A friend and I have been looking at the total games lines for mens’ Wimbledon matches this week in the hope for some arbitrage opportunities, so I collected some data on past matches at Wimbledon tournaments to help guide our research. While the original intention was to find out the probability of different games totals for Wimbledon matches, i ended up stumbling upon something far more interesting:** an odd number of total games has a 57.9% chance of occurring for a match expected to be one-sided. **You can bet on odd or even total games with a few bookmakers, and I fully expected the distribution between even and odd total games to be around 50:50, but the result was quite surprising.

Above is the table I collated for past mens’ Wimbledon tournaments, with the second top row indicating the pre-match odds of the favourite. There are 1745 matches in the dataset, with 447 of those matches having a pre match favourite with odds between $1.00 and $1.11, corresponding to approximately a 90% chance or greater of winning the match. If you look down the the columns, you will see the frequency with which total game amounts occur (There are results past 54 total games but I could not quite capture the whole table in a screenshot. Sorry John Isner and Nicholas Mahut). When the favourite is given a 90% or greater chance of winning, then scorelines leading to a total of 25, 27, 29, and 31 games are the four most common results. 259 of the 447 matches ended up with an odd number of total games, which is 57.9% of matches.

**Odd and Even total games frequencies for past Wimbledon tournaments. Top row is pre-match odds of the favourite.**

It seems like such an odd result (pun intended) and I was scratching my head to why it showed up. I trawled through my spreadsheet looking to see if i had made a syntax error somewhere but I could not comprehend why that why even lead to biasing an odd amount of total games.

I subsequently looked at the Australian Open to check whether i had made a mistake, whether it was just a Wimbledon thing, or if it is just more likely for an odd number of total games for one-sided Mens’ grand slam matches. The Australian Open dataset revealed the same bias towards odd total games, however it wasn not as strong.

Above contains the data for Australian open one sided mens matches, where the favourite is given a 90% or greater chance of winning. 104 of the 198 matches ended up with an odd number of total games, or 52.5%, which is not nearly as strong as the effect at Wimbledon, and has a much greater chance of being attributed to random variation compared to the Wimbledon bias.

I’m still not *completely *convinced by the phenomenon, but it sure is weird. My guess is that the the slight differences created by a grass surface change the probabilities of breaking and holding serve such that different games totals become slightly more or less likely. I found a total games middle where you could bet under 37.5 total games at one bookmaker, and over 36.5 total games at one bookmaker, however i then noticed that that the probability of 37 total games occurring is quite low. If you look at the two tables below you will see that a total of 37 games is quite a rare total, at least relative to either 36 or 38 games. Random variation, or just a less likely combination of set results?

Ultimately, this is not an insightful result, just a fun little oddity, and something which initially seemed bizarre when i first noticed it. If you are really keen, and confident in the above result, then you could make a small profit margin by betting on total games in one-sided Wimbledon matches to be odd. Riveting stuff!

**Notes**

Source: http://www.tennisexplorer.com