Listen to the commentary during tennis tournaments and you’ll hear a lot about “living up” or “playing up” to one’s seed. In other words, a seed implies a certain level of performance. If you’re #10, you should reach the round of 16, but it would take an upset to get to the quarterfinals.
Of course, most players aren’t that consistent. Sometimes they beat expectations (even Igor Kunitsyn won a tournament) and sometimes they crash out early (hello, Andy Murray!). While guys like David Ferrer seem to steer a middle course, each player’s ranking is really just a weighted average of the tournaments where they ruled the world and the events where they shouldn’t have gotten out of bed.
And the more you think about it, the more the notion of “living up to your seeding” falls apart. In order for the top seed at a tournament to meet expectations, he has to win. That happens considerably less than half the time. For the second seed to go home happy, he needs to reach the final. But with rare exceptions, someone who lost in the final every week would quickly amass enough ranking points to be #1. So at least at the top, we shouldn’t expect that level of consistency. Also, the whole idea sets the same expectations for the 9th seed as the 16th, the 17th seed as the 32nd. We can do better.
I looked at the last 20 years of slam results and figured out the average result for every seed. In that time span, the top seed has won 5.0 matches per slam–on average, then, he has lost in the semifinals. That number has increased since the majors started seeding 32 players in 2002: In the last 10 years, the top seed has won 5.3 matches per slam, as he has generally coasted through the first two rounds.
Here’s a look at how each seed has done over the last 20 years. After the top few guys, no one should be expected to reach the quarters–certainly not the #8 seed!
Seed Wins 1 5.0 SF 2 4.2 QF+ 3 3.7 QF- 4 3.4 R16+ 5 2.7 R16- 6 2.9 R16- 7 2.5 R32/R16 8 2.1 R32+ 9 2.5 R32/R16 10 2.7 R16- 11 2.2 R32+ 12 2.6 R16- 13 2.1 R32+ 14 2.2 R32+ 15 2.1 R32+ 16 1.6 R64/R32 17-32 1.6 R64/R32 UNR 92-01 0.7 R64- UNR 02-11 0.6 R128/R64
A more sophisticated way of looking at this is with probabilities. Sure, the smart money is on the top seed winning five matches, but beyond knowing that he wins the tournament between 35 and 40 percent of the time, what are the odds that he reaches the final? Crashes out early?
Here are those odds for the same sets of players:
Seed R64 R32 R16 QF SF F W 1 97.3% 90.5% 83.8% 75.7% 62.2% 48.6% 36.5% 2 88.5% 78.2% 70.5% 60.3% 51.3% 34.6% 24.4% 3 93.5% 80.5% 70.1% 57.1% 36.4% 19.5% 5.2% 4 84.4% 75.3% 64.9% 55.8% 39.0% 14.3% 7.8% 5 84.2% 71.1% 47.4% 36.8% 15.8% 7.9% 2.6% 6 84.2% 67.1% 56.6% 38.2% 21.1% 13.2% 7.9% 7 81.3% 69.3% 52.0% 32.0% 16.0% 4.0% 0.0% 8 80.3% 61.8% 47.4% 22.4% 2.6% 1.3% 0.0% 9 86.3% 70.0% 53.8% 28.8% 13.8% 5.0% 0.0% 10 88.2% 69.7% 52.6% 31.6% 10.5% 5.3% 2.6% 11 93.2% 63.0% 34.2% 15.1% 4.1% 1.4% 0.0% 12 84.8% 70.9% 51.9% 34.2% 19.0% 5.1% 2.5% 13 79.5% 61.5% 48.7% 12.8% 7.7% 3.8% 2.6% 14 82.7% 60.0% 42.7% 18.7% 9.3% 2.7% 0.0% 15 81.8% 67.5% 41.6% 15.6% 7.8% 3.9% 0.0% 16 72.7% 44.2% 28.6% 7.8% 5.2% 2.6% 1.3% 17-32 72.5% 51.8% 19.7% 8.2% 2.2% 0.9% 0.4% UNR 92-01 42.6% 15.8% 5.7% 1.9% 0.6% 0.2% 0.0% UNR 02-11 40.1% 12.8% 4.3% 1.2% 0.4% 0.2% 0.0%
The same sample of no more than 80 slams means that these numbers don’t give us a smooth curve, but they still provide a pretty good idea. In fact, they look awfully similar to my pre-tournament slam predictions, with the exception of the big gap between the top two seeds and the rest of the field.