Wild Cards

One of the more peculiar features of the Major League Baseball playoffs (or “postseason”, as the league prefers to call it) is the fact that five teams from each league qualify. The three division winners each get a bye, and the two non-winners with the best records play a single game to see which will join the other three. Including the World Series, then, the MLB playoffs are, essentially a single-elimination tourney on a 16 bracket with six first-round byes.

Six byes? A single-game first round? My first reaction is that this has got to be one of the worst formats in use for a major professional sport. But, working through the ramifications, I’ve come to opposite conclusion. The Major League Baseball wild card system is a stroke of genius.

First, why have wild cards in the MLB postseason at all?

One wild card makes sense – there are three divisions in each league, to adding one wild card in each league fills out the bracket to a power of two: six division winners, and two wild cards for a tidy three round playoff. But what sense does it make to have more than one wild card per round, which brings the total up above the power to two, so that you need a fourth round to handle them, and probably a bunch of byes to pad out the 16 bracket?

Major League Baseball is happy to have a fourth round in its postseason, but only so long as it is kept to manageable limits. Adding a full round to a knockout tourney consumes a lot of resources – it doubles the number of teams, and slightly more than doubles the total number of games. And the fourth round is inherently less compelling than the final, the semi-finals, or even the quarter finals. So it makes sense to keep it short and sweet.

That’s just what MLB does by having two wild cards from each league. The don’t need to fuss with a full fourth round, which would entail eight pairings – they only need one pairing in each league to have some sort of fourth round, and that’s just what they get. Those two pairing don’t have to compete with any other baseball except each other. And by making the wild card a single game affair, they keep this bit of a fourth round very short, and they make sure that that one game is crucial to each team. It’s got everything going for it as a spectator event.

Adding wild card teams also adds interest to the regular season, or at least to the last part of the regular season. With more places to play for, there will be more teams with a reasonable chance to make the postseason.

So, MLB is glad to have an extra round of postseason play to sell, but it avoids most of the difficulties they’d encounter if they had to stage a complete fourth round by shrinking that round into a single game in each league.

Very clever. But is it fair? It is fair to have a round in which there are a lot of byes, and the fixtures that aren’t byes are single games? It seems that there will be a heavy price to pay in the coin of fairness (C).

As we’ve seen in other contexts, fairness (C) generally varies inversely with the number of players in a competition – the more teams or players there are, the greater the chance that someone other than the best one will win. Add to this the fairness problems that flow from all those byes and the single-game format for the round. Doesn’t this suggest that the playoff format with two wild cards in each league is going to be less fair?

In this case, no. Here’s a table showing the fairness (C) figures for various possible wild card formats. The bold figure simulates the actual format. In all of the simulations, perfect seeding is assumed.

f(C )
wild cards single game 3 of 5 games
1 67.4 67.4
2 67.3 67.2
3 68.0 67.7
4 72.4 71.5
5 95.4 85.4

A few things to note about these results. First, all of the numbers are pretty high. When I calibrated the match model using the 638 predictions in The Only Thing that Matters is October, I discovered I needed a luck factor of six – much the highest luck parameter I’ve found and practical use for. Baseball may not use formal randomizing devices like cards or dice, but chance still plays a huge part in determining who wins.

Second, the two-wild format, which leads to a ten-team bracket, is predictably better than any format with more teams. But it’s also a tiny bit better than the one-wild format, with a balanced bracket of eight. A moment’s reflection show why this is so. The only difference between the 1/8 format and the 2/10 format is that in the 1/8, the number one seed’s first round is against the fourth-best team, while in 2/10 that round will sometimes be played against the fifth-best team. And, as a practical matter, the number one seed’s benefit is greater because no matter which team they face, that team will have somewhat depleted pitching, as they’ve had to pull out all the stops to make sure they win the previous game.

Finally, note that expanding the play-in round to best three out of five gives almost no benefit until the bracket gets pretty full. The length of the play-in round doesn’t really matter very much unless the best teams have to play it.

The current MLC postseason format seems to achieve it’s goal: creating a valuable extra round to sell to television, and adding interest to the last part of the regular season. And it does it without materially compromising the fairness of ultimate result. This would seem to be a pretty unambiguous positive result.

As I found when I looked into the seeding practices of professional tennis, I find that what initially looked to me like a silly mistake is really no mistake at all.

 

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