Rating the Rankings

With her win on Saturday in the Australian Open final--Serena Williams jumped from #7 to #2 in the official WTA Rankings. Lindsay is still #1 despite her loss. My friend Craig Cochrane pointed out that the 2004 year end WTA rankings don't accurately reflect the relative strength of the tennis players on the tour. Here's the year-end ranking:

1. Davenport
2. Mauresmo
3. Myskina
4. Kuznetsova
5. Dementieva
6. Sharapova
7. Henin-Hardenne
8. Williams, S.
9. Williams, V.
10. Capriati
11. Zvonareva
12. Petrova

Alicia Molik is #13. However, if you were to just consider the Win-Loss records of the best players for 2004, you would obtain this different list:

1. Davenport, 63-9 (87.5%)
2. Mauresmo, 63-11 (85.1%)
3. S. Williams, 39-9 (81.3%)
4. Sharapova, 55-15 (78.6%)
5. V. Williams, 44-12 (78.6%)
6. Myskina, 55,-18 (75.3%)
7. Kuznetsova, 60-23 (72.3%)
8. Capriati, 29-12 (70.7%)
9. Molik, 46-20 (69.7%)
10. Zvonareva, 54-27 (66.7%)
11. Dementieva, 39-23 (62.9%)
12. Petrova, 40-25 (61.5%)

Technically, Henin-Hardenne has the best Win-Loss record of 2004, with 35-4 (89.7%) but she played the least matches of any player ranked in the Top 10 by the WTA last year. I'm not arguing that the WTA should switch to only considering Win-Loss percentages but the points system used by the Tour does seem to produce anomalous results (Dementieva ranked #5? Serena ranked #7?).

The question is, what information does one want to obtain from the rankings? The answer is, who is the best player, right now? In other words, when two players meet one should expect the higher ranked player to win more often than not. The highest ranked player should be the person who is least likely to lose to any other person playing. Of course, these ratings must vary with time, so that as results happen, the ranked order changes.