The Structural Biases of Tiebreaks

There is more to tiebreaks than meets the eye. As we’ve learned recently, big servers don’t seem to have an advantage in tiebreaks over more balanced players, and very few professionals win more tiebreaks than we would expect them to.

In one of those discussions, commenter Håkon Mørk raised a related issue. Is the format of the tiebreak itself biased toward certain types of players? That is: Who benefits by playing tiebreak sets instead of “deuce” sets in which one player must win by a margin of two games?

When we put the question this way, it is straightforward. The primary beneficiaries of the tiebreak format are underdogs.

Think of it this way. The better player is likely to win, regardless of the format. The bigger the margin of victory required, the more likely the better player is to win. If Kenny De Schepper were to play a single tiebreak against Roger Federer, he’d have a decent chance of winning. But in a full-length set, that chance would be much lower. In a best of three match, lower still. Best of five: even lower. Best of five with no tiebreak in the final set: lowest of all.

Any change in the format of a tennis match that causes the match to hinge on fewer points gives the underdog a greater chance of lucking his way into victory.

On average, the underdog’s benefit from tiebreak sets isn’t much, compared to a hypothetical world in which the ATP played only deuce sets. For an individual set in the average tour-level 2012 match, the underdog’s chance of winning was 1.3% higher in a tiebreak set than they would have been in a deuce set.

But there’s more to the story. First of all, matches that are very close (in which both players win about 50% of points) drag down the average, since when the players are evenly matched, the format doesn’t matter — 50% is 50%. Second, matches that are very lopsided also drag down the average–if one player dominates, he has a very high percentage chance of winning a set regardless of the format.

Thus, in a somewhat closely (but not too closely) contested match, the underdog gains quite a bit more from the tiebreak format.

Structural biases

In some of these matches, the gain is much more than in others.

In fact, in six matches this year, the difference between the winner’s chance of winning a deuce set would have been more than ten percent greater than his chance of winning a tiebreak set.

(All of the chances I’m referring to are derived by calculating the winner’s winning percentages on serve and retun points, then running those through my set probability python code, which now provides an option for the probability of winning deuce sets.)

Two of the three most extreme such matches this year (and five of the top 14) were won by–could it be anyone else?–John Isner.

The most extreme case is Isner’s match against Janko Tipsarevic in the London Olympics. Isner won 84.7% of service points and 23.3% of return points, ultimately taking the match 7-5, 7-6(14). Those percentages translate to a 71.1% chance of winning a tiebreak set or an 84.1% chance of winning a deuce set.

If you were Isner, which would you prefer?

Compare that to a match between Jo Wilfried Tsonga and Xavier Malisse at the Miami Masters, which Jo won 7-5 7-5. This match went very differently than Isner-Janko. Tsonga won 68.1% of service points and 43.1% of return points. Those would give the Frenchman an 84.1% chance of winning a deuce set (sound familiar?) or an 82.7% of winning a tiebreak set.

This is just another illustration that fewer pivotal points gives the underdog a better chance. To win a tiebreak against Isner, you need to win one point against his serve (as long as you hold your own). To break an Isner service game, you need to win at least four.

Thus, an extreme big server like Isner appears to suffer from the tiebreak format. If the ATP went back to playing every set as a deuce set, he would have a much better chance of avoiding the lucky upset when he posts stats like those of the Janko match.

The big-serving underdog

There’s still more to this story. As we’ve seen, underdogs benefit from the tiebreak format: A structure with fewer points is more susceptible to luck. And big servers seem to be hurt by the tiebreak format.

What about when big servers are underdogs?

The tiebreak format isn’t biased against big servers, it’s biased against big servers who are better than their opponents. In matches already decided by a small number of points (like a couple of break points or minibreaks in an Isner-Federer match), the underdog benefits from playing tiebreaks.

And when one player has the big-serve/weak-return package, he effectively turns the other player into a bigger server and weaker retuner. We don’t usually think of Philipp Kohlschreiber as a big server, but when he played the serve-and-volleying Dustin Brown in Halle this year, he won 82.1% of service points and only 29.9% of return points. That type of match hinges on a very small number of points, and as such, gives the underdog a greater chance to pounce.

More mathematically speaking, the degree of the advantage given to the underdog by playing tiebreak sets is positively correlated with the overall percentage of service points won.

This presents something a conundrum for the big server. His style of play is beneficial in tiebreak sets while he is the underdog, but it becomes a hindrance once he is the favorite. When so many matches are decided by a single break or even a couple of minibreaks, a big-serving, weak-returning favorite will lose more than his share of matches he “should have” won, simply because of the way he plays.

One solution for such players is to win more tiebreaks than the numbers would suggest they should, as Isner does. Another tactic, of couse, is to hit better returns.

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10 Comments

Filed under John Isner, The Rules, Tiebreaks

10 responses to “The Structural Biases of Tiebreaks

  1. You raise some very interesting points in this article! I always hate watching tiebreaks because they generally mean that the player I’m backing loses a key set, especially since my favourite player is Federer and of late his game level fluctuates more than the stock markets. I also don’t personally enjoy the very idea of a tiebreak because, as you so eloquently illustrated, they tend to favour the underdog and general good fortune – I don’t like the idea that a large portion of a well-fought tennis match can suddenly hang on a few poor serves/returns. Then again it’d also be nice if there were no lines on the tennis court but what are you doing to do!?

  2. Excellent, complete analysis. I think it argues for the tiebreaker being good for the sport, since tennis is a game in which upsets of top players happen infrequently.
    Would it be interesting further evidence for your analysis to look at the percentage of sets lost in breakers by narrow favorites in close contests vs. the percentage of sets they lost in breakers to opponents over whom they were heavily favored?
    Rick

    • I hadn’t thought about that. It would certainly be interesting to know. Seems like all of the top guys have had their share of head-scratching tiebreak-set losses to much inferior players, even if they came back to win the match decisively.

  3. stebs

    Hi Jeff,
    this is actually unrelated to this specific (and excellent) analysis. I was meandering through some of your archives and saw the article conjecturing about why the ATP is more popular than the WTA. Do you have any good reasons for believing this to be the case? I think it is true as well, but can you confirm that as a fact?

    Thanks,

    Stebs

    • Nope, nothing I can cite offhand. If you ever go to a slam, there are consistently more people watching men’s matches than women’s matches, often a drastic difference. I think I read something making a much stronger case around the time I wrote that article, but can’t find it now.

  4. Tom Welsh

    Well, for what it’s worth, the three women in my family prefer watching men’s tennis to women’s. (I don’t watch women’s matches at all). Why? Well, almost everything good players do, the top men do better than the top women. (Without the shrieking).

    • That’s essentially why I shifted my balance from 50-50 to 90-10.

      What’s interesting, though, is that many die-hard WTA fans explain their preference with almost exactly the same reason. People have told me they prefer slower-paced, less flawless tennis, particularly since it can lead to longer rallies. One guy even told me that he views high-school girls’ tennis as the most enjoyable level of the sport.

  5. “[The big server's] style of play is beneficial in tiebreak sets while he is the underdog, but it becomes a hindrance once he is the favorite. When so many matches are decided by a single break or even a couple of minibreaks, a big-serving, weak-returning favorite will lose more than his share of matches he “should have” won, simply because of the way he plays.”

    I guess I’m a bit confused here. I agree with the second sentence, but not the first – at least, not when you have two big servers facing off, one of whom is a poor-returning underdog, and the other of whom is the favorite because he has more than just the big serve.

    I’m thinking in particular of the Del Potro v. Anderson match I watched last week. Anderson was doing very well in the first set holding serve, and playing reasonably well in his return games, but not returning nor rallying (in the few rallies that occurred) as well as Delpo. Neither player was threatening to break the other, and one might have thought that Anderson would have a decent chance in the tiebreak simply because he was serving so outrageously well that day. But my gut conviction before a single point of the tiebreak was played was that Anderson would lose, simply because compared to Delpo, he is a weaker returner and rallier. So it proved.

    • Well, the more I think of it, the more I’ve made a muddle of my reply. Delpo doesn’t fit the type of server you’re talking about so it makes no sense to throw him into the mix here.

      • Well, let me try to shed some light.

        It’s perhaps overly complicated to talk about types of players, since really we’re talking about types of matches. When *either* player has a big serve/weak return combo (as KA does), it turns the entire match into more of a server-friendly match than average. In your example, KA’s serving makes Delpo a worse returner than usual, and KA’s returning makes Delpo a better server than usual.

        (When you have two such players, like KA vs Isner, the effect is even more extreme.)

        In the match you’re talking about, remember that I’m not saying KA is particularly likely to win, just that he is much more likely to win in a tiebreak than in a deuce set. If he’s rallying poorly, he’s not likely to win either one, but in a tiebreak he could hit a bunch of aces and take advantage of a single double fault or weak point from Delpo. But in a deuce set, he’d need to string a whole game together to break Delpo.

        Or perhaps most to the point: In the first sentence you quote, “beneficial” just means that the big-serving style of play makes breaks and minibreaks less likely, making it more likely that the match will hinge on luck. And in cases like Delpo vs KA, luck is really the only way KA will win.

        On Thu, Nov 1, 2012 at 3:21 PM, Heavy Topspin: A Tennis Blog

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