points; Cory Booker and Amy Klobuchar are each down 1 point.

But some other Democrats have also gained ground. Warren is up 3 points, on average, in the new national polls. So is Buttigieg, although that’s a little misleading since the previous HarrisX, Quinnipiac and CNN polls were conducted before his surge had really kicked in. In the poll that offers the most recent basis for comparison, Morning Consult, Buttigieg is actually down 1 point from last week’s edition.

Biden’s support is driven by older Democrats and by nonwhite Democrats — two groups that aren’t always well-represented on social media or in other forums that sometimes dictate the conventional wisdom about the candidates. Biden had 50 percent of nonwhite voters in the CNN poll, well ahead of Sanders’s 14 percent. In Morning Consult’s poll, Biden polled at 43 percent among black Democrats, compared to Sanders’s 20 percent. Biden had 46 percent support from Democrats age 50-64 in CNN’s poll and 50 percent support from those 65 and older.

In addition to the various national polls, Suffolk University also released a poll of New Hampshire on Tuesday, and it can’t leave any of the Democratic contenders feeling especially satisfied. Biden was in first place at 20 percent, with Sanders and Buttigeg tied for second at 12 percent and Warren in fourth place at 8 percent. Suffolk has not previously polled New Hampshire this cycle, but compared with other recent polls of the state, this is clearly a poor result for Sanders, while it’s roughly in line with the previous polling for the other candidates.

The latest New Hamphire poll shows weakness for Sanders

Recent New Hampshire Democratic primary polls as of April 30, 2019

Latest Poll Earlier Polls in April
Candidate Suffolk UNH Saint Anselm Coll.
Biden 20% 18% 23%
Sanders 12 30 16
Buttigieg 12 15 11
Warren 8 5 9
Harris 6 4 7
O’Rourke 3 3 6
Booker 3 3 4
Klobuchar 1 2 2
Yang 1 2
Gabbard 1 1 1
Ryan 0 2
Gillibrand 0 1 1
Delaney 1 0 1
Messam 0 1
Swalwell 0 1
Hickenlooper 0 0 1
Castro 0 0
Bullock 0
Williamson 0 0
Inslee 0 0 0
Bennet 0
de Blasio 0
Moulton 0
Gravel 0

Source: POLLS

What should we make of all of this? I have roughly four conclusions:

Biden’s bounce will probably fade. Biden’s not the only candidate to have seen his numbers improve following his announcement; Sanders and Harris did too, and so, to a lesser extent, did O’Rourke. All of those candidates have since seen their numbers revert to their previous position, however. Sanders has fallen back to the low 20s in his better polls and the low-to-mid teens in his worse ones, and Harris and O’Rourke are now back to polling in the mid-to-high single digits.

And it’s not clear that much has changed in terms of voters’ underlying attitudes toward the candidates. Biden’s favorability ratings are strong in the Morning Consult poll, but they’re also largely unchanged from earlier editions of the poll, which suggests that some of his new support is fairly soft and consists of people who are suddenly hearing his name a lot more often in the news, and who might switch candidates again once the news cycle moves on.

Nonetheless, the bounce is sorta important. At least in the medium term — basically, from now through the Iowa caucuses — Biden is more likely to lose support than to gain it. Other candidates will become better known, and they will tend to take support from candidates such as Biden and Sanders who already have essentially universal name recognition. Biden is doing very well among black voters for now, but Harris and Booker might have something to say about that later in race. Biden benefits a lot from perceptions that he’s electable, but that could also fade over time as voters grow more comfortable with the rest of the field.

But it’s precisely for that reason that starting from a higher perch is important. If you’re polling at around 28 percent — where Biden was before his announcement — you don’t have much margin for error, given that it usually takes support in at least the low-to-mid 20s to win Iowa and New Hampshire. If you’re at 37 percent, however, you can lose 5 or 10 points and still hold up in the early states against a candidate making a late surge.

In addition, Biden’s bounce comes near an empirical inflection point of when early polling leads tend to hold up and when they don’t. Well-known candidates polling in the mid-30s in the early going2 are about even money to win the nomination, historically. Well-known candidates polling in the mid-to-high 20s have roughly a 1 in 4 shot, conversely.

In some ways, the bounce exposes the weakness of the other candidates — especially Sanders — as much as Biden’s strength. Although previous bounces, such as Harris’s, have faded, that doesn’t necessarily mean the candidates who were hurt by those bounces have regained ground. Instead, it has sometimes opened up an opportunity for yet another candidate to surge instead.

What that means is that it’s time to take stock of the three candidates who have clearly fallen from their peak (so far) in the polls — Sanders, Harris and O’Rourke. You might think that on the basis of his current polling, Sanders remains in a better spot than the other two. However, he’s also much more of a national brand name. And as I wrote last week — and as you can see from the chart — polling at 20 percent is not all that strong a position for a candidate with near-universal name recognition. Sanders, however, polled at just 16 percent in the average of the four national polls released on Tuesday. And he was at only 12 percent in New Hampshire, which should be one of his strongest states. Sanders can win — he’ll raise a lot of money, he came from way far back last time, and he’d likely benefit from scenarios where the field remains divided. But given his name recognition, those polling numbers put him right at the divide between someone whose campaign is going well and someone whose campaign is going poorly.

Harris and O’Rourke are not as widely known as Sanders, and they still have reasonably good favorability ratings and plenty of cash on hand, which suggest that they have upward potential if and when the media’s attention turns to them again. But it’s become harder to make the case that they’re on the lead lap with Biden, especially for O’Rourke, who is competing against a field that’s overstatured with white male candidates and whose polling has fallen further than Harris’s.

Buttigieg doesn’t have any reason to be unhappy; given his low name recognition, polling in the mid-to-high single digits — sometimes higher than that, especially in polls of Iowa and New Hampshire — is a pretty decent position. But if you were expecting a further immediate surge into the teens or beyond — and I sort of was — it isn’t as clear now whether that’s coming. Instead, Buttigieg will need to work to expand his support beyond his initial coalition of highly educated white voters and survive media coverage that’s both less plentiful and more skeptical than it was initially.

But Warren is in an intriguing position. Warren’s the candidate who we thought might have the least overlap with Biden and therefore would be least hurt by his entry into the race — and the polling seems to bear that out. Although both candidates are broadly within the Democratic mainstream, she’s toward the left half and he’s toward the moderate half. She’s a woman and he’s a man, obviously. His case rests heavily on electability and big, abstract, meat-and-potatoes themes; she appeals to voters on the basis of her highly detailed policy proposals. Her base is college-educated whites; his is non-college-educated white voters and black voters. Biden and Warren have directly clashed over issues such as bankruptcy laws.

In short, Biden and Warren make pretty good foils for one another, probably better foils than Biden and Sanders make, as both are old white men who aren’t especially well-liked by party activists. A showdown between Biden and Buttigieg, or Biden and O’Rourke, could also leave big segments of the party unhappy, including parts of the left and many women and nonwhite voters.3

So in the scenario where the nomination comes down to a battle between Biden and one other Democrat — not the only way the race could unfold, but one plausible path — Warren could turn out to be that Democrat. Together, they capture most of the major Democratic constituencies. I’m less convinced that you could have a Biden-versus-Sanders showdown. I think a lot of voters, and certain parts of the Democratic establishment, would go shopping for a third candidate in that eventuality.

But Warren could also become a major player in the race in other ways. Independently of Biden’s entry to the race, she seems to be gaining ground from the candidates who are fading, including gathering some of Sanders’s support on the left, some of O’Rourke’s college-educated whites, and perhaps some of Harris’s support among women.

With that in mind, it’s time for one more rendition of my not-to-be-taken-too-seriously presidential tiers. I’d already had Biden as the front-runner — note that doesn’t mean I think he has a better-than-50-percent chance to win (I don’t), just that I think he’s more likely to win than anyone else. But we probably need to create an additional half-step between Biden and everyone else. That means I’m demoting Harris, Sanders and Buttigieg from tier 1b (which we’ll leave empty for the moment) into tier 1c. However, I’m moving Warren up to tier 1c from tier 2. Harris, Sanders, Buttigieg and Warren can all make interesting arguments for why they’re the next-best-positioned candidate after Biden, and I really have no idea whose argument is best, so it makes sense to group them together.

Nate’s not-to-be-taken-too-seriously presidential tiers

For the Democratic nomination, as revised on April 30, 2019

Tier Sub-tier Candidates
1 a Biden
b [this row intentionally left blank]
c Harris ↓, Sanders ↓, Buttigieg ↓, Warren ↑
2 a O’Rourke
b Booker, Klobuchar, Abrams*
3 a Yang, Castro, Gillibrand, Inslee
b Hickenlooper, Bennet*, Ryan, Bullock*, Gabbard ↑

* Candidate is not yet officially running but is reasonably likely to do so.

Beyond that, O’Rourke, Klobuchar and Booker probably belong in the next tier down. But the safest conclusion right now is that this is a race with one frontrunner — Biden, who has both some clear weaknesses and some overlooked strengths — and no clear No. 2.


From ABC News:
Joe Biden on his 2020 run and Barack Obama


Check out all the polls we’ve been collecting ahead of the 2020 elections.

PJ Tucker Does More For The Rockets By Doing Less. A Lot Less.

Creative shot makers and flashy passers are the easiest players to appreciate as fans. Less obvious are the role players who contribute to winning even when they don’t have the ball — and few such role players have had a bigger impact than Houston’s PJ Tucker.

There isn’t a formal definition for what constitutes a role player, but role players do have some defining characteristics. For instance, think of the relationship between a player’s minutes per game and his usage rate, which is the share of a team’s plays used by a player while he is on the court. Star players — your LeBron Jameses and Steph Currys of the league — log heavy minutes and have high usage rates. Role players may also log heavy minutes but tend to be comparatively less involved on offense.

Below is a scatter chart that shows the relationship between usage rate and minutes played per game. The relationship is flat for players who see fewer than 20 minutes per game, but there is a strong, positive relationship among starter- and rotation-level players. After all, if you weren’t producing on the offensive end, you wouldn’t be worth playing for long stretches of time. Unless you’re Tucker.

No one in the NBA this season logged more minutes while doing less on offense. Tucker is the first player since Shane Battier in 2008-09 to post a usage rate of less than 10 percent while also playing at least 30 minutes a game. In Game 1 of the Rockets’ series against Golden State, the Rockets were +9 in net points with Tucker on the court even though he scored no points and took only four shots while logging 39 minutes — the same time spent on the floor as James Harden.

Tucker ranks near the bottom in passes made per game and touches per game, and on average he had the ball in his hand for the shortest amount of time per possession of anyone who played at least 30 minutes per game this season. On offense, Tucker’s role is to stand in the corner and wait for a teammate to pass him the ball so that he can shoot an open three, which is the point of Houston’s spread-out, isolation-heavy offense.

So why can Tucker stay on the court for as long he does without doing much on offense? Two reasons.

First, Harden had the highest usage rate in the NBA during the regular season, and Harden and Tucker are on the court together more than any other two-man combination for the Rockets.3 Since usage rate is a zero-sum game among the five players on the floor, any increase in Tucker’s usage would come at the expense of Harden’s.

Second, Tucker’s defense is vital to the Rockets. While he might not be widely known as an elite defensive stopper, he has the profile of one. Five of the seven players he guarded most often during the regular season were Paul George, LeBron James, Kevin Durant, Kawhi Leonard and Giannis Antetokounmpo. Nobody matches up with those guys that often unless he’s built for it.

Only nine players since the 1977-78 season have played at least 30 minutes a game while using less than 10 percent of their teams’ plays. The list is a who’s who of the best defensive specialists in NBA history, including Dennis Rodman, Ben Wallace, Mark Eaton, Bruce Bowen and the aforementioned Battier. Most of those guys went on to win defensive player of the year, earn All-NBA honors or play a critical role on a championship team. Meanwhile, Tucker has never made so much as an All-Defensive team.

Even though the casual fan might not recognize Tucker for his defensive prowess, his peers do. Earlier this year, DeMar DeRozan praised Tucker’s defensive intensity. “PJ is one of the most intense individual defenders on the defensive end,” he told The Athletic. “I don’t think he gets enough credit for it.”

The good news for Tucker is that he has the chance to raise his profile during the Rockets’ second-round matchup against the Warriors. The bad news is that he has to prove his mettle by trying to guard Durant.

During the regular season, Tucker matched up with Durant on 111 possessions and held him to shooting 48 percent from the field, a tick below Durant’s 52 percent season average. Durant scored 35 points during the Warriors’ Game 1 victory on Sunday, though only 13 of those points were scored while Tucker was guarding him. In reality, the only person that can stop Durant is Durant. But as long as Tucker doesn’t allow him to shoot over 60 percent from the field like he did when he was guarded by Patrick Beverley during the Warriors’ first-round series, the Rockets will have a chance to pull off the upset.

Check out our latest NBA predictions.