Italian translation at settesei.it
I’m not sure how we got here, but we now live in a world where a lot of people consider a 10-point tiebreak equivalent to a set. Apparently it’s more fan-friendly and better for television. And of course it’s faster.
Whatever its practical uses, it’s obvious that the first-to-10 breaker isn’t the same as a set. I’ll leave the moral debate to others; let’s take a statistical approach.
In general, the more points (or games, or sets) required to win a match, the more likely it is that the better player wins. Some commentators have taken to calling the 10-point breakers “shootouts,” and for good reason. Reduce the number of points required to win, and you increase the role played by luck.
Of course, sometimes a shootout is the best idea. You’ve got to end a match somehow, and when players end up equal after two sets, four sets, or four sets and twelve games, it’s all the more likely that luck will have to intervene. But the structure of the match determines just how much luck is permitted to play a part.
To compare a 10-point tiebreak with the set it replaces, we need to know how much more luck it introduces into the game. For that, we need an example to work with.
Take two players: Player A wins 70% of points on serve, and Player B wins 67% of points on serve. Playing best of three tiebreak sets, Player A has a 63.9% chance of winning the match.
If A and B split sets, A’s probability of winning falls to 59.3%. In other words, the shorter time frame makes it more likely that B gets lucky, or is able to put together an unusually good run of play long enough to win the match.
If the match is decided by a 10-point tiebreak, however, A’s probability of winning falls all the way to 56.0%, erasing more than one-third of the favorite’s edge in the third set. In fact, the 10-point breaker is barely more favorable to A than a typical 7-pointer, in which A would have a 55.1% chance.
(If you like playing around with this stuff, see my python code to calculate tiebreak odds.)
Somehow I don’t think anyone would advocate replacing the deciding set with a 7-point tiebreak. Yet a 10-point tiebreak is much closer to its 7-point cousin than it is to a full set.
Adding a few more points doesn’t resolve the discrepancy, either. To maintain Player A’s 59.3% chance of winning, the third set would have to be replaced by a 26-point tiebreak. But that, I’m sure, wouldn’t attract many new advertisers.
Always with the facts and figures and sober analyses! Can’t you just be driven by fear and politics like the rest of us?
Who said I was sober?
Wow! Thanks for doing the math for those of us not so gifted! This is fascinating. The numbers tell the story.
Jeff – Good post on a topic that needed revisiting. I recall reading that before the SuperBreaker (10 points) was introduced instead of 3rd sets in doubles, the Bryans and most other top seeds were opposed to it on the grounds that they would lose more often than they would in a 3 settter. Their acceptance after a year was influenced by the results of a study of the first 12 months’ results of all matches between seeds and unseeded teams, indicating that seeded teams had won almost the exact same percentage of the time.
If this was this case then, I wonder if it’s continued to be the case, and if so, what might explain it.
Rick
That’s interesting–I’ll have to look that up. The gap between 10-point breakers and full sets may be smaller in men’s doubles because of the huge server advantage ( http://tennisabstract.com/blog/2012/07/08/how-underdogs-could-win-wimbledon-doubles/ ), which would mean that the third set is already a bit of a shootout. I’ll check the numbers on that.