In a recent post for FiveThirtyEight, Carl Bialik covered this topic, referring to matches in which a player wins, despite winning fewer points, as a "lottery match". Using data from Tennis Abstract, he found that 7.5 percent of mens' matches ended in this way.
For this post, I will take a closer look at these lottery matches and use it to define a "luck" measure for tennis, which will be added to my tennis win probability graphs.
Using data from Matchstat (ATP matches from 2008-2013), I looked at how often a player wins a match as a function of the percentage of points that were won. The table below summarizes the results, split by whether the match was a best of 3 or best of 5 format.
|best of 3||best of 5|
|% points won||matches||% won||matches||% won|
As you can see, the chances of winning the match accelerates rapidly as a function of points won, where winning at least 53% of points will virtually guarantee a match victory.
I took this same dataset and built a simple logistic regression model that quantifies the probability of winning the match as a function of the percent of points won. Here are the formulae:
- Best of 3 Sets:
- match win probability = 1 / ( 1 + exp(-128 * MOV))
- Best of 5 Sets:
- match win probability = 1 / ( 1 + exp(-154 * MOV))
MOV stands for "margin of victory", and it is the percentage of points won, minus 0.5.
For my tennis win probability graphs, I convert the probability into odds and call this "luck". So, the higher the "luck" factor, the more unlikely the result of the match. The luck factor is now a sortable option for my Top Match Finder. For example, here is the luckiest match of the Wimbledon Womens Singles: Irena-Camelia Begu's three set victory over Virginie Razzano.
Begu won the match despite having won just 47.7% of the points (a net point differential of -9).
Using data from Matchstat, the luckiest match in ATP play from 2008-2013 was Juan-Martin Aranguren's 6-3, 0-6, 6-4 victory over Carlos Berlocq in 2010 at Orbetello, in which Aranguren won just 44.4% of points in the match. The odds of winning a best of 3 match with only 44.4% of the points is 1300 to 1 (or a probability of 0.08%).