Of all the strategic elements of baseball, few are more fascinating than the poker game between pitcher and hitter. Each participant knows his strengths and those of his adversary, and that knowledge informs both players’ tactics in a complex entanglement of actions and counteractions.If the best pitch in a hurler’s repertoire is his fastball, for instance, he might be inclined to use it really frequently. But batters will pick up on that proclivity, and in time, the fastball will lose its effectiveness if it’s not balanced against, say, a change-up — even if the fastball is a far better pitch on paper.Eventually, we would expect this pitcher’s arsenal to settle into the optimal mix for retiring opposing hitters: a mix of fastballs and change-ups that’s impossible for a batter to exploit.1Hitters nudge a pitcher toward a better mix every time they correctly guess which pitch is coming. In game theory terms (and assuming the batter adapts accordingly), this is a version of the famous Nash equilibrium, which describes a situation in which neither party in a game has anything to gain by changing his or her strategy.That’s all, well, theory. But how can we detect which real-life pitchers are closest to their equilibria? One idea is to look for hurlers whose effectiveness is relatively equal on every kind of pitch he throws. And fortunately, Fangraphs tracks not only the frequency with which each pitch type is employed, but also its potency, estimated in terms of runs added or subtracted per 100 pitches. Using that data to find out how balanced a pitcher’s performance is across his entire repertoire, I computed a metric that I’m dubbing the “Nash Score.”Here’s how it works: Start by measuring for each pitch type the difference2Squared difference, to be exact. between its effectiveness and that of all the pitcher’s other pitches combined. Then weight those differences according to the frequency with which each pitch is thrown. The resulting average is the Nash Score, a sort of variance that measures whether a pitcher is close to his equilibrium (lower score) or could conceivably benefit from varying the distribution of his pitches (higher score).Take R.A. Dickey as an example. The Blue Jays starter, known for his mesmerizing knuckleball, throws the pitch 87 percent of the time — about as much as any pitcher in baseball uses his No. 1 pitch. Yet Dickey’s Nash Score isn’t especially low, so under the concept of equilibria outlined above, he should be using the knuckler even more. Dickey’s fastball — his No. 2 (and essentially only other3Dickey uses a third pitch, the change-up, only 2 percent of the time. pitch) — is far less effective than his knuckler, even in its limited use as a complementary, change-of-pace pitch. According to game theory, Dickey could conceivably boost his overall effectiveness by throwing the knuckleball on an even greater proportion of his pitches.Going beyond Dickey, here are the (qualifying4Minimum 5,000 weighted pitches, or about 830 pitches per season.) pitchers with the most and least optimal mixtures of pitches over the past three seasons,5Weighted for recency according to Marcel’s values — namely, a weight of three for 2015, two for 2014 and one for 2013. at least according to this method:In the chart, a pitch type’s “relative value” is its run value (per 100 pitches) compared to that of all the pitcher’s other pitches combined. So this method surmises that Tanner Roark of the Washington Nationals is closer to operating at equilibrium than any other pitcher6At least among pitchers in our 2013-15 sample. because his two most frequent pitches (fastball and slider) are each barely more effective than the rest of his repertoire and his third choice (change-up) is barely less effective. Based on our game theory of pitch selection, it stands to reason that Roark wouldn’t get much of a performance boost by altering his frequencies.But is this actually true? Roark was very good in 2013 (mostly out of the bullpen) with what this system considers a less-optimal mix of pitches than he has now. He was merely solid last year (as a starter) even though his pitch frequencies were far closer to the theoretical equilibrium. And he has been pretty dismal in 2015 (mostly back in the ’pen) despite maintaining a supposedly optimal pitch mix. Therein lies one problem with this methodology: Pitcher performance is notoriously unstable in small samples — and small samples are all we have when trying to zero in on the equilibrium frequencies for a pitcher’s current repertoire.The year-to-year correlation of a pitcher’s Nash Score, for instance, is essentially zero. Optimally mixing pitches one season is no guarantee of doing it the next, in part because per-pitch performance measures are themselves fickle, but also because the batter-pitcher chess match is in a state of constant flux. Furthermore, there’s little relationship between how good a pitcher is7On a runs-saved-per-pitch basis. and how well he optimizes his repertoire. The Miami Marlins’ Jose Fernandez is one of the best pitchers on Earth, yet this method says he’s still drastically overusing his fastball and underusing his breaking pitches.Then again, Fernandez might also be illustrative of how a pitcher can evolve toward his equilibrium. His fastball, despite good scouting assessments and improved velocity, has been average at best (in terms of run-prevention) since the 2014 season.8He was injured during the 2014 season, only returning from Tommy John surgery last month. Meanwhile, his slider has always been nothing short of brilliant on a per-pitch basis. Perhaps it’s no coincidence, then, that since his debut in 2013, Fernandez has gradually thrown fewer fastballs and more sliders.Moreover, for the entire population of pitchers I looked at, a one-standard-deviation increase in optimality9That is, a one-standard-deviation reduction in Nash Score. results in an earned run average about a quarter of a standard deviation10Or about a fifth of a run per nine innings. lower. It’s not a huge effect (it only amounts to a handful of runs per season), but it does suggest that a pitcher can reap some benefit from trying to find an equilibrium that evens out every pitch’s effectiveness.Baseball players have always known the value of mixing up pitches to disrupt a hitter’s rhythm. As Hall of Fame pitcher Warren Spahn once said: “Hitting is timing — pitching is upsetting timing.” Now, though, sabermetric tools can help quantify the blend of pitch types to best do so — that is, until the batters adapt and the cycle starts all over again. read more

Photo by Getty Images.Nine months after tearing the medial collateral ligament in his left knee, Derrick Rose returned to the basketball floor at the United Center in Chicago over the weekend. And the Chicago Bulls fans warmly embraced him.Playing with Team USA in a blowout win over Brazil, Rose performed on the court where he was injured for the first time since Nov. 22. And the reception he received was heart-warming, he said.“I’ve been preparing for this for a long time,” Rose said. “Probably, if this was a couple weeks ago, I wouldn’t have been emotional, but right now it feels great. We won the game so that’s the only thing I could be happy about — we won. We didn’t lose. If we had lost my whole attitude would have been different. Just take this win, go to New York  and just try to keep this going.”Team USA headed to New York this week to continue training for the World Cup.Rose scored seven points in 24 minutes in his Chicago return Saturday, but the fact that he was out there at all after playing just 10 games in the past two years because of two serious knee injuries is what made fans so happy. Rose was the last player introduced before the game as fans roared and chanted “MVP!”“I’m playing the way I normally play in the trials,” Rose said. “Push the ball, play defense and get guys shots. When the shot is available, take the shot, and I think that’s what I did tonight. I had one or two turnovers, but that could easily be changed.”“It’s great to watch Derrick play again,” Bulls coach and Team USA assistant Tom Thibodeau said. “I couldn’t be more pleased with the way he played.” read more

NOTHING abt that mans demeanor said he’d kill himself, ESPECIALLY after he just beat the case & was goin try to get an appeal… FOH— Wild Wild Seth (@SpikeReeds) April 19, 2017 Either Aaron Hernandez was guilty & the guilt ate him alive resulting in suicide, or someone killed him based on the not guilty verdict.— Chad Williams Sr. (@CHADWILLIAMSSR) April 19, 2017 Of course I don’t believe #AaronHernandez committed suicide. The man was killed ??‍♀️.— kid Griffin (@BirdCat21) April 20, 2017 Aaron Hernandez helped lead the New England Patriots to Super Bowl XLVI. (Pat Greenhouse/The Boston Globe via Getty Images)Aaron Hernandez’s lawyer doesn’t believe the former New England Patriots tight end took his own life and has vowed to launch an investigation.Jose Baez believes fellow inmates or prison staff murdered Hernandez and the athlete’s “devastated” family doesn’t believe he wanted to kill himself, TMZ reported. Baez released a statement hours after authorities announced Hernandez died of an apparent suicide Wednesday, April 20 saying the family and his client’s representatives were “shocked and surprised at the news of Aaron’s death,” according to USA Today.“There were no conversations or correspondence from Aaron to his family or legal team that would have indicated anything like this was possible,” Baez’s statement said. “Aaron was looking forward to an opportunity for a second chance to prove his innocence. Those who love and care about him are heartbroken and determined to find the truth surrounding his untimely death. We request that authorities conduct a transparent and thorough investigation.”Hernandez was acquitted Friday of the 2012 double murder of Daniel de Abreu and Safiro Furtado. He had been serving a life sentence without parole for the 2013 shooting of Odin Lloyd, which CBS Boston reported would be appealed with Baez’s counsel.An investigation is ongoing at the Shirley, Mass., Souza-Baranowski Correctional Center where Hernandez was discovered hanged from bed sheets. Spokesman Christopher Fallon told the Associated Press there was no reason to believe Hernandez was suicidal and he would have been transferred to a mental health unit if he were.When Hernandez’s body was discovered, guards reportedly found “John 3:16” written on his forehead and on the in red marker. Sources told Fox 25 a Bible was flipped open to the verse, which reads, “For God so loved the world that he gave his only Son, that whoever believes in Him shall not perish but have eternal life.”Investigators also believe Hernandez possibly smoked synthetic marijuana Tuesday night before his death, according to CBS Boston.“I just think it got to him — the guilt,” Mixson Philip, a family friend of LLoyd’s told the AP. “Each man has to live with himself. You can put on an act like nothing happened, but you’ve got a soul. You’ve got a heart.”Hernandez’s former agent, Brian Murphy voiced suspicion about the circumstances of the star footballer’s death.Absolutely no chance he took his own life. Chico was not a saint, but my family and I loved him and he would never take his own life.— Brian Murphy (@A1Murph) April 19, 2017Others also questioned Hernandez’s alleged suicide.One day, got off a double murder charge.Next day, found dead. 100% guarantee that Aaron Hernandez did not commit suicide.— T T (@TajTaylor_) April 19, 2017 #AaronHernandez was murdered on suicide watch. FIRE THE STAFF!FED. INVEST. NEEDED ASAP! @RookwoodAmbrose @scoobysnahx @330Kingish #coverup pic.twitter.com/k3LF4ZB0rS— DeShaunneLoveHoliday (@Deshaunnea) April 20, 2017 read more

From left, Caiti Donovan, executive director of SheIS; Brenda Andress, commissioner of Canadian Women’s Hockey League; Lisa Borders, President of WNBA; Stacey Allaster, Chief Executive for the US Tennis Association and Dr. Jen Welter, first female NFL coach, all meet to speak with sponsors, investors and other commissioners of leagues in New York. (AP Photo/Doug Feinberg)NEW YORK (AP) — Women’s sports leagues are banding together with a new initiative, SheIS.Eight leagues, including the WNBA, U.S. Tennis Association, Women’s Pro Fastpitch League and Canadian Women’s Hockey, will try to help each other increase resources, viewership and attendance.“Each commissioner has agreed to come to one and another’s events,” WNBA President Lisa Borders told The Associated Press. “Women have to support women before you ask other people to support you. I’ll buy a ticket to a hockey game in Canada or a fast-pitch softball game.”All the league commissioners signed a pledge and filmed a public service announcement promoting the effort. Those ads will start rolling out Tuesday.“It’s a social media campaign for now but will grow,” Borders added. “This is only tier one.”The initiative was the brainchild of Brenda Andress, commissioner of the Canadian Women’s Hockey League, who came up with the idea last November.“This collective sports voice has never been heard. I wanted to create some type of program or challenge to bring women together that was born out of positivity,” Andress said. “So I thought of SheIS. When I thought of myself, she is a grandmother with young kids. She is a commissioner. She is a hockey player. She is anything she wants to be. That’s where SheIS came from.”Andress reached out to Borders and USTA chief executive Stacey Allaster, who quickly jumped on board.“Right off the bat, they were so supportive,” Andress said. “We have to do it together. Let’s do it, but let’s do it right. It’s going to be professional, top notch. It’s about us as females recognizing we can bring the fans not just to hockey, but to the WNBA. Tennis needs more eyes on the TV. It’s not about everyone else making the difference for us, but us making the difference for ourselves.”There has been much discussion over the years about the wage gap in sports between the sexes. Tennis is one of the few sports where the women have some parity — all four Grand Slam events pay both sexes equally.“I think the secret sauce for women’s tennis started with our athletes,” Allaster said. “It took their advocacy and courage to stand up to the establishment much like soccer players and female hockey players have. It was Billie Jean King and the ‘Original 9′ saying they’d do this back in the 1970s. The athletes have the power and SheIS is a great time to energize our athletes.”The SheIS group can point to a Seattle group already using the multisport format. Force 10 Sports Management owns and operates the WNBA’S Seattle Storm. The group also runs the Seattle Reign of the National Women’s Soccer League and the Seawolves of Major League Rugby. There is cross-promotion among the sports.“Seattle is absolutely the model,” Borders said. “They were doing that before SheIS is born.”The city has embraced female athletes such as Sue Bird, Megan Rapinoe and Breanna Stewart.Before the launch Tuesday, members of the founding committee, league commissioners and prominent figures from across sports gathered at the WNBA office in New York to sign the SheIS pledge.“The heroes who run, walk and play among us make up 51 percent of the global population, yet have little to no visibility in the sports world,” said Dr. Jen Welter, who was the first female coach in the NFL.“SheIS will give the first true platform for these real-world, real-women heroes who have been living among us. With that comes the opportunity to be much more visible and for female athletes and their supporters to join forces in a really positive way. I love that this bubbling movement is coming from the sports industry, because sports has the ability to change the world.”The other leagues that already joined are Women’s Pro Lacrosse, Canada Basketball, Rugby Canada and the National Women’s Hockey League. Andress expects other sports like soccer, gymnastics, swimming, cycling and running to join soon, too. Through the initiative, the leagues also aim to help increase young girls’ participation in sports.“Women for so long have been competitive no matter what they do in life,” WNBA player Chiney Ogwumike said. “We are even more powerful when we are collaborative. In public, we have to support each other.”The initiative also has support from the WWE. Stephanie McMahon, the chief brand officer of the company, signed the pledge .“We need to encourage audiences to watch and attend games and live events, and young girls to stay in sports,” she said. “Girls need to see themselves across sports, entertainment and business, and it’s going to take all of us to show the world that SheIS anything she wants to be.”___ read more

With the elimination of the Montreal Canadiens from the playoffs last week, Canada will extend its streak to 20 NHL seasons without a Stanley Cup. But Canadian hockey fans might have a mild rooting interest in the outcome of the Stanley Cup Final in favor of the New York Rangers. If the Los Angeles Kings win, it would move the Stanley Cup Center of Gravity further in the direction of the United States.What the H-E-double-hockey-sticks is the Stanley Cup Center of Gravity? It’s a concept we came up with, which is calculated by averaging the geographic location of all Stanley Cup winners. (There’s some room for debate about which team qualifies as the first champion, but we date the series back to 1915 and the Vancouver Millionaires.)After 1968, for example — the first Stanley Cup contested during the NHL’s expansion era — the Stanley Cup Center of Gravity was in southern Ontario, a little to the northwest of Toronto. It steadily moved eastward through 1983, with teams such as the Canadiens, the Boston Bruins and the New York Islanders winning the Stanley Cup consistently. At one point, it breached the shores of Lake Ontario.The rest of the 1980s saw a sharp shift in a west-northwest direction, as the Edmonton Oilers won five Stanley Cups and the Calgary Flames added another. As of 1990, the Stanley Cup Center of Gravity was somewhere near Owen Sound, Ontario.The long streak of U.S.-based winners has since moved the Center of Gravity to the south-southeast. It crossed into Lake Huron a few years ago. And, after the Kings won their first Stanley Cup in 2012, it shifted to the American side of the maritime border. U.S.A.!A Rangers win would move the Center of Gravity eastward toward Ontario — not enough to bring it back into Canadian waters, but it would be close. By comparison, another Kings win would shift it to the south and west, putting it on the U.S. mainland for the first time in many decades — near Sandusky, Michigan.P.S. Ever hear the one about the statistician who drowned crossing a river that was 3 feet deep, on average? read more

While the wild-card round of this year’s NFL playoffs was wild, a lot of the action followed familiar scripts: Skeptical Football regular Andrew Luck continued to impress in the Indianapolis Colts’ win against the Cincinnati Bengals. The Detroit Lions jumped out to a big lead — uncomfortable territory for gunslinger extraordinaire Matthew Stafford — against the Dallas Cowboys and, sure enough, Tony Manning Romo successfully engineered a double-digit comeback victory — though possibly with a little help from the officials. The Carolina Panthers brought their record back to (exactly) .500 for the first time since October against the Carson Palmer-less Arizona Cardinals. And the Baltimore Ravens beat high-flying Ben Roethlisberger and the Pittsburgh Steelers, on the road.But while the wild-card games were a nice diversion, the big guns will only come out after the bye.This weekend will see the playoff debuts of last year’s Super Bowl participants, the Peyton Manning-led Denver Broncos and the potentially historic Seattle Seahawks, along with the ever-contending New England Patriots and the Green Bay Packers’ enigmatic Aaron Rodgers.1As we know, a New England vs. Green Bay Super Bowl matchup is inevitable.At this stage of the playoffs, there are an equal number of bye teams and wild-card game alums. Not only are the bye teams better-rested and more accomplished, but they have home-field advantage — both this week and against any surviving non-bye teams in the conference championships. So our eventual Super Bowl winner will almost certainly come from that cohort, right?If recent history is a guide, the answer is no. The wild-card veterans have more than held their own, winning seven of the past 14 Super Bowl trophies.Consider what this takes: First, having just won a game for the right to make the final eight, a team has to turn around and play a fresh top-two seed in the divisional round — on the road. And if it wins that game, more often than not it has to play the other top seed — on the road. And if it wins again, more often than not it has to play one of the other conference’s top seeds in the Super Bowl.Compare that to the route a bye team takes: It plays only two playoff games before the Super Bowl, and at least one of them is at home, against a lower seed.While anyone with a rooting interest would prefer his team take the easier road, teams that do manage to survive the playoffs’ “trial by fire” are disproportionately successful the deeper into the postseason they get.This chart goes back to the introduction of the salary cap in 1994. Prior to the 1997 John Elway-led Broncos victory, few teams survived the trial by fire (“TBF”) for long (i.e., none made the Super Bowl), so I typically consider that the start of the TBF era.As we would expect, a large share of TBF teams (meaning wild-card round veterans) are eliminated by their higher-seeded opponents right away. Over the entire period, TBFers won just 24 of 80 divisional round games (30.0 percent). And in the TBF era, including 1997, they’ve done only slightly better, winning 21 of 64 games (32.8 percent).But if they survive that second game, all bets are off. Since 1997, of those 21 TBF teams who made it to the conference championship games, 17 faced a top-two-seeded bye team on the road (the other four faced each other). The TBF teams in that scenario won 9 of the 17 games (52.9 percent) they played.2I should also note that the overall 45 percent win rate in this round in the salary cap era is still extremely high for road teams against higher-seeded competition. That’s right, TBFers who made the conference round have won a majority of their games against bye teams, despite playing in hostile territory.Those nine all faced another top-two seed from the other conference in the Super Bowl — such as the New York Giants against the then 18-0 New England Patriots in 2007 — and seven of nine triumphed. Overall, TBF teams have an 8-3 record in Super Bowls (in the salary cap era), including a 6-1 record in their last seven appearances.That one losing team was the Arizona Cardinals,3One of the TBF teams that had to beat another TBF team in its conference championship rather than beating both top seeds. who lost 27-23 against the Pittsburgh Steelers in 2009, but covered the 6.5-point spread. TBF teams have gone 10-0-1 against the spread in Super Bowls, and 11-6 in conference championships since 1997.That stunning 21-6-1 record against the line is meaningful even if you’re not a sports bettor. It means that this phenomenon isn’t just an artifact of stronger teams happening to be lower seeds for incidental reasons. TBFers legitimately exceeded expectations — even market expectations.It also makes it fairly unlikely that the phenomenon is purely a result of chance. The probability of going 21-6 on what should be a 50/50 proposition is roughly 0.002, or about 1 in 500.Of course, 1-in-500 events happen all the time, so it could just be that these teams have gotten lucky. But the probability that an unlikely phenomenon results from something other than chance is proportional to how plausible the other explanations are. If a coin comes up tails on 21 of 27 flips, you say “wow,” but the coin is still unlikely to be weighted. But say a tennis player wins 21 of 27 matches — she could have gotten lucky, but a more likely explanation is that she’s good.And in this case — while perhaps not accounting for all the good fortune TBF teams have seen — there are plenty of reasons to expect the TBF phenomenon to exist and persist.4Though I would expect the market to adjust accordingly.The first reason — at which I’ve already strongly hinted — is that, by virtue of the tougher road that TBF teams face to get deeper into the playoffs, their continued presence tells us more about their quality than that of their bye-having opponents.At the very minimum, the team that wins the wild-card round has one more win going into later rounds than its regular-season record. In some cases, this is enough to cover or exceed any gap between it and a higher-seeded team. Such is the case with this year’s Cowboys, who, at 13-4, now possess the best record in football (though they will still be on the road against the Packers). Moreover, that extra win didn’t come against an average NFL team, it came against a playoff team, meaning it’s probably worth a little more than an average win.With each road win against top competition, a TBF team’s pedigree gets stronger and stronger. A lot of teams win a lot of games without ever getting road wins against top teams.Obviously upsets happen, and they don’t always mean that the upsetting team is a secret powerhouse. But such upsets are much more likely to happen if the upsetting team is actually better than previously thought (such as when it’s actually much better than its record or playoff seed would indicate). So as a matter of Bayesian inference, it’s not so shocking that teams that accomplish one seemingly unlikely result may continue to accomplish more.In subsequent rounds, a TBF team’s opposition has also won playoff games, but against weaker opponents and usually at home. Since these are more expected results, they have much less of an impact on our assessment of those teams.As a test case, if the playoffs were seeded completely randomly, we would expect to see this effect: A team that had won three road games would be a favorite over one that had won two home games, simply because winning on the road is harder.And the real case can be much more drastic: By the time we get to the Super Bowl, we may have a TBF team — which got there by winning three road games against the top three teams in its conference — facing off against a bye team that has won only two playoff games, at home, against teams with worse records.The problem with that explanation is that it only gets us so far. With an entire season of games under their belts, the difference between a big underdog and a big favorite shouldn’t be reversible merely as a result of three strong wins versus two mediocre wins.Unless those wins come in games that are substantially more important to our assessment of those teams than normal games.5For a somewhat extreme example: This is what things would be like if team quality in the NFL behaved like a ladder ranking, where each time a team beats a team of higher quality, it assumes the other’s position. Under such circumstances, a team like the 2011 New York Giants would have been a favorite against the 2011 New England Patriots by virtue of having beaten the 15-1 Green Bay Packers in the NFC divisional round. Playoff wins seem to be just that.Normally I’m somewhat skeptical of taking whether a team is “hot” or not too seriously. In regular-season contexts, recent performance is typically not much more predictive of future performance than past performance is. But the NFL playoffs appear to be an exception. That the results of playoff games are more indicative of a team’s quality makes sense. It’s easy to speculate on any number of reasons:Playoff rosters are more current, reflecting injuries, trades and the like.Playoff results are unlikely to be affected by the various late-season tactical strategies that teams employ, whether that be “tanking” to get a top draft pick, resting starters to avoid injury and fatigue, etc.Although I reserve my right to skepticism, it’s possible that playoff football actually does have a different nature than regular-season football — whether because playing strong teams entails a different skill set than beating up on scrubs, or because playoff games are more likely to be played in cold weather, or something else.There’s a phenomenon that I think is real by which teams often “save” something for the playoffs or more high-leverage situations in the regular season — such as innovative or “trick” plays.Using a couple of different regression methods to estimate the value of a playoff win relative to a regular-season one, I’ve come up with figures as high as one playoff game being worth three to five regular-season games.6This can be somewhat reproduced by using an Elo system with a very high k (meaning calibrated to adjust very rapidly). But this whole line of analysis is tainted because it’s ex post facto. That is, we already knew there was some effect, because that effect is the reason we’re looking into it. So measuring its strength kind of begs the question.We could just modestly assume a mid-sized multiplier (like each playoff game being worth two to three regular-season games), but before we start artfully reflecting on our priors, it would be nice to have a little more insight into the nature of what’s going on.The league only adopted the 12-team, four-bye playoff structure in 1990, and introduced the salary cap in 1994. The “trial by fire” phenomenon begins to appear in earnest shortly after that, yielding its first Super Bowl contender in 1997, and has seemed to get even stronger in recent years with TBF teams actually winning six of the last nine Super Bowls. The emergence of this effect has coincided with the supposed era of “parity” in the NFL — so it’s tempting to think that it may just result from lower-seeded teams getting stronger. Here’s a comparison of how the winning percentage of TBF teams versus bye teams in each round has changed over time, as well as the winning percentages of TBF teams versus bye teams in the regular season:The difference between a TBF team and a typical bye team in the regular season hasn’t changed much, with bye teams having won those matchups around 70 percent of the time. That seems high, but it’s partly because the bye teams have better records and/or hold head-to-head tiebreakers to get in their position. The key isn’t the raw value, it’s that the trend has remained essentially flat. In other words, “parity” — the bogeyman often used to explain a variety of NFL phenomena — probably isn’t the answer.From the other panes, we can see that the percentage of TBF teams winning in subsequent rounds has risen sharply in each case. Considering the sample sizes, those trends certainly shouldn’t be considered too probative individually, but the consistency between them supports the idea that the importance of playoff games has been on the rise.7We would also expect it to rise more sharply in later stages is because the effect is compounding.Is it reasonable to think that this reflects a real development in the game?I think so. At least anecdotally, I think teams have been getting more strategic about playing for the playoffs, and treating the regular season as more of a qualifying period than an end in its own right. Not only have we seen a lot of resting of players (where QBs like Brett Favre used to take every snap to the bitter end) and tanking, but we’ve also seen things like experimenting with young quarterbacks, and benching reasonably decent ones as a scapegoating maneuver.Also, football has evolved into more of a passing or finesse/strategy game, which may be contributing to teams sometimes being substantially better or worse at different times in the season (for example, if you figure out how to use a previously unheralded third receiver in a particularly effective way, it may transform your offense overnight). And this may make matchups more important as well. When the balance of power between teams rests on intricate relationships of many variables rather than just size and strength, it’s easy to see how matchup problems might hinder a team’s regular-season outcomes, or bolster its playoff ones — depending on whom it faces.But I’m not sure any of this gets us 100 percent of the way there. In fact, virtually nothing explains the status quo over the last 14 years (much less the past nine), wherein divisional road teams have been winning as many (or more) Super Bowls as their home opponents.That is, to some extent, just freaky-deaky. Let me demonstrate by imagining an absurd case: Say there were one single best team in the playoffs, and that team won every game it played, and thus won the Super Bowl 100 percent of the time — and then assume playoff seeding were completely random. Since twice as many teams play in the wild-card round as those that get byes, the Super Bowl winner would end up being a TBFer two-thirds of the time. Thus, under the most absurdly extreme case imaginable, we would still expect the “trial by fire” to produce a champion at the same rate that the real-world trial by fire has over the past nine years.That absurd case is so crazy that it’s very unlikely that the TBF trend will continue as vigorously as it has in recent years. But I wouldn’t expect the phenomenon to go away, either. I expect that teams that win against strong opponents in a playoff environment will continue to be extremely dangerous, regardless of appearances.Sizing up the wild-card winnersOne thing we can do practically and theoretically is to consider what types of teams are most likely to exhibit the TBF power-up effect. So let’s take a gander at this year’s winners in the wild-card round.Dallas and Indianapolis are two division-winners who won in the wild-card round against fairly strong teams (the 11-5 Detroit Lions and 10-5-1 Cincinnati Bengals, respectively), and who weren’t that far behind their rivals to begin with. Counting the playoffs, Indianapolis now has the same number of wins as the Denver Broncos and New England Patriots, and as of this moment Dallas has the best record in football (at 13-4). Both the Cowboys and the Colts face tough road games against the Packers at Lambeau and the Mannings in Denver. That makes it less likely that they’ll be picking up the TBF banner — unless they win. The difficulty of these games would make victories in them even more meaningful.The Baltimore Ravens had probably the most impressive win in the bye round against the Pittsburgh Steelers. They also have experience winning championships “the hard way” twice. And they’re playing the Patriots, who have been vulnerable to TBFers before. Since winning their last championship in 2004, the Patriots are only 5-4 against TBF teams as a bye team themselves, most notably losing to the Giants in the 2007 and 2011 Super Bowls, and to the eventual-champion Ravens in the 2012 AFC championship game.Of course, the most fun TBF case would be if the Carolina Panthers somehow kept winning. But at the moment, they haven’t accomplished much. In addition to their awful regular-season record, it’s not clear that beating the Arizona Cardinals without Carson Palmer on the field meant much (the Cards ended up 0-3 with Ryan Lindley starting this year). But if the Panthers somehow pull off a win against the powerhouse Seattle Seahawks this week, watch out!Charts by Reuben Fischer-Baum. read more

For the past three seasons, high-speed player-tracking cameras have been logging every possession of every NBA game; over that same time, NBA.com has hosted some cool observational stuff — like how far players run in a game, how often they drive the lane or spot up and, most important, how often they are passed the basketball. Now, ESPN has gotten its hands on advanced tools to analyze the game’s nuances, stats that can measure things like how difficult a given shot was or how often a given defender is torched off the dribble. We’ll be using them throughout the playoffs, but I figured we may as well slap a few of them on some charts to establish a baseline (and, hopefully, to confirm a few petty biases along the way).On our maiden voyage, we’ll take a look at which players make shots they have no business making and which miss the ones they have just as little business missing. For all these charts, we’re looking at players who logged at least 300 minutes across at least 20 games — rotation players in a quarter of the season, basically. You’ll also notice that we’re using effective field goal percentage (which weights 3-point attempts more than 2-point attempts), not true shooting percentage (which does the same but also factors in any free throws a player shoots), so we’re losing the effect of getting fouled, which is a big deal! But given the relative infancy of these stats, this is what we have. If you must, keep a running tally in your head of which players put themselves in position to really need to pile up foul shots to boost their efficiency and then go check where they stand afterward. Here’s a head start: In 2014-15, Russell Westbrook had a free throw rate of .445 (meaning he took .445 free throws for every field goal attempt); in 2013-14, Kevin Durant’s was .477; this season, Kobe Bryant had a free throw rate of .252 — the lowest of his career. Anyway, to the charts.First up, we have shot difficulty versus shots per game over the past three seasons. We explained quantified shot quality (qSQ) at some length here, but simply put, it uses the NBA’s SportVU data to measure how tough a shot was by calculating where the shot came from, where defenders were positioned and how the rest of the league fared on similar shots. In the chart below, the lower a player is, the tougher his shots were; the further to the right, the more shots he took: If you compare this chart to the yellow one above, our nicely defined trend of good shooters getting the rock has loosened considerably. It’s probably safe to assume this happens because the profile of a bench player who comes in and shoots the leather off the ball for 20 minutes a night is very different from a guy who’s asked to keep up that rate for an entire game.It’s probably a mistake to make a bunch of sweeping conclusions based on the aggregate here, as it is with most stats. But in an era of analysis in which “volume scorer” is still a pejorative, it’s notable that the players who shoot the most are also typically the best at converting tough shots, unless they are 37 years old and Kobe Bryant.Check out our latest NBA predictions. In this chart, players’ positions above and below the line for 0 represents how good or bad they were at making shots relative to how difficult the shots were.On the whole, what we see here is that as a player’s shots per game increase (we’re leaving per-play numbers for later), there’s a greater likelihood that he is good at making tough shots. This is conventional wisdom — stars get the ball — but not something we’ve been able to observe directly before.Remember that line about KD, Russ and Kobe’s free throw rates? Here’s where it comes back into play. Durant and Westbrook both had high free throw rates in their seasons on the chart, so they’d both get a boost from their positions here — Durant’s free throw rate in his MVP season was even higher than Westbrook’s, so it’s not like 2014-15 Russ catches up in efficiency. But eyeballing is enough to conclude that he would probably move up if we included free throws, and grandpa Kobe would stay in the toilet. Last thing: Notice that DeAndre, who was off the charts in shot quality this season, falls some here but is also well above average versus expectation on those good shots, evidence that he isn’t simply spoon-fed easy looks from Chris Paul but is among the best finishers in the game; this is tanked somewhat by his absurd 1.219 free throw rate, which has climbed to 1.553 in the playoffs (last season, it was 1.938 in the postseason — meaning that Jordan took just about two free throws for every field goal attempt).Moving on, we’re doubling back to the first chart again. Higher dots still mean a player took easier shots and lower that he took harder ones, but left and right track a player’s shots per 100 possessions instead of his raw per-game number: This chart mostly serves to show that the relationship we showed you in that first chart holds true when we look at per-possession. We also see guys who don’t take a lot of raw shots, like Marreese Speights, bunch up with gunners who play more minutes. But since we’ve already gone over low usage and carefully selected shots and all that, this seems like a good place to tell you that over our three seasons of data, last season’s vintage of Kobe Bryant picked his spots least carefully of any player in the data set.Kobe took not only an enormous number of shots, but also an enormous number of enormously difficult shots. Just look at him go! Many players down in that area of the chart were the primary option on their team and combined workload with a lot of long 2-pointers (the Carmelo, Blazers-era LaMarcus, Dwyane Wade crew). In Kobe’s case, that was true, but he was also old and feeble and slow and the Lakers would be bad no matter what he did. After that routine put him in traction after just 35 games, Bryant ran it back this season by getting to the line even less and shooting 467 threes; he shot 28.5 percent, but as you can see on the chart … at least he was a little more open? (Although one side effect may have been the embarrassing rash of airballs Bryant chucked from three this season, so maybe it was more of a give and take.)Anyway, here’s our last chart, which shows shots per 100 possessions against shot-making ability. As above, guys who shot better than their shot quality would predict are higher, guys who shot worse are lower, and dots farther to the right are guys who shoot a lot when they’re on the floor, even if they don’t have a lot of shots per game: This looks a lot like charts we’ve run in the past, or those that have run elsewhere, that plot workload against efficiency. True shooting percentage against usage percentage, for example, looks more or less identical. As workload increases, easy shots are harder to come by; as it decreases, players can pick their spots more carefully.Roll call: That cluster of dots in the top left of the chart is Tyson Chandler and DeAndre Jordan wrestling back and forth for the title of Guy Who Only Does Dunks. In the upper portion of the high-workload guys (on the right), we see players like LeBron James and Stephen Curry this season — those on great offensive teams that can space the floor for pretty good looks even for their highest-usage players. A little further down, still in the high-usage region, we see guys on teams that often need their stars to carry them, like Westbrook last season or Durant two seasons ago, or Carmelo Anthony, DeMar DeRozan or past iterations of LaMarcus Aldridge. Kobe this season was in the lurch, though by this measure not quite as depressing as his truncated 2014-15.But again, we’ve seen charts that show, if not this exact relationship, relationships that imply it; and while the shot difficulty stats are new, we could pretty much make assumptions based on the drops in efficiency. Here’s something truly new: read more

See more NBA predictions Oh, and don’t forgetCapitalism is great All newsletters ella:oh hm interestingneil:That caused our favorite to change! Nova now No. 1walt:Browns legend Joe Thomas announces his retirementthat’s kind of heartbreakingneil:Just as they might get good again, too(and just as @walt and I were going to make our bet on Cleveland as 2020 Super Bowl champs)walt:i’ll still put my name on that postPredictions NBA Things That Caught My EyeBest of the best of the bestThis season’s University of Connecticut women’s basketball team was the very best of an already outstanding legacy of UConn teams. Of the five UConn teams since 2014 — all of whom were ranked #1 in adjusted offensive efficiency, adjusted defensive efficiency and adjusted net efficiency — this one stands out with the highest in every rating of all five teams. [FiveThirtyEight]Best of the worst of the bestThe Ivy League sent the University of Pennsylvania to the NCAA men’s tournament, and the team was seeded 16th up against Kansas. Now no 16-seed has ever defeated a 1-seed, and that record remains unbroken as Kansas defeated Penn 76-60. However, Penn will go down as the highest-Elo rated, best-ever No. 16. [FiveThirtyEight]Try out our interactive, Which World Cup Team Should You Root For?Ten upsets in the cardsThe Localized Upset Classification model gave a 50 percent chance or higher of an upset in 10 NCAAM tournament games, eyeing Murray State, NC State, Buffalo, Loyola Chicago, San Diego St., South Dakota St., Butler, Florida St., Syracuse, and Stephen F. Austin as potential first round upset contenders. [FiveThirtyEight]Preseason matters in a sport!Preseason AP and coaches polls were outstanding at predicting NCAA men’s basketball games from 2002-17, with higher rated teams in those preseason polls beating lower ranked rivals 71.8 percent of the time. Contrast that with Ratings Percentage Index, which the committee uses to seed the field of 68, which correctly called the outcome only 69.1 percent of the time. [FiveThirtyEight]Arizona and Missouri know many kinds of painThere are 16 different seeds you can lose a round of 64 game from, and several schools appear to be gunning for at least one first-round loss from all 16 of them. Thirteen different schools have lost from six different numbered seeds, and two — Providence and Princeton — with a loss from seven different seeds. It’s Arizona and Missouri, though, that are the connoisseurs of failure. Both of them have lost from a 2, 3, 4, 6, 8, 9, and 10-seed; Arizona also lost from a 5-seed and Missouri an 11-seed. [FiveThirtyEight]The West is going to be a crazy finaleThere are seven teams in the Western conference separated by only two games, and only Houston and Golden State have guaranteed their ticket. That means that there are eight teams who could enjoy any seed between 3rd and “not appearing in this tournament,” which is quite a swing. [ESPN]Big Number10.24 yards per attemptFrom 2015-17, the best quarterback in the NFL when there were two tight ends on the field was Kirk Cousins, previously of Washington but who recently became an extremely well paid member of the Minnesota Vikings. Minnesota may want to invest seriously at the tight end position given that Cousins got 2,621 yards on 177 completions over the 256 pass attempts thrown with two TEs playing. [FiveThirtyEight]Leaks from Slack: walt: We’re launching a sports newsletter. 🏆  Join the squad. Subscribe read more

It’s probably clear by now just what a steal Cousins is at $5.3 million, but here’s one more note: Our CARMELO projection system, which spits out fair dollar values for every player’s production, thinks Cousins should be worth about $46.1 million next season. The NBA’s maximum salary rules preclude him from getting quite so much, of course, but he still figures to be worth far more than the mid-level pittance Golden State is doling out for his services.From Cousins’s perspective, it does make some sense to cut this particular deal. He’s coming off a major injury last season, and he may not be available to the Warriors until after the 2018-19 season begins. The Pelicans’ unexpected surge without him during the playoffs reinforced old questions about Cousins’ ability to win, and the market for bigs was looking cash-poor anyway this summer, with the repercussions of 2016’s wild spending spree crashing down on teams’ cap and luxury-tax budgets. According to The Undefeated’s Marc J. Spears, Cousins didn’t receive any “significant” contract offers when free agency opened up. So instead, Cousins is gambling that he can fit in with the Warriors’ legendarily unselfish group for a year, produce solid numbers, ease back into health, win a ring — and in the process, ditch his longtime label as a me-first malcontent. If all goes according to plan, he’ll be due for a much bigger payday next summer than he could’ve gotten had he played the normal free-agent game this summer.But even if things work out well for Cousins, it will have meant dealing another blow to whatever competitive balance is left in the league. For a brief while, things seemed to be taking a turn toward increased excitement: The Rockets spent a season suggesting the Warriors weren’t as unbeatable as they seem — coming within a Chris Paul injury and some historically cold shooting of possibly proving it in the playoffs — and James is just starting to form his own Western Conference challenger in LA. But then, Golden State strengthened their grip on the NBA with another deal that turned the salary cap’s rules against their own underlying purpose. The Warriors proved once again that the most exciting time on the pro basketball calendar is during the summer free-agent frenzy — when no games are played, but the fate of the following season is sealed. Just when you thought competitive balance in the NBA couldn’t be worse, the two-time defending champion Golden State Warriors swooped in Monday night, stole the thunder from LeBron James’s coronation in Los Angeles and signed DeMarcus Cousins (the best big man still available in free agency) for well below market value. Now, what already felt like the biggest foregone conclusion in sports — yet another Warriors championship — seems even less in doubt, somehow.Doesn’t the NBA have an incredibly complex set of salary-cap rules to prevent this kind of thing from happening? In theory, yes. But from Kevin Durant’s discount contract to Klay Thompson’s talk1Which his father, former NBA player Mychal Thompson, later downplayed. of leaving millions on the table to remain with Golden State (not to mention the coups the team scored with veterans like David West), the Warriors have a long history of convincing stars to take less money for the sake of the dynasty. Cousins is just the latest example — and maybe the most shocking, since he signed for less than Aron Baynes, Marco Belinelli or Mario Hezonja will reportedly make next season.The Warriors were able to sign Cousins as a free agent despite being tens of millions of dollars over the cap thanks to one of the NBA’s many salary-cap loopholes: in this case, the mid-level exception, or MLE. The MLE comes in several different varieties depending on how far past the cap a team’s payroll is, but the Warriors used the so-called taxpayer MLE to give Cousins his $5.3 million next season. It’s all legal, at least according to the letter of the salary cap rules. (As for the spirit? Not so much.)The MLE was introduced in the NBA’s 1999 collective bargaining agreement as a way for capped-out contenders to still be able to add quality role players in support of their stars. Perhaps the best examples of the MLE working as originally intended are Shane Battier, who joined the Miami Heat in 2011 and played a vital role on two title squads, and Shaun Livingston, who signed with the Warriors before the first of their three championship runs over the next four years. Those are the kind of guys who are supposed to be available via the mid-level exception — solid players, not stars.Cousins, however, is much, much better than your typical MLE pickup. Sure, there are questions about how he’ll fit on Golden State’s roster. But he also made the All-NBA second team as recently as 2016, and has generated 11.2 points of value over replacement player (VORP) — worth roughly 30 wins — over the previous three seasons according to Basketball-Reference.com, a tally that ranks tied for 16th best in basketball during that span.Using archives of Basketball-Reference’s database of contracts going back to the 2012-13 season, I identified 175 instances of the MLE (or one of its variants, including the taxpayer/“mini” mid-level and the so-called “room exception”) being used to sign a player in recent years, prior to the summer of 2018. In that group, the average MLE signee had generated 1.2 VORP in the three seasons leading up to his contract — meaning Cousins was worth about 27 more wins (!) than the typical MLE-worthy player in the years before signing his new contract. No other MLE pickup in our data set was even remotely close to as valuable going into his new deal as Cousins was: read more