The Summer of Jeff

Single Game Win Expectancy Tables

Posted in tennis by Jeff on December 3, 2010

Compared to working out the single set tables, this was a breeze.

For each score, I’ve shown three sets of two columns.  The numbers (0.60, 0.65, and 0.70) refer to the estimated percentage of service points won.  In my set tables, I assumed that the players were equal; here, we don’t have to.  A 65% estimate might be the result of a very good server facing a very good returner, or the result of a weak server facing a weak returner.

The first of the three estimates, “0.60,” refers to a situation where a server doesn’t have a big edge.  Yesterday I called that my “clay court” estimate.  The second, “0.65” is a bit above the ATP average, and might be appropriate as a general hard court table.  The third, “0.70,” reflects a dominant server.  Only three players sustained that level for the entire 2010 season.

Here you go:

          0.60            0.65            0.70                                                
Score     p(W)   p(L)     p(W)   p(L)     p(W)   p(L)  
00-00    73.6%  26.4%    83.0%  17.0%    90.1%   9.9%  
00-15    57.6%  42.4%    68.9%  31.1%    78.9%  21.1%  
00-30    36.9%  63.1%    47.7%  52.3%    58.8%  41.2%  
00-40    15.0%  85.0%    21.3%  78.7%    29.0%  71.0%  
15-00    84.2%  15.8%    90.5%   9.5%    94.9%   5.1%  
15-15    71.4%  28.6%    80.4%  19.6%    87.5%  12.5%  
15-30    51.5%  48.5%    61.9%  38.1%    71.6%  28.4%  
15-40    24.9%  75.1%    32.8%  67.2%    41.4%  58.6%  
30-00    92.7%   7.3%    96.0%   4.0%    98.0%   2.0%  
30-15    84.7%  15.3%    90.3%   9.7%    94.4%   5.6%  
30-30    69.2%  30.8%    77.5%  22.5%    84.5%  15.5%  
30-40    41.5%  58.5%    50.4%  49.6%    59.1%  40.9%  
40-00    98.0%   2.0%    99.0%   1.0%    99.6%   0.4%  
40-15    95.1%   4.9%    97.2%   2.8%    98.6%   1.4%  
40-30    87.7%  12.3%    92.1%   7.9%    95.3%   4.7%  
40-40    69.2%  30.8%    77.5%  22.5%    84.5%  15.5%

Note that the scores “Advantage [server]” and “Advantage [returner]” are logically equivalent to 40-30 and 30-40, respectively, so their win expectancies are the same. (30-30 and 40-40 are equivalent, as well, but it seemed wrong to leave “deuce” out of the table.)

One major limitation of these tables is that is does not distinguish between the “deuce” and “ad” sides of the court.  For some players, there probably isn’t much of a different, but for others–especially lefties–there certainly is.  If there is some general tendency toward better serving in one direction or the other, that would affect some of the percentages above.

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  1. [...] If you’re joining in progress, here’s an intro, along with single set tables and single game tables. [...]

  2. [...] factor working in the other direction is that of strategy.  As we saw in the single-game probability table, a reasonably good server at 30-0, 40-0, or 40-15 has little to fear.  Nobody is tanking points [...]


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