The Major League Playoffs begin tonight with the “wild card” game between the Twins and the Yankees. This event is being promoted by one of the networks with the tag line “The only thing that matters is October”. This reflects the structure of the playoffs, where the entire 2430-game regular season matters only for qualification and seeding for a relatively brief knockout postseason.
It would be hard to argue that this arrangement is designed to award the championship to the best team. Instead, it appears that the intention is to create as much interest as possible for a limited time. October, for baseball, is like March for NCAA basketball – a special time when the attention of less avid fans can be captured by a series of high-stakes games. Fairness, at least in the sense of fairness (C), is less important than creating good spectacle.
So how severely is fairness (C) compromised? This post, and a few to follow, will look at the structure of the playoffs, and compare it in fairness (C) terms to some possible variations.
The good folks at 538.com have an elaborate model, which will be updated as games are played, to predict the outcome. I can’t (and don’t want to) compete with 538 in the prediction game – they’ve included such subtleties as home-field advantage and individual pitchers into their model. Instead I’ll use my simpler model to try to answer some what-if questions about how the MLB playoffs would be different if they were structured differently. And I’ll use 538’s Elo ratings for my measure of actual skill, and their model percentages to help calibrate the luck factor for my model.
Here is a summary of the structure of the 2017 playoffs: MLB2017. It is, to say the least, rather odd-looking. I’ll explore some of these oddities in the next few posts.
Let me begin by using the 538 model to calibrate my simulator. My two main parameters are the luck factor, which governs how much influence chance has in the outcome of any single game, and the elite threshold, which governs the distribution of skill levels.
538 predicts that the most successful team in the draw, the Indians, will win 27% of the time, followed by the Dodgers at 18% and the Astros at 15%. That means that the luck factor is going to have to be high. I find that I need the highest luck value I’ve ever used in a practical model, which is five.
Now to set the elite threshold. 538 has the three least likely teams, the Twins, Rockies, and Diamondbacks, winning at 1%, 1%, and 4%, respectively. By manipulating the elite threshold, I control the spread of skill levels – how much worse the worst teams are compared with the best teams. I seem to need an elite threshold of about -0.5 to get success rates in the proper range for the bottom of the distribution.
But now, allowing for such a wide spread of skill levels, the best teams are doing too well, so I need to ramp up the luck factor even further, which means that I’ll have to relax the elite threshold even further. After going back and forth for a bit, it looks like I need to set luck at six, and the elite threshold at minus one.
Running a million simulations with these parameters, I get predicted win percentages that are roughly equivalent to those of 538. The most striking result is the low percentage of wins for the Yankees. According to the Elo ratings, the Yankees are the fourth-best team. But, as wild card qualifiers, they have to play a one-game round against the Twins and single game series is a substantial risk, even for a team that’s substantially higher rated. 538 gives them a 6% chance, and my simulation has them with only 5.3%. The difference is most likely caused by the fact that my model doesn’t give them their home-field advantage in the wild card round.
Now, it’s not clear what we should make of the way the Yankees are seeded in the playoffs. They might be considered to be mis-seeded – on current form, they’re the fourth-best team, but they get treated as the eighth seed, which means that they don’t get a first-round bye. From a pure fairness (C) perspective, this is unfair. But they didn’t win their division – they needed up two games behind the Red Sox in the American League East. If the playoffs were seeded strictly according to current form, that would make the regular season even more meaningless than it is now.
So perhaps the Yankees are fairly seeded in the actual tourney. But even if their seeding is sensible, it’s hard on some of the other teams. The Twins, who have to play the Yankees in the wild card round get a tougher opponent than they ought to get, and that hurts their chances. As both the 538 prediction and my model show, they have the worst chance of winning the World Series, even though they’re not the worst team in the post-season.
Just for fun, let’s consider how the expectations of these teams would differ if the bracket were drawn with conventional full seeding (again, with the skill levels set by current form as reflected by the 538 Elo ratings. The Yankees’s expectations doubles from 5.3% to 10.6%. And the Twins, with a somewhat weaker opponent in the wild card round, do slightly better, rising from 1.45% to 1.61%.
Overall, the tourney with conventional, accurate seedings is more fair, with the Indians and Astros winning more, though the Dodgers do a little less well because they get a #3 seed line rather than a #2 line. The fairness (C) statistic for the actual tournament is 70.0. With accurate seeding, it does a good deal better at 64.2, though that’s still nothing to write home about.
Next time, I’ll comment on one of the more curious features of the MLB playoffs – the wild card round.