Shedding Tiers

The U.S. Open tennis tournament, like the other tennis majors, has a 128 draw that’s seeded in tiers along much the same lines as the Western and Southern. The first six tiers are the same: {1, 2, 3-4, 5-8, 9-12, 13-16}. To this, the U.S. open adds two new tiers: {17-24, 25-32}, which doubles the number of seeded players, from 16 to 32. There are no byes in the U.S. Open, so the tier boundary between 5-8 and 9-12 is less significant. But apart from this, the tiered seeding system has much the same effect on players’ expectations.

Next year, however, the Grand Slam Board – a body that sets policy for the tennis majors – has decreed that there should be only 16 seeds, which will presumably be accomplished by shedding the 17-24 and 25-32 tiers. For much interesting background on this change, see here.

What effect should we expect from such a change?

I ran 500,000 simulated tournaments with, and a equal number without, those two tiers, in both cases assuming perfect seeding, using the payout schedule for the coming U.S. Open.

This chart shows the difference in the expected prize money by seed number.

Expectation

As might be expected, the big losers are the players ranked 17-32, who will no longer be protected. But the 17-24 tier suffers much more than the 25-32 tier. That’s because the 25-32 seeds are scheduled to meet the 1-8 seeds in the third round. They still suffer because they lose a lot more games in the first and second rounds, where (stripped of their seeding protection) they might have to play anyone at all. But when they’re seeded they are much more likely to run into one of the tourney’s top players in the third round. So, for example, the 25 seed wins 46.5% of their third-round matches when they’re not seeded, but only 31.8% when they are seeded and likely encounter a 5-8 seed. The 24 seed, in contrast, is likely to face someone in the 9-12 range. Allowing for a somewhat larger chance that the seeded player will be upset in the first two rounds, the 24 seed wins 49.5% of their third round matches when seeded, and 47.1% when unseeded.

Here are the differences expressed in terms of the percentage gain or loss, by tier:

1               0%
2              -1%
3-4           -1%
5-8           -2%
9-12        +1%
13-16        0%
17-24     -15%
25-32       -9%
33-128     +7% to +3%

There are small effects, mostly negative, on the expectations of the other seeded tiers. But there’s a major shift in money to seeds 33 through 128, with the players seeded 33 to about 43 enjoying +7%, on down to about 120 to 128, who gain only 3%.

The move from 32 seeds to 16 seeds will be a boon for this bottom 75% of players. From reading the press coverage, one could get the impression that the change is generally opposed by the players, but that’s because the players who are most likely to be asked for opinions are the ones at the top of the rankings.

So, is shedding the 17-24 and 25-32 tiers a good idea? That’s hard to say. I’d be inclined to think that it’s a good idea to send more money down to the lower parts of the ranking, but perhaps that’s a matter of taste.

By weakening the seeding, a little, the majors will show a modest improvement in fairness (B), 137.9 to 135.4, and a modest worsening in fairness (C), 18.46 to 19.79.

Seeding systems are almost always controversial because they trade one kind of fairness for another.

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