The Luck of the Tiebreak

Yesterday, I introduced a method to separate “good tiebreak playing” from “good tennis playing.”  For the most part, better players win more tiebreaks, but some guys win more tiebreaks than their general betterness would suggest.

That impels some questions: Why do those players win more tiebreaks than expected?  Do they do so regularly?  Is it their style of play?  Is it magical tiebreak-fu?  Is it possible to get through two paragraphs of a post about tiebreaks without mentioning John Isner?

Here are two hypotheses, which I will discuss in turn:

  1. Players who win more tiebreaks than expected do so because their game is suited to tiebreaks–which probably means that they serve particularly well.
  2. Player who win more tiebreaks than expected do so because, in some intangible way, they are very good at tiebreaks, perhaps due to clutch play, calm under pressure, or intimidation of their opponents.

The server advantage hypothesis

Earlier this week, I reported my results that players seem to serve worse (fewer aces, fewer points won) in tiebreaks than in the sets that preceded those tiebreaks.  If everyone declined the same amount, everyone would win roughly the number of tiebreaks we expect of them.

But much more likely, some players do not see their serves decline in tiebreaks.  Some might even improve in breakers.  If they do, they outperform the average, and they win more tiebreaks than expected.

Another angle here is that for some players, a bit of serve decline doesn’t matter much.  In last week’s match between Isner and Kevin Anderson, Isner won 79% of service points and Anderson won 77%.  Nearly one in five serves for the entire match went for aces–imagine how many more were service winners.  If both players served a bit more conservatively in the breakers, would we even notice?  When Fernando Verdasco starts playing it safe, it’s impossible not to notice–and easier to beat him in a breaker.  Perhaps that isn’t so for the likes of Isner.

These are appealing theories.  (Especially to me–I thought them up myself and believed in them for several hours.)  However, the numbers don’t bear them out.  There is no consistent statistical relationship between big serving and outperforming tiebreak expectations.  To take a few examples: Isner is a tiebreak monster–probably the best tiebreak-player of this generation.  Pete Sampras and Roger Federer are also among the greats.  Below average, though, are the likes of Ivo Karlovic, Sam Querrey, Marc Rosset, and Robin Soderling.

Let’s try another…

The intangibles hypothesis

If there is some intangible mental factor that causes some players to win more tiebreaks than they would otherwise, it’s impossible to test for that effect directly–if it were possible, it wouldn’t be intangible.

But, if some players had that tiebreak-fu, they would probably hold on to it for more than a single season.  For instance, when Novak Djokovic won an impressive 19% and 16% more tiebreaks than expected in 2006 and 2007, respectively, we should have been able to assume that he’s really good at tiebreaks, then predict that he would continue to excel in breakers in 2008.  Yet in 2008, 2009, and 2010, Djokovic barely outperformed average, winning 2% or 3% more than expected.  Ok, so we have a new forecast for Novak in the new decade: just a bit more tiebreak-magic than others.  Yet in 2011, Djokovic won 10% fewer tiebreaks than expected.  He’s 9% below average this year.

Sometimes, these changes might be explained by confidence.  But more often, they are just plain random.  While a few players (including Isner and Federer) put up great numbers every year, the vast majority of the field fluctuates, seemingly at random.  The year-to-year correlation for the population of players with at least 15 tiebreaks in two consecutive years (going back to 1991) is almost exactly zero.  (Set the bar higher if you wish; still barely distinguishable from zero.)

If tiebreak-related intangibles were widespread, there would be some kind of year-to-year correlation.  Perhaps a small number of players do have that magic, but for the purposes of most analysis, it is more accurate to assume that when it comes to a player’s overperformance in tiebreaks, his record one year has very little to do with how he’ll perform the next.

One tiny ray of light

This gets a bit frustrating after a while.  It seems that something should turn up as the cause of tiebreak excellence.  One simple stat does, to a small degree: number of tiebreaks played.  In other words, the guys who play the most tiebreaks tend to be the ones who beat expectations in those tiebreaks.

The connection that immediately springs to mind (after serving prowess, which we’ve already discarded) is practice.  The more match-court breakers you play, the better you become.  Isner, Federer, Sampras–they spend more time at 6-6 than almost anyone, and their tiebreak records are among the best.

Of course, the causation could go the other way.  Perhaps confidence in one’s tiebreak skills cause a player to be more comfortable going to a breaker.  While Djokovic or Andy Murray would press particularly hard for a break a game away from a 6-4 or 7-5 set, Isner is comfortable cruising into a tiebreak.

It’s a minor effect (r < 0.2), one that doesn’t explain anywhere near the observed year-to-year variance in tiebreak under- and over-performance.  But it’s something.

The implications of the luck of the tiebreak

What if overperforming or underperforming your expected tiebreak performance is, essentially, luck?  Or more generally (and safely) speaking, what if it says little about you likelihood of being good or bad at tiebreaks in the future?

For one thing, it would have a major impact on forecasting.  If tiebreak performance one year doesn’t predict tiebreak performance the next, players with extreme under- or over-performances one year can be expected to regress to the mean the following year.  It’s unclear exactly what that would mean in practice, but if you take away Feliciano Lopez‘s five tiebreaks more than expected in 2011, you’re left with a player who probably isn’t ranked within the top 20.  You would expect a decline as he stops winning quite so many breakers.

On a more practical level, these implications might aid the confidence of players with middling tiebreak records.  If you’re Andreas Seppi, who has a career losing record in breakers, you might be excused for some negativity when you reach 6-6 against, say, Karlovic.   But if you know your own poor record is only loosely related to your skills, and Karlovic’s record isn’t nearly as good as it looks, you might take a different approach.  Indeed, Seppi underperformed tiebreak expectations every year from 2006 to 2011, but has won more than expected this season–including one breaker each against Djokovic and Isner.

There’s plenty more work to do here–calling a couple of popular hypotheses into question hardly puts the issue to bed.  But if we’ve learned nothing else this week, it is that tiebreaks are not at all what they seem.  The players you think are masters are often middling performers, and regardless of the conventional wisdom, the breaker is about a whole lot more than a big serve.

13 thoughts on “The Luck of the Tiebreak”

  1. Hi there,

    Very interesting article, again, and thanks for your work studying the tiebreak “thing” as I am currently using it to try to predict winners in tennis. Now I do not know what should I use… the average tiebreak winning % for the career or the last year tiebreak winning %…

    Although being a big server may not help (that much) a player to win a tiebreak, it surely helps the big servers reaching the 6-6.


  2. I think there is merit in the idea that the more you are used to breakers and breaker like pressure, the better you do.
    Sent from my Verizon Wireless BlackBerry

  3. While you’re investigating tiebreaks, I have a possibly interesting query. In normal play, you need to win four out of six – or 5/8, or 6/10, etc., of the points on return to win a game. In tie-breaks, theoretically, only 1 point on return is enough to take the set.

    Does this fact – disregarding everything about momentum, intangibles, etc. and just assuming a model where points are randomly distributed – give a greater advantage to the big-serving player who wins, say, 90 % of points on serve but 30 % on the return?

    1. What are you thinking to compare? Comparing the 90/30 player to an 89/31 player? Comparing the 90/30 player in tiebreaks to a 90/30 player in a no-tiebreak set?

      If we compare 90/30 to 91/29, keep in mind that we’re essentially making *both* players bigger servers. Running some variations on my tiebreak code, it looks like the bigger the servers, the bigger the advantage to the favorite, but until we get into the stratosphere of 85-90% points on serve (which is extraordinarily rare — Isner/Anderson tops out around 80, usually), the difference between 90/30 and 91/29 is slim.

      That does make sense — if we keep adjusting to 92/28, 93/27, and so on, eventually the favorite will win 100% of points on serve while the other one does not, and the favorite is unbeatable … even if it takes an awfully long time for him to win.

      1. Thanks for replying – I guess my question was a bit poorly formed, sorry. I’m probably more interested in

        ‘Comparing the 90/30 player in tiebreaks to a 90/30 player in a no-tiebreak set?’

        as this would be an element of ‘good tiebreak playing’ which is given by the special rules. As I understand this series of posts and this comment, Isner both gets an advantage of having such a slant of points won on serve vs. return AND winning more TBs than that method would indicate?

        I think a better way to measure the TB advantage would be to compare it to the chance of winning a no-tiebreak set, because most tennis sets are still decided without the tie-break. It doesn’t really communicate the advantage of a particular type of player in the TB compared to the sets they’d win in regular play, which I think is a more natural way of measuring ‘tiebreak-fu’.

        1. Hmm, I don’t have code handy to run tiebreak/no-tiebreak comparisons. I’ll post something if I’m able to do that.

          On this: ” I think a better way to measure the TB advantage would be to compare it to the chance of winning a no-tiebreak set, because most tennis sets are still decided without the tie-break.” We’re comparing different (though complementary) things. It may be that the tiebreak is structurally biased toward Isner-like players, and if it is, that would be valuable to know. But if we have 10 players who fall into the same category, the method I’ve discussed today and yesterday aims to differentiate among those 10 — if indeed it is possible to do so.

  4. I for one never bought the idea that there is any genuine advantage for a big server in a tie-break. It’s not as if the game changed. If you win more points with a combination of serve and return than your opponent you are highly likely to win a tennis match (matches in which the winner has a lower % of serve and return points won are very rare). If you win more points with the same combination of serve and return in a tie-break, you necessarily win that tie-break. So, it’s clearly the same exact skills that are good sui generis that are good in a tie-break. Obviously there is the hypothesis that certain skills are easier to perform under pressure, this is at least a feasible reason for the claim. I generally find it very annoying that it seems to be taken as a fact that big servers have some advantage in breakers. Either explain it, back it up, or drop it.

    1. Just to clarify, I’m not denying the possibility that something like the ‘more practice’ hypothesis is true. In that case, being a player of type x (big server) is directly correlated to having more practice, with that being directly correlated with greater success. What I AM vehemently denying, is that there is any such thing as what you describe as ‘structural bias’, toward any specific type of player. % of service points won and % of return points won are the things which determine the winner of a tennis match (barring matches which play on the quirks of the tennis scoring system like a 1-6 7-6 7-5 type result). It is these very same statistics that will always determine the winner of an individual tie-break. Tie-breaks and non-TB-sets aren’t instances of a different game, they are instances of the SAME GAME with a different scoring system. /end-of-rant

      Great work again Jeff.

  5. After some amateur investigation – largely doing probability simulation in Python – it appears stebs is correct and that I’ve misunderstood the probability calculations in play here. As I posted initially, I thought that the system of having to win 4 points to break meant that there was more of an advantage for good returners in normal play, but this seems not to be the case.

    Apologies if this is too far off the topic, but I’d just like to check my working. Consider two players – say Mr. Server and Mr. Claycourter. Both players are expected to win 53 % of all points if we don’t know whether they serve or return; however, we assume Server wins 72 % on serve and 34 % on return, while Claycourter wins 53 % of points regardless.

    In the normal deuce games:
    Server wins 92.3 % of his service games, and 15.4 % of his return games (average 53.9 % games won)
    Claycourter wins 73.6 % of his service games, and 40 % of his return games (average 56.8 % games won)

    Thus, if we were to choose a game at random, Claycourter would be more likely to win a game against his opponent than Server against his. Nevertheless, my simulation tells me that in long sets, both players win roughly 71 % of the time.

    Meanwhile, in tie-breaks, both players win 60 % of the time, as there are fewer confrontations and more randomness – something our jhost has outlined on this blog many times already, I think. But this effect is constant for both styles of play.

    I’m yet to convince myself of the mathematical argument (particularly how you get from a higher percentage of game wins to the same chance of a set win), but I haven’t found anything wrong with the simulation, so I must conclude that there is no evidence for my hypothesis about a structural bias in the tie-break.

    1. On this: “(particularly how you get from a higher percentage of game wins to the same chance of a set win)”

      It’s the same reason why a player has a higher chance of winning a *game* if there is a bigger gap because his *point* probability on deuce and ad points.

      Since almost all of tennis is about accomplishing something twice in a row–and those things are different–the key here is the probability that those two different things can be accomplished. A player who wins 60% of games, regardless of serve or return, allows his opponent to win two in a row 16% of the time. A player who wins 60% of games, 70% on serve, 50% on return, allows his opponent to win two in a row 15% of the time. The bigger the gap, the lower that number goes.

      BTW, my set probability code suggests your Server does win ~92% of service games and ~15% of return games, but that he wins only 68.2% of sets, while Claycourter wins 70.5% of sets.

      1. That 3rd paragraph cleared up a little. (If you make the player win 100 % on serve, he eventually wins 100 % of games, so that sort of hints at what happens before the limit. It runs counter to my intuition, but that is hopeless in working out probabilities anyway.)

        Still, I didn’t see that effect when simulating tie-breaks…I guess it only turns up at a huge split as you said yesterday, like 90/16? Or is there something else at play there?

        Just to tie up a loose end, my 71 % numbers were for long sets, pretending TBs do not exist.
        I guess Server would have a lower percentage in normal ATP sets, because he is playing more tie-breaks (he wins the same amount of long sets, but with a lower percentage of games, so his sets are longer) and the tie-breaks are more random. I think I did Server in TB as well – iirc he won 49 % before TB and 60 % of the 32 % = 19.2 % of the TBs, for a total of 68.2 %.

  6. Perhaps those that win many tie breaks never should have been in a tie breaker in the first place. Complacent play got them there and it took the tie breaker to snap them out of it.

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