# Measuring the Impact of Wimbledon’s Seeding Formula

Unlike every other tournament on the tennis calendar, Wimbledon uses its own formula to determine seedings. The grass court Grand Slam grants seeds to the top 32 players in each tour’s rankings, and then re-orders them based on its own algorithm, which rewards players for their performance on grass over the last two seasons.

This year, the Wimbledon seeding formula has more impact on the men’s draw than usual. Seven-time champion Roger Federer is one of the best grass court players of all time, and though he dominated hard courts in the first half of 2017, he still sits outside the top four in the ATP rankings after missing the second half of 2016. Thanks to Wimbledon’s re-ordering of the seeds, Federer will switch places with ATP No. 3 Stan Wawrinka and take his place in the draw as the third seed.

Even with Wawrinka’s futility on grass and the shakiness of Andy Murray and Novak Djokovic, getting inside the top four has its benefits. If everyone lives up to their seed in the first four rounds (they won’t, but bear with me), the No. 5 seed will face a path to the title that requires beating three top-four players. Whichever top-four guy has No. 5 in his quarter would confront the same challenge, but the other three would have an easier time of it. Before players are placed in the draw, top-four seeds have a 75% chance of that easier path.

Let’s attach some numbers to these speculations. I’m interested in the draw implications of three different seeding methods: ATP rankings (as every other tournament uses), the Wimbledon method, and weighted grass-court Elo. As I described last week, weighted surface-specific Elo–averaging surface-specific Elo with overall Elo–is more predictive than ATP rankings, pure surface Elo, or overall Elo. What’s more, weighted grass-court Elo–let’s call it gElo–is about as predictive as its peers for hard and clay courts, even though we have less grass-court data to go on. In a tennis world populated only by analysts, seedings would be determined by something a lot more like gElo and a lot less like the ATP computer.

Since gElo ratings provide the best forecasts, we’ll use them to determine the effects of the different seeding formulas. Here is the current gElo top sixteen, through Halle and Queen’s Club:

```1   Novak Djokovic         2296.5
2   Andy Murray            2247.6
3   Roger Federer          2246.8
5   Juan Martin Del Potro  2037.5
6   Kei Nishikori          2035.9
7   Milos Raonic           2029.4
8   Jo Wilfried Tsonga     2020.2
9   Alexander Zverev       2010.2
10  Marin Cilic            1997.7
11  Nick Kyrgios           1967.7
12  Tomas Berdych          1967.0
13  Gilles Muller          1958.2
14  Richard Gasquet        1953.4
15  Stanislas Wawrinka     1952.8
16  Feliciano Lopez        1945.3```

We might quibble with some these positions–the algorithm knows nothing about whatever is plaguing Djokovic, for one thing–but in general, gElo does a better job of reflecting surface-specific ability level than other systems.

The forecasts

Next, we build a hypothetical 128-player draw and run a whole bunch of simulations. I’ve used the top 128 in the ATP rankings, except for known withdrawals such as David Goffin and Pablo Carreno Busta, which doesn’t differ much from the list of guys who will ultimately make up the field. Then, for each seeding method, we randomly generate a hundred thousand draws, simulate those brackets, and tally up the winners.

Here are the ATP top ten, along with their chances of winning Wimbledon using the three different seeding methods:

```Player              ATP     W%  Wimb     W%  gElo     W%
Andy Murray           1  23.6%     1  24.3%     2  24.1%
Rafael Nadal          2   6.1%     4   5.7%     4   5.5%
Stanislas Wawrinka    3   0.8%     5   0.5%    15   0.4%
Novak Djokovic        4  34.1%     2  35.4%     1  34.8%
Roger Federer         5  21.1%     3  22.4%     3  22.4%
Marin Cilic           6   1.3%     7   1.0%    10   1.0%
Milos Raonic          7   2.0%     6   1.6%     7   1.7%
Dominic Thiem         8   0.4%     8   0.3%    17   0.2%
Kei Nishikori         9   1.9%     9   1.7%     6   1.9%
Jo Wilfried Tsonga   10   1.6%    12   1.4%     8   1.5%```

Again, gElo is probably too optimistic on Djokovic–at least the betting market thinks so–but the point here is the differences between systems. Federer gets a slight bump for entering the top four, and Wawrinka–who gElo really doesn’t like–loses a big chunk of his modest title hopes by falling out of the top four.

The seeding effect is a lot more dramatic if we look at semifinal odds instead of championship odds:

```Player              ATP    SF%  Wimb    SF%  gElo    SF%
Andy Murray           1  58.6%     1  64.1%     2  63.0%
Rafael Nadal          2  34.4%     4  39.2%     4  38.1%
Stanislas Wawrinka    3  13.2%     5   7.7%    15   6.1%
Novak Djokovic        4  66.1%     2  71.1%     1  70.0%
Roger Federer         5  49.6%     3  64.0%     3  63.2%
Marin Cilic           6  13.6%     7  11.1%    10  10.3%
Milos Raonic          7  17.3%     6  14.0%     7  15.2%
Dominic Thiem         8   7.1%     8   5.4%    17   3.8%
Kei Nishikori         9  15.5%     9  14.5%     6  15.7%
Jo Wilfried Tsonga   10  14.0%    12  13.1%     8  14.0%```

There’s a lot more movement here for the top players among the different seeding methods. Not only do Federer’s semifinal chances leap from 50% to 64% when he moves inside the top four, even Djokovic and Murray see a benefit because Federer is no longer a possible quarterfinal opponent. Once again, we see the biggest negative effect to Wawrinka: A top-four seed would’ve protected a player who just isn’t likely to get that far on grass.

Surprisingly, the traditional big four are almost the only players out of all 32 seeds to benefit from the Wimbledon algorithm. By removing the chance that Federer would be in, say, Murray’s quarter, the Wimbledon seedings make it a lot less likely that there will be a surprise semifinalist. Tomas Berdych’s semifinal chances improve modestly, from 8.0% to 8.4%, with his Wimbledon seed of No. 11 instead of his ATP ranking of No. 13, but the other 27 seeds have lower chances of reaching the semis than they would have if Wimbledon stopped meddling and used the official rankings.

That’s the unexpected side effect of getting rankings and seedings right: It reduces the chances of deep runs from unexpected sources. It’s similar to the impact of Grand Slams using 32 seeds instead of 16: By protecting the best (and next best, in the case of seeds 17 through 32) from each other, tournaments require that unseeded players work that much harder. Wimbledon’s algorithm took away some serious upset potential when it removed Wawrinka from the top four, but it made it more likely that we’ll see some blockbuster semifinals between the world’s best grass court players.