In case you missed the first 4 parts of “Playoffs are a Crapshoot”, here they are:
- Playoffs are a Crapshoot, Part 1
- Playoffs are a Crapshoot, Part 2
- Playoffs are a Crapshoot, Part 3
- Playoffs are a Crapshoot Part 4
Last year the Braves won 97 games. But we know that this record is partly skill and partly luck. We also know the aggregate contribution of luck and skill across all teams. But there is no way to precisely to assign the actual influence of luck and skill to any particular team’s results. But we can make an intelligent guess, and we call this guess regression to the mean.
As we said last time, we know that the variance induced by luck is 6.3 games per season. That means that (on average) one team per year is getting about seven extra wins from luck alone. Someone else is getting about seven less wins. Most teams have variances under three wins, but a few are very luck or unlucky. The central insight into regression to the mean is that the teams that have good records are much more likely to have gotten the best luck and the teams that have the worst records are much more likely to have gotten the worst luck. It’s not impossible that Houston was really a 115 win team that had eight net unlucky losses, but 115 game winning teams because of skill are so rare, that it is much more likely that they were a 99 win team that had eight lucky wins; being a 99 win team (from skill) is much more common than being a 115 game winning team.
Thus, if we were to make out best estimate of the true skill variations of teams, we need to subtract from the observed success of the teams with the best records and add to the observed success of the teams with poor records. This sort of an adjustment is called a shrinkage estimator, because every record is shrunk towards 50 percent to accommodated our best estimate of the unobservable component: luck.
It turns out that there is an optimal way to do this which, remarkably, doesn’t depend on the length of the season, so that it is just as applicable to the regular season as to the playoffs. We calculate the length of a hypothetical season in which the effect of luck would just equal the effect of skill and add an extra set of 0.500 performance of that length to everyone’s record. For those interested in the mathematics of this adjustment which is due to the pseudonymous sabermetrician Tom Tango, I refer you to Phil Birnbaum’s explanation here.
Using the last four years’ estimation of the talent-luck division, the magic number is about 50. This means that we need to add a 25-25 record to everyone’s record to get a regressed-to-the-mean estimate of skill alone. Since all the teams in the playoffs are above average teams, this reduces everyone’s rating, but not uniformly: the better the team, the more adjustment you do. This compression then reduces the head-to-head win probabilities for the best teams and increases them for the worst teams, inducing more crapshootiness.
To implement this, I took the 2019 game by game results and then gave each team 50 more games against the fearsome opponent, the Middletown Meanies. Each of them finished 25-25 against this team. I then reran the Bradley-Terry rating estimators on this new season and recalculated everyone’s chances of being World Series champs. The Dodgers, still the best team but now only slightly better than Houston, was now estimated to have a World Series winning probability of 21.7%. This is over 5 percentage points lower than their probability before we adjusted for regression to the mean, and raises our crapshootiness index to 0.89. So talent does matter in the playoffs, but the winner is nine parts luck to one part talent. Ladies and gentlemen: that’s pretty much a crapshoot.
I’m certainly not the first person to make this finding. Indeed, Pete Palmer, using somewhat different methods and earlier data, calculated the probability of the best team winning the playoffs at 22 percent on average, and came to a very similar conclusion:
Most people think luck is a lot less important than it is. A team’s record from year to year includes a great deal of luck, and luck contributes about equally as skill to a team’s eventual regular season record. (And in the postseason, it’s nearly all luck.)
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