How Five Sets Favours Grand Slam Favourites

How Five Sets Favours Grand Slam Favourites

By Jack Ratcliffe Dec 18, 2012

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The Australian Open marks the first Grand Slam of the 2013 tennis season, and gives ATP players their first five-set matches of the year. Obviously the extra sets affect Australian Open betting, but did you know it could make the favourite almost 5% more likely to prevail?

The difference between Grand Slam best-of-five sets versus traditional best-of-three sets is obvious when the outcome of a set is reduced to a simple win percentage for each player.

Consider a match between two players – “A” and “B”, where “A” will win each set 60% of the time. If the probability of A to win each set (W) equals 0.6, and the odds of him not winning a set (L) are 0.4, then the odds him winning a three-set match are:

A = (w*w) + (w*l*w) + (l*w*w)

The above three terms mathematically depict the three possible ways to win a three-set match. Player A can win the first two sets (w*w), the first and third set while losing the second (w*l*w), or lose the first and win the last two sets (l*w*w).

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Therefore the odds of “A” winning this match up are:

A = 0.6*0.6 + (0.6*0.4*0.6) + (0.4*0.6*0.6) = .648 or 64.8%.

Due to the extra sets that must be played in a five-set match, the calculation is slightly more complicated. Player A can win the match in three ways: win 3 straight sets; win 3 sets to 1, or win 3 sets to 2.

There is only one possible way to win 3 straight sets (w*w*w). There are 3 possible ways to win 3-1 (w*l*w*w), (l*w*w*w) and (w*w*l*w). There are also six ways for the match to end 3-2 (w*l*l*w*w), (w*w*l*l*w), (l*l*w*w*w), (l*w*w*l*w), (l*w*l*w*w) and (w*l*w*l*w).

Therefore, the odds of “A” winning a best of five match are:

A = (w*w*w) + (w*w*w*l)*3 + (w*w*w*l*l)*4

A = (0.6*0.6*0.6) + (0.6*0.6*0.6)*(0.4)*3 + (0.6*0.6*0.6)*(0.4*0.4)*6 = 0.683 or 68.3%

This example shows how much of a difference it makes in playing a best of five versus a best of 3. And this is only if Player A has a 60% chance of winning each set – the greater the difference in skill level, the bigger advantage the better player has over five sets.

A Practical Example

A potential – although simplistic – method for calculating a player’s probability of winning a set is to take his head-to-head record with his opponent, add together how many sets each player has won against the other and work out their win percentage.

For example, before the 2012 ATP World Tour Finals, Federer had won 11 sets over Novak Djokovic in the last three years, while the Serbian had taken 17 sets from his Swiss counterpart. That means Federer held a 39.3% record compared to Djokovic’s 60.7%.

Using these figures as the probability for a player to win a set and inputting it into the above formula, this suggests that there was a 69.5% chance that Djokovic would prevail over Federer – which proved true.

The odds at Pinnacle Sports for the contest were Djokovic at 1.637, which implied a probability of 61.1%.

Other Uses Outside Tennis

Aside from tennis, you can also use this method of analyzing matches to set lines for any series bet, or many prop bets such as “Will the Yankees win its playoff series in exactly 6 games?”

Once you have the tools in place to analyze these kinds of problems, you’ll be surprised at how many opportunities present themselves to gain an edge over the bookmaker. Often bargains can be found on American sports’ series plays, where you are laying 1.250 or greater, since these types of bets mainly attract underdog money from public bettors.

*Odds subject to change

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