I blogged about this before and in honor of the start of the French Open I gave it some thought again and here are two ideas.

**Deuce**. Each game is a race to 4 points. (And if you are British 4 = 50.) But you have to win by 2. Conditional on reaching a 3-3 game, the deuce scoring system helps the stronger player by comparison to a flat race to 4. In fact, if being a stronger player means you have a higher probability of winning each point then any scoring system in which you have to win by n is better for the stonger player than the system where you only have to win by n-1.

You can think about a random walk, starting at zero (deuce) with a larger probability of moving up than down, and consider the event that it reaches n or -n. The relative likelihood of hitting n before -n is increasing in n.

This is confounded by the fact that the server has an advantage even if he is the weaker player. But it will average out across service-games.

**Grouping scoring into games and sets**. Suppose that being a stronger player means that you are better at winning the crucial points. Then grouped scoring makes it clear which are the crucial points. To take an extreme example, suppose that the stronger player has one freebie: in any match he can pick one point and win that point for sure.

In a flat (ungrouped) scoring system, all points are equal and it doesn’t matter where you spend the freebie. And it doesn’t change your chance of winning by very much. But in grouped scoring you can use your freebie at game- or set-point. And this has a big impact on your winning probability.

Conjecture: freebies will be optimally used when you are game- or set-point *down, *not when it is set-point in your favor. My reasoning is that if you save your freebie when you have set-point, you will still win the set with high probability (especially because of deuce.) If you switch to using it when you are set-point down, its going to make a difference in the cases when there is a reversal. Since you are the stronger player and you win each point with higher probability, the reversals in your favor have higher probability.

Any thoughts on the conjecture? It should have implications for data. The stronger players do better when they are ad-down then when they have the ad. And across matches, their superiority over weaker players is exaggerated in the ad-down points.

My French Open forecast: This could be the year when we have a really interesting Federer-Nadal final.

## 4 comments

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May 24, 2010 at 12:56 pm

NikoJeff, you’re right that the scoring system helps better players, because weaker ones have to string together points. But the whole idea of clutch performance is bunk. Sure, better players perform better in the clutch than do lesser players, but that’s because they perform better all the time than the lesser ones do.

May 24, 2010 at 1:13 pm

jeff“Clutch performance” is just an interpretation. You don’t have to believe that better players find a higher gear when they need to. It is enough to assume that everyone can raise their standard of play at any moment but subject to a budget constraint. You have a stock of “energy” or “effort” or “focus” and you decide when to tap into it.

Then the assumption is that better players have a bigger stock. It is observationally equivalent to clutch performance.

May 27, 2010 at 9:53 am

NateYour point about winning by 2 sounds right – but the issue with service advantage makes it interesting. I’m not sure we can wave it off by saying it averages out in the long run. Suppose the service advantage is quite high (making the underdog player a medium-favorite to win his service games and the favorite player a virtual lock in his service games). In that scenario, the win by 2 deuce scoring has little impact when the favorite serves (prob. of winning already asymptotic to 100%) but has a big impact on the underdog service games (helps the underdog because he is a favorite with respect to his service game). In those cases, the deuce scoring gives the underdog an advantage over “win by 1” scoring in that there is a better chance they get to a 6-6 set tiebreak.

Also, I think that Niko is correct in that the clutch performance argument does not hold up.

May 28, 2011 at 7:35 am

French Open Notes « Cheap Talk[…] implication of a theory I have written about before is that a best of 5 set match confers a greater advantage on the stronger player than a best of 3 […]