The US Open is here. From the Straight Sets blog, food for thought about the design of a scoring system:

A tennis match is a war of attrition that is won after hundreds of points have been played and perhaps a couple of thousand shots have been struck.On top of that, the scoring system also very much favors even the slightly better player.

“It’s very forgiving,” Richards said. “You can make mistakes and win a game. Lose a set and still win a match.”

Fox said tennis’s scoring system is different because points do not all count the same.

“Let’s say you’re in a very close match and you get extended to set point at 5-4,” Fox said, referring to a best-of-three format. “There may be only four or five points separating you from you opponent in the entire match. And yet, if you win that first set point, you’ve essentially already won half the match. Half the match! And not only that — your opponent goes back to zero. They have to start completely over again. And the same thing happens in every game, not just each set. The loser’s points are completely wiped out. So there are these constant pressure points you’re facing throughout the match.”

There are two levels at which to assess this claim, the statistical effect and the incentive effect.  Statistically, it seems wrong to me.  Compare tennis scoring to basketball scoring, i.e. cumulative scoring.  Suppose the underdog gets lucky early and takes an early lead.  With tennis scoring, there is a chance to consolidate this early advantage by clinching a game or set.  With cumulative scoring, the lucky streak is short-lived because the law of large numbers will most likely eradicate it.

The incentive effect is less clear to me, although my instinct suggests it goes the other way.  Being a better player might mean that you are able to raise your level of play in the crucial points.  We could think of this as having a larger budget of effort to allocate across points.  Then grouped scoring enables the better player to know which points to spend the extra effort on.  This may be what the latter part of the quote is getting at.

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