Three Maxims of Tournament Design

In a very early post, I proposed what I then thought would be the first of several maxims of tournament design. Here it is, in a slightly altered form:

Unbalanced designs are likely to be inequitable, and so are to be avoided unless there is some good reason that the design needs to be unbalanced. (maxim 1)

The alteration is the substitution of “design” for “bracket”, so as to make it applicable to tournaments that are not run in brackets.

To date, I have had less occasion than I thought I would to make such grand pronouncements. But I think it’s time to propose another two maxims. Here’s a second:

In a well-designed tournament, there should never be a situation in which a team or player has an incentive to lose or draw rather than win an individual match. (maxim 2)

In addition to avoiding giving a team an incentive to lose, it is also well to avoid, as much as possible, situations in which a player or team is indifferent to winning or losing, especially where their opponent is not indifferent. This suggests a third maxim:

In a well-designed tournament, one should avoid as much as possible, matches for which the reward for winning, or penalty for losing, is very different for the two competitors. (maxim 3)

Violations of maxim 2 are uncommon. But they surface, now and again, in unexpected circumstances, and there are sometimes difficult decisions to be made about how much other values should be sacrificed in order to avoid the mere possibility that there might be a match or two in which one side (or, comically, both sides) has an incentive not to win.

Violations of maxim 3 are, unfortunately, very common in the later rounds of round robin tournaments, particularly the large round robins that make up the regular season in many professional sports leagues. It’s common, for example, for a team whose seeding for the NBA or NFL playoffs has been settled to rest some of its best players for the last game or two of the regular season, even though its playing a team whose playoff chances are not yet determined.

Occasionally, these late-season games implicate maxim 2 as well as maxim 3. One way this can occur is when there are future advantages that accrue to teams that do poorly in the regular season.

A notorious example was the 2011 NFL season, with the “suck for Luck” phenomenon. The Indianapolis Colts and the St. Louis Rams were each 2-13 on the season going into the final game. The team that ended with the worst record would have the first pick in the 2012 draft, and it appeared that the first pick was going to be much more valuable than the second pick because Andrew Luck, a quarterback of exceptional promise, was thought to be a much better prospect than whoever was second. The Colts were widely suspected of losing on purpose.

The top picks in the NBA draft are not strictly allocated to the teams with the worst records. The fourteen teams that do not make the playoff one year are entered into a complicated lottery for the next year’s draft, with the teams having the worst records given the best chance to get an early draft pick. This should reduce the incentive for a team to lose games intentionally, but the incentive is apparently still there. The Philadelphia 76ers, in recent years, seem to have hobbled their winning chances even fairly early in the season, apparently in hopes of building a better team in future years with high draft picks.

Another scenario that implicates maxim 2 is when a team that’s already securely in the playoffs is scheduled late in the season against a team that’s fighting to get in. If the secure team deems it’s opponent a lesser threat in the playoffs themselves than the team that would otherwise get the playoff berth, there’s an incentive to let the lesser team win so as to eliminate the better team from contention.

Somewhat related to these two new maxims are situations in which players might find it profitable to collude with their opponents. This possibility will be the subject of a future post.