Thursday, 4 July 2013

Conventional Tennis Strategy Wins Out.

Aside from partnering John McEnroe to seven Grand Slam doubles titles, Peter Fleming was also noted for his uncompromising second serve in which accuracy was sacrificed for power. Although the tactic of using power on both first and second serves is open to anyone, it is seldom used apart from as an occasional surprise, or desperation tactic. The payoff between a reduced second serve success rate and an increased chance of winning the subsequent rally because of the greater power of the initial shot of that rally has yet to be tested in top class competition.

The changed aesthetics of the game that would result from a likely shorter, serve volley spectacle, especially on the faster grass courts of Wimbledon would probably not be welcomed by spectators, but we can use maths to see how close the current game has come to make the adoption of such a tactic potentially profitable.

To calculate the likelihood of winning a point under the two different serving scenarios, the traditional fast serve followed by a slower one and one using two full bloodied "first" serves, we need to know four things.
These are;

The Probability of a Fast Serve not being a Fault, (F(nf)).
The Probability of a Slower Serve not being a Fault, (S(nf)).
The Probability of winning the point following a successful Fast Serve, (F(wp))
The Probability of winning the point following a successful Slower Serve, (S(wp)).

These probabilities are easily pulled for the top players from the various tennis stats websites. For F(nf) the top ranked players hit around 64%, S(nf) is in the region of 90% and F(wp) and S(wp) are 75% and 56% respectively.

Now we need to map out the two routes for each scenario that lead to a player winning a point. For the traditional fast/slow routine she can serve a successful fast serve (with probability of 0.64) and win the subsequent point (with probability of 0.75). The probability of this occurring is 0.48

In addition she can serve a first serve fault (with probability (1-0.64)) followed by a successful slower second serve (with probability of 0.9) and then win that subsequent point (with a probability of 0.56). Overall, a probability of 0.18 for this route to a winning point for a combined likelihood for both routes of 0.66.

The adventurous use of two fast serves follows the same sequence as above except that the slower second serve is replaced by a fast, conventional first serve (with probability of 0.64) and an enhanced probability of winning the point of 0.75 instead of just 0.56. Overall this commitment to speed and brevity gives the generic, top class player a point winning probability of a marginally inferior 0.65.

Wimbledon can look forward to longish rallies for the moment.
Therefore, by happy accident rather than design the current court dimensions and tennis equipment leads to the conventional, more rally friendly serving strategy having a small, but cumulative and often repeated advantage over a power orientated alternative. Federer's dominance may be declining, but longer, second serve induced rallies, especially in the men's game and on the faster courts are still hanging on in there.

I've added some player specific figures from 2013 here.


  1. Would be interesting to calculate this for players individually. I can imagine big servers (like Isner e.g.), should already be playing 2 fast serves. Well actually, I don't know, that's why it would be interesting :P.

  2. Great idea,
    I'll check out the Wimbledon site and post up some player specific scenarios.