As discussed before, seeding tends to enhance fairness (C), which measures the tendency of a tournament to distribute its rewards to the better players, at the expense of fairness (B), which measures the extent to which every entrant is given an equal chance.
But the extent to which the better players are given an advantage is not uniform through the skill distribution. Seeding creates a pattern of advantages and disadvantages that affect different parts of the skill distribution differently.
Take, for example, the fate of the number 8 – 12 seeds in the annual NCAA basketball tournament. Considering only the first round, it’s better to be seeded 8 or 9 than 10, 11, or 12. But whichever of the 8 or 9 seeds wins their first round match against each other then will almost certainly face the number 1 seed in the next round. 10, 11, or 12 seeds that get by the first round will have an easier opponent in the second round. Thus, despite facing a tougher first-round opponent, experience shows that the 10, 11, and 12 seeded teams are actually somewhat more likely to reach the “sweet 16” than the 8 or 9 seeds.
Here is a chart that shows the log of the expectations for the top 50 players in a hypothetical U.S. Open tennis tournament, run both as a blind draw, and as a fully-seeded tourney. The red curve for the blind draw tourney is smooth, representing a more or less gradual decline in the player’s expectation. The blue curve for the fully seeded tourney shares this basic pattern, but also shows a secondary effect that makes the line a bit wavy. To make the wave pattern clearer, here’s another chart, showing differences in the log of the expectations, this time for the full 128-player draw:
The benefit of better seeding comes and goes, on a period relating to the powers of two. In general, it’s less desirable to be the 9th, or the 17th, or the 32nd, or the 65th seed because that tends to give you matches against top-ranked players.
Depending on the parameters of the competition, this wave can be large enough that it’s actually desirable, in terms of overall expectation, for a player to have a lower seed than a higher one. In the hypothetical U.S. Open simulation, this wave effect overcomes the general decline at only one position, and there just barely. The expectation for the 17th seed is $188,616, and for the 18th it is $189,223. Otherwise the expectation curve declines monotonically.
But the possibility that a player might do appreciably better with a lower seeder than a higher one is a matter of concern for tournament administrators. If the U.S. Open were run as a fully-seeded tourney, it might well be desirable for a player to throw a match at the Western and Southern in order to avoid creeping up into an undesirable seeding position.
This, then, might be a good reason for the unusual tiered seeding procedure used by professional tennis. By randomizing the positions of seeds 17 through 32, for example, there can be no incentive for a player to seek a lower seed (and a very strong incentive to break into the next-higher seeding tier by reaching number 16).