“Saving” baseball with game theory

The conventional wisdom this summer is that baseball is struggling. Games are boring and long, too many teams are really bad, and so no one is watching. Unsurprisingly, this supposed sorry state of things has prompted people to offer “advice.” 

The worst piece I’ve seen so far is this article from the Wall Street Journal. I’ll save you the read. The author reports on a proposal called the “Catch-Up Rule.” When a team is ahead, they only get two outs per inning instead of the usual three. This makes the games closer and faster, and this is supposed to make them more appealing.

The original proposal appears to come from a game theorist and a computer scientist at NYU. If you needed proof that “game theory” isn’t actually about what we usually think of as games, this is it. 

The proposal is absurd, but it’s worth considering just what is so bad about it. First, the common complaint against baseball these days is that there isn’t enough action. This proposal would reduce the amount of action by reducing the number of outs. Second, the authors propose that the rule would reduce inequality between teams by artificially hindering the ability of the good teams to succeed. I doubt this would happen. Instead, the good teams would assume even less risk, and thereby continue their dominance, just at a faster clip. More generally, a lot of baseball is about random chance–this is why there are 162 games–and reducing the number of baseball events will emphasize the randomness.

But these are minor quibbles compared to the basic mistake the authors make. They seem to think that the purpose of playing a baseball game (and to be fair, they propose similar changes to basketball and football) is to see who wins. Rule changes that reach that end state more efficiently are therefore regarded as desirable.

This way of thinking confuses the goal with the point of the game. But the distinction between the goal and the point of a game is what makes it a game. A game is an activity in which we voluntarily, and for the purposes of playing the game, rule out the most efficient means to the goal. Consider soccer (a game that doesn’t seem friendly to a “catch-up” rule). Two of the most important rules of soccer specifically prevent the most efficient means of scoring: no hands, and no off-sides. People sometimes complain that soccer is too slow, there isn’t enough scoring, the attacks are opaque, etc. How much better would it be if you could just pick the ball up? Well, it wouldn’t be better soccer, because it wouldn’t be soccer. Though a game must have a target or goal of some sort–some action or event that is aimed at–the purpose of playing (or enjoying) the game is the joy of playing itself.

I think most serious baseball fans would object not for the sake of tradition, but because they enjoy the game, and not just the result. Reducing the number of things that happen isn’t desirable, even if it gets to an end faster. But let’s grant that serious fans aren’t bothered by the lethargic pace these days. (I’m not sure that’s true, but let’s grant it for argument.) Will the causal fans be better off? I kind of doubt it. First, to the casual fan, we’d be adding a rule that seems manifestly unfair. I’m not sure that it would be so easy to explain why competitive balance is more desirable than more exhibitions of baseball skill, but this is exactly the proposed tradeoff. Second, the rule would reduce the amount of skill displayed by limiting the opportunities for the better team to hit. Supposedly the problem is that there isn’t enough hitting, but the proposal suggests reducing it even more. And third, I think that a casual fan would likely intuit that something seems off when we have to redesign the game to finish it faster. 

The authors point out that having more people watch a game would be good for baseball revenue. Shorter games would permit more watchers, and so shorter games means more revenue. But baseball isn’t hurting for revenue, and changing the game to make it not just unrecognizable as baseball, but a deficient game seems likely to be counterproductive.

But the proposal as a whole is a perfect illustration of how suck the life out of something by making a theory of it. Baseball fans, like any sports fans, can get nerdy about the details of their passion, but fundamentally that obsession is driven by a love of the game, not a love for the theory of the game. And perhaps there’s a lesson in that for other things too. 

Why did UVA lose to UMBC?

It is sad that UVA’s basketball team’s historic season will likely be remembered for all the wrong reasons. UVA was great during the regular season, and for their efforts earned a #1 seed in the NCAA tournament, only to be the first #1 to fall to a #16.

In several attempts to analyze the historic upset, the writers have repeated a familiar trope: UVA isn’t built for the postseason. Though under Tony Bennett UVA has been a reliable force in the regular season, somehow they’ve been unable to find even modest success in the Big Dance.

The question is, “Should UVA change?”

Lots of basketball pundits dislike the slow pace and deliberate tactics that UVA uses, but at least this year they’ve been forced to admit that the strategy works pretty well. Yet now some who seemed to grudgingly accept the effectiveness of the Pack Line will surely want to revisit their concessions.

The thought is that the slow pace and suffocating defense typically comes at the expense of offense, and so when the need is for better scoring, UVA just doesn’t have what it takes. Therefore, the argument goes, UVA’s consistency and discipline undermines its ability for success in the post-season, when it is more likely that they will need to make up deficits quickly. UVA would do better if they would sacrifice a little defensive skill in exchange for some better scorers. They might even do better if they would play defense the “normal” way, thereby increasing the number of possessions and making it easier to catch up.

I think that this argument is understandable, but mistaken. More to the point, I think using Friday’s night’s upset by UMBC as evidence for the claim that UVA should change misunderstands what happened.

The upset

So why did UBMC win? A few factors seem relevant.

First, UMBC has a smart coach who knows how college basketball works. He had his guys prepared and calm, and kept them focused on the prize.

Second, the game plan itself was smart. UVA has long been susceptible to teams who can overload with guards and make 3-pointers. UMBC exploited this deficiency to perfection (almost literally, as we’ll see).

Third, UVA was terrible. I’m not sure that I’ve seem them play so badly under Tony Bennett.

But mostly, it was luck. In fact, sheer luck is probably as important as all of the other factors put together.

Even before the tournament, UMBC was already the luckiest team in Division 1. And it’s not really that close. UVA was slightly above average in luck; UMBC was already a few standard deviations above the mean. They’ve had a magical season.

When we consider the game itself, the first half was pretty unremarkable. Sure, it’s cool for the #16 to be tied with the #1 at halftime, but UVA fans probably weren’t surprised. DeAndre Hunter was out, Devon Hall and Isaiah Wilkins were in some foul trouble, but UMBC had only 21 points. It looks pretty familiar to UVA fans. A few more points on UVA’s side would have been nice, but it wasn’t way out of the norm. And UMBC had already been hot, especially from 3-pt range. UVA was shooting about 10% from 3, and UMBC was over 40%. UMBC’s three-point shooting was keeping it close.

The second half was another story. UMBC’s performance was close to as efficient a performance as is possible. We can note first that UMBC scored 53 points in the second half, which is the average number of points UVA allowed per game this year. UMBC ended up with the highest score against UVA this season.

So did UMBC just take a ton of shots? Did UVA’s defense just completely fall apart? Did UMBC finally figure out how to speed UVA up? Not really.

Usually win percentage correlates pretty well with field goal percentage.

At extremes of pace (very few or very many attempts) the numbers aren’t quite as consistent. But in this chart, you can see that the basic relationship is pretty stable. For reference, the blue dot is UVA’s performance on Friday. The red dot is UMBC’s performance for the whole game. And the purple dot is UMBC’s second half performance, if that rate had continued for the whole game. The data producing this plot is all NCAA Div I games since the 2009 season. There are only a dozen or so team performances better than UMBC’s since then.

If we look just at UVA’s games, we can see an even more dramatic outlier.

Here are all of UVA’s (regular season) games since Tony Bennett became the head coach. Each dot shows the field goal attempts and percentage for each opponent. The orange dots represent opponent wins and the blue are opponent losses. The red dot is UMBC’s game on Friday, and the orange dot at the very top is the second half of that game, extrapolating the number of FG attempts to two halves.

Two features of this graph deserve note. First, there are a couple of UVA losses surprisingly close to the bottom left. Occasionally UVA just can’t score. Second, no one has shot over 60% for a game against UVA. 

In general, though, UVA is dominant against other teams. The boxplot shows the last four years of UVA versus other teams. The values here are scaled so that we can see how far from the norm UVA’s opponents are. Because the scores are scaled, UVA’s numbers center around 0. When UVA’s opponents don’t play UVA, they’re about 0.5 standard deviations above average in FG%, compared to all teams. (Most of them are in the ACC, which historically is a good to great conference.) When they play UVA, they are between 0.5 and 2 standard deviations below average. Ordinarily, UVA dominates pretty decent teams.

But, as is the case with any statistical distribution, there is a lot of overlap. Shooting 30% better than UVA is possible, even if it is very unlikely. But we already knew that UMBC’s win was unlikely. This chart just reminds us that it wasn’t impossible, even given the existing distributions of performance.

UVA and the NCAAs

So why does UVA struggle so much in the NCAA tournament? If we take the pundits’ view, it’s because of the style. But if we take the data analysis view, it’s just as likely that they haven’t had enough chances yet. Indeed, UVA fans can easily think of some quirky reason that made a solid season turn into a sketchy tournament. Injuries (most recently Hunter), bad draws (MSU twice?), etc. all seem like viable possibilities.

Sometimes people say that UVA struggles in March. But that’s not quite right. They struggle in the NCAA Tournament, but fans of other ACC teams should quickly realize that UVA doesn’t struggle in March. They’ve won the ACC or been close for several years in a row. So it seems as if there is something about the NCAA tournament that causes problems. If it’s not just random luck (still I think the best explanation), then what changes from the ACC tournament to the NCAA one?

The obvious thing that changes is the officials. And I wonder if this has something to do with it. UVA plays a distinctive kind of game, and I wonder if the ACC officials get used to it, as do ACC teams, and UVA gets used to the others being used to it. Then we get to the big tournament, and now there are officials who aren’t as familiar with the tactics, and call them differently. UVA does seem to get more fouls in the NCAA tournament, even though during the regular season they usually get very few. This seems like a small thing, but it might matter in tight games.

As I mentioned above, some people say that UVA just plays too slowly, so they can’t generate offense when necessary. I think folks should take a close look at the last 60 seconds of the game at Louisville this season. UVA can score fast when they need to, and focusing on pace of play misses the simpler point.

Fundamentally, UVA just struggles to score at all sometimes. For the last few years (basically since Anthony Gill graduated) UVA has been almost incapable of any kind of post game. Their big guys are excellent defenders, but they can’t score reliably.

This is, I think, the better way to think about UVA’s style. Their offense is one-dimensional, and though their guards are talented shooters, they understandably struggle when the opponent can load up opposing guards, feeling safe to ignore the big men. UVA would be very good indeed if the offense could alternate between an inside post game and the typical blocking/screening scheme they use.

Perhaps the best argument against UVA needing to change is UMBC itself. The Retrievers won basically by imitating UVA.

Other consistently excellent teams have sometimes struggled at the highest level. I’m a long-time fan of the Atlanta Braves, who won 15 consecutive division titles, but only one World Series. Consistent excellence isn’t showy, but it is excellence. UVA is building that kind of program, and I suspect that eventually the trend will swing the other way, and everyone will suddenly forget why they thought Tony Bennett’s teams were incapable of March success.