Millimeters

During the Tsonga vs Federer Aussie Open semi final Chris Fowler saw a Shot Spot replay of a ball 2 mm wide and said "We often hear that tennis matches are decided by millimeters. There's an example."

So is it true that tennis is a game of inches? Are matches decided by the slimmest of margins? Do matches turn on a crucial point?

The accepted wisdom is that yes, tennis is a game of inches and that matches hinge on pivotal points or moments. I'm suspicious.

I think the vast majority of matches are not decided by such things. Several years ago I wrote a little program to play simulated tennis matches. I used no-ad scoring to simplify my programming (I'm not a programmer). I played simulated 2 out of 3 tie-break set matches between players of varying skill. I varied the skill by varying the probability of each player winning a point. The greater the relative probability of winning any point, the greater the relative skill. Simple enough. Objective.

So I played matchees between evenly matched opponents, each having a 50-50 chance of winning any given point. Then I gave one player a 51-49 edge and ran a hundred matches or so. I did this up to a 60-40 edge where it was no longer interesting. Why not? Because the 60% player won every set easily.

My take on this after doing all my simulations is that tennis is not a game of inches and does not turn on big points most of the time. I think a better, though less dramatic, way to think of tennis is as a game where small advantages accumulate. The better player is more likely to win the longer the match. That's why Federer is so hard to beat in best of 5 set matches. He's better than his opponents so his advantage grows the longer the contest.

If you're going to beat Federer in a match, make it as short as possible. If you're going to beat Tiger Woods in golf, play him over one hole, not 72.

I did one other thing, too, to test the turning points theory. I charted a few matches, juniors and professionals. I had point-by-point data. I compared the accumulation of points to a random-walk and couldn't tell the difference. The random-walk point patterns looked indistinguishable from the randomly generated point sequences. So much for dramatic turning points in matches.