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.
Cheap Talk 
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September 1, 2009 at 1:33 am
Shrik
I wouldn’t mess with the scoring in tennis. It remains one of the few sports where a player (or a team) down 0-6, 0-6, 0-5 (40-0) can still mount a comeback. i.e. there are no temporal constraints as such like say in basketball/football (time – 27 points down/3 goals down and 20 seconds left on the clock? Yeah ok tyvm..) or cricket (56 runs to win, 1 over left..)
September 1, 2009 at 1:08 pm
Vinnie
I think the player whose actual abilities would be most distorted by his match win-loss record would be the player that freezes up in the clutch. Then again, the conventional wisdom is that such players don’t exist on the highest professional levels. The talented chokers are coaching in a high school somewhere.
Another potential distortion caused by incentives–and one that applied to my (totally un-noteworthy) high school tennis career–is the tendency to lose patience after dropping a hard-fought first set. Because (as Jeff points out), you get squat whether you lost 6-0 or 7-6, the letdown and fatigue after a close loss are immense. My usual reaction was more or less, “F— it. All winners next set.” One way or another, I wanted to keep the points short so that I didn’t have to move my feet much. If I was in a zone that day, I’d get a third set; if not, I’d slam my racket, utter some obscenities, and get on with life. I bet you can guess the more common scenario. Again, though, you don’t get to the U.S. Open by being a defeatist slouch.
November 19, 2009 at 3:50 pm
Walter
Very interesting, I thought it was worth crunching some numbers on this one. Let’s say the weaker player can win points 45% of the time. You need to win 4 out of 7 points in a game of tennis (let’s call this no-ad scoring to simplify). The “Cumulative Probability” of 4 or more successes in 7 tries is 0.39 or 39%.
This means the weaker player, just by chance will win 39% of games.
Now a 39% game win rate applied to 7 out of 13 games per set (again, to simplify I’m counting a tiebreaker as a regular game) gives a cumulative probability of 21%.
Not bad! The consistently weaker player is expected to win 21% of sets!
Finally, applied one more time to best of 3 sets, gives an 11% result.
The weaker player can expect to beat the stronger player 1 time out of 9!
You’re correct that in a cumulative scoring, timed event such as basketball, a consistently weaker team wouldn’t have such success, and you have to find other ways to explain a loss – whether you call it a hot streak, choking, bad coaching, whatever! I know the law of big numbers comes into play, but if you’ve ever simulated a random walk you know you can “end up” very far from the origin too….
November 30, 2009 at 10:09 am
Tim Randall
The important thing to take into account when considering tennis scoring is the qualified two-point lead. To win a game, you need to be two points ahead (and have won four). To win a set you need to be two games ahead (and have won at least six), and to win a tie-break to take a set, you need to be two points ahead (and have won at least six).
If both players have scored enough points but haven’t got the necessary two-point lead, the game (or set) can go on indefinitely. The requirement to demonstrate superiority in this particular way is, I think, unique to tennis.
March 18, 2014 at 7:54 pm
Eslah
Thanks for sharing. Your post is a useful coortibutinn.