# Seedy Doings at the Western and Southern

In the previous post, I showed how seeding affected fairness in general terms. In this one, I’ll relate it to the actual bracket that was played in the men’s singles draw at the Western and Southern.

To begin, here’s the summary information for the results that were reported from the simulation:

Actual Draw: f(C) = 0.235; f(B) = 111.2
f(b:A-F) = 111.2, 72.1, 48.0, 35.7, 18.9, 4.2

And here’s a graph showing the differences, by skill level, between the expectations for the 16-team partial seed, and the actual tourney. I choose the 16-team partial because it’s the idea distribution most nearly applicable to the actual draw:

There are three different elements of the difference between the expectations of the actual draw and those of the theoretical one: (1) The tiered draw for the 16 seeds (this is the distinctive feature of seeding in professional tennis); (2) The difference between the actual skill level of the entrants and their putative skill levels represented by their ranking in terms of ATP points; and (3) The substitution of “lucky losers” from the last round of qualifying for late scratches in the main draw.

The Tiered Draw

The first difference is the difference between standard partial seeding, where the seeded teams stay put on the same lines they’d have in a fully seeded tourney, and the seeding that resulted from the tiered draw. Here’s the difference chart taking only this element into account:

The only teams much affected by the non-standard way the sixteen teams were drawn are the sixteen teams themselves. The effects are substantial, though they are mostly a good deal smaller than the ones shown on other chart, which shows the aggregate effect of all three sources of variation.

The biggest winner (+\$11,760) from the tiered draw is the number 4 seed. In a standard bracket the 4 seed is in the same quadrant of the draw as the 5, 12, and 13 seeds. But as it happened in this year’s Western and Southern, the 4 seed shares a quadrant with the 6, 12, and 14 seeds. Facing this slightly less skillful opposition improves the 4 seed’s chances of reaching the semi-final.

In contrast, the biggest loser in the draw (-\$10,397) was the number 3 seed. In a standard bracket, the 3 seed shares a quadrant with the 6, 11, and 14 seeds, but in the Western and Southern draw the 3 seed was thrown in with the 5, 11, and 15 seeds.

Mis-seeded entrants

The most dramatic spikes in the expectation chart are caused by seeding that does not track the actual skill level of the entrants.

These results need to be taken with a grain of salt, of course, because it’s impossible to know actual skill levels with a high degree of confidence. But where, as here, there are substantial divergences between the seedings that are based on accumulated ATP points and the pre-tourney betting odds, it stands to reason that the betting odds are a better estimate of actual skill. The ATP points do tend to track skill, but they’re also part of a system that rewards players for playing the tournaments that the ATP wants them to play, and punishes them for not playing them. The betting odds are not perfect skill indicators, but they probably do represent the best generally-available information. If there were better skill estimates available, canny punters would put enough money on the undervalued players to rectify the odds.

So who are the big winners and losers from this mis-seeding? The biggest loser was Nick Kyrgios, at -\$62,510. According to the ATP rankings, Kyrgios was the 19th best player in the original field, and thus was not seeded at all. But the punters had Kyrgios as the 7th favorite. We need not grieve much for the unfairness visited on Krygios – last night he defeated Nadal in the quarter finals, so he’ll do just fine. But perhaps the punters were on to something. And it probably was a bit unjust that he had to meet Goffin in the first round (where he, by virtue of his skill, was entitled to a bye), and Nadal in the quarters.

The next biggest loser is John Isner, at -\$59,529. Isner was seeded 14th by the ATP, but the punters had him the fourth favorite. He too should have had a bye. Part of the explanation for Isner’s short odds may be his nationality – the punters assumed (I think correctly) that he would get some benefit from the support of American fans. And he too has made the semi-finals, though he hasn’t had to play another seeded player yet, as the big fish in his section of the draw, Alexander Zverev, was unexpectedly defeated in the second round by Frances Tiafoe, a “wild card” entrant.

A couple of other losers of note are Juan Martin Del Potro (-\$48,976), and Thomas Berdych (-\$12,086). Berdych was pretty fairly seeded – he was 9th best, according to the punters, and seeded 10th by the ATP. But he had the misfortune to draw Del Potro in the first round, and Del Potro was badly under-seeded. Del Potro was 25th according to the ATP, but 8th (and thus in line for a first-round bye) according to the betting odds. So Berdych suffered not from his own mis-seeding, but from Del Potro’s. The two played a terrific match, which Del Potro won in three sets.

So who are the winners from mis-seeding? Some of the winners were the players who got the favorable seeds that should have gone to players like Kyrgios, Isner, and Del Potro. Roberto Batista Agut was +\$25,314. He was seeded 12th, but according to he betting odds he was only the 17th best player, and so shouldn’t have been seeded at all. He also benefitted from the scratch of Milos Raonic, the only other seed in his eighth of the bracket, who was replaced by a lucky loser. So part of his good fortune belongs to the last of the three causes.

Late Scratches and Lucky Losers

The third factor that causes spikes in the expectation graph for the Western and Southern is the extraordinary way the tourney deals with late scratches from the competition. They are replaced by “lucky losers” – players who just missed qualifying because they lost in the final round of the qualification mini-bracket.

As it happened, there were four late scratches from the Western and Southern, and three of these were players who had been seeded in the top eight, and thus had byes. The result was that it was, on balance, better to lose in the last round of qualifying than to win, surely a perverse result.

The three large spikes at the tail end of the expectation chart belong to Janko Tipsarevic (+\$32,527), Thomas Fabbiano (+\$31,431), and Christian Harrison (+\$34,415), who were the three lucky losers who received byes. The fourth lucky loser, Ramkumar Ramanathan, actually won one round in the main draw, and so ended with the same actual reward (\$32,780) as his even luckier peers, none of whom won a match in the main draw.

The replacement of seeded players by lucky losers also benefitted others in the draw, as with Batista Agut, who found themselves in parts of the bracket where highly-seeded scratches were replaced by relatively low-skilled replacements.