Is There an Advantage To Serving First?

There’s no structural bias toward the player who serves first.  If tennis players were robots, it wouldn’t matter who toed the line before the other.

But the conventional wisdom persists.  Last year, I looked at the first-server advantage in very close matches, and found that depending on the scenario, the player who serves first in the final set may win more than 50% of matches–as high as 55%–but the evidence is cloudy.  And that’s based on serving first at the tail end of the match.  Winning the coin toss doesn’t guarantee you that position for the third or fifth set.

Logically, then, it’s hard to see how serving the first game of the match–and holding that possible slight advantage in the first set–would have much impact on the outcome of the match.  There’s simply too much time, and too many events, between the first game and the pressure-packed crucial moments that decide the match.

Yet, the evidence points to a substantial first-serve advantage.

In ATP main-draw matches this year, the player who served first won 52% of the time.  That edge is confirmed when we adjust for individual players.

39 players tallied at least 10 matches in which they served first and 10 in which they served second.  Of those 39, 21 were more successful when serving first, against 17 who won more often when serving second.  (Marcos Baghdatis didn’t show a preference.)  Weigh their results by their number of matches, and the average tour-level regular was 11% more likely to win when serving first than when serving second.  Converted to the same terms as the general finding, that’s 52.6% of matches in favor of the first server.

That’s not an airtight conclusion, but it is a suggestive one.  One possible problem would arise if lesser players–the guys who play some ATP matches against that top 39, but not enough to show up in the 39 themselves–are more likely to choose returning first.  Then, our top 39 would be winning 52.6% of matches against a lesser pool of opponents.

That doesn’t seem to be the case.  I looked at the next 60 or so players, ranked by how many ATP matches they’ve played this year.  That secondary group served first 51% of the time, indicating that the guys on the fringe of the tour don’t have any kind of consistent tendency when winning the coin toss.

For further confirmation, I ran the same algorithm for ATP Challenger matches this year.  That returned another decent-sized set of players with at least 10 matches serving first and 10 matches serving second–38, in this case.  The end result is almost identical.  The Challenger regulars were 9% more likely to win when serving first, which translates to the first server winning 52.2% of the time.

This is a particularly interesting finding, because in the aggregate, these 38 Challenger regulars prefer to serve second.  Of their 1110 matches so far this year, these guys served first only 503 times–about 45%.  Despite such a strong preference, the match results tell the story.  They are more likely to win when serving first.

When we turn our attention to the WTA tour, the results are so strong as to be head-scratching.  Applying the same test to 2013 WTA matches (though lowering the minimum number of matches to eight each, to ensure a similar number of players), the 35 most active players on the WTA tour are 28% more likely to win when serving first than when serving second.  In other words, when a top player is on the court, the first server wins about 56.3% of the time.  24 of the 35 players in this sample have better winning percentages when serving first than when serving second.

For something that cannot be attributed to a structural bias, a factor that can only be described as mental, I’m reluctant to put too much faith in these WTA results without further research.  However, the simple fact that ATP, Challenger, and WTA results agreed in direction is encouraging.  The first-server advantage may not be overwhelming, but it appears to be real.

13 thoughts on “Is There an Advantage To Serving First?”

  1. Maybe the better servers choose to serve first, and are generally more likely to win than those who rely more on returns.

    – serving first may require confidence
    Sent from my Verizon Wireless BlackBerry

  2. Logical results for ATP. When you serve first in the first set you usually serve 2nd in the 2nd and first again in the third.
    I m surprised with the WTA results as the probability to win a point on serve is lower than for ATP I m pretty sure that serving first is a smaller advantage than in ATP.

  3. Jeff, I always thought there *was* a very slight structural advantage to serving first, and that this was what the conventional wisdom represented.

    In other words if we built tennis robots to resemble humans, we would likely build them to incorporate a certain random percentage of bad serves and bad strokes, sufficient to cause a robot who was serving to lose serve X percentage of time. If X is large enough, then if we have identical robots playing, the robot serving first in the set has a structural advantage to win that set. And extrapolating, this would eventually give an even smaller, but still determinable, structural advantage to winning the match. Wouldn’t it?

  4. To me, this is a very significant finding. It is very similar to stats showing that in UEFA two-leg clashes, the team that plays the second leg at home advances 55% of time. (In soccer, this is a much clearer result since the order of playing at home is completely random, whereas in tennis the coin-toss winner gets to choose, but I’ll sidestep that for this comment.)

    55% for soccer, and 52% to 56% doesn’t sound like much, but I would argue that it’s very significant if you look at it in another way:
    This means that, respectively, 10%, 4%, and 12% of these matches are decided by the coin. That, to me, sounds astonishing.

    I’m not a betting man, but I wondered if it was exploitable to always bet on the coin toss winner, as soon as it is decided.

  5. Interesting. Obviously, serving first can represent one of several events and I wonder if you can differentiate between the cases in the data. The player might have won the toss and chosen to serve (he’s confident, feeling good, ready to go). In that case, maybe we expect him to win with higher than 50% probability. Another case is that he loses the toss, but his opponent chose to receive – this one might be harder to justify a >50% probability, but maybe the other guy is not feeling his best, and doesn’t want to risk losing serve immediately, so he chooses to receive. There are other things to consider such as choosing a side, or deferring, but it would be interesting to see if the two events (choosing to serve first) and (serving first after opponent chose to receive) appear to be statistically equivalent. I imagine some players choose the same thing every time (serve or receive), while others base it on the opponent and their current level of confidence, sun, wind, etc.

    1. That would be nice to distinguish. Alas, it’s not in the data I have. The best I could do would be to approximate based on those players who always make the same choice (e.g. if Federer is serving second, the other guy won the toss and chose to serve), but I was surprised to see how many top players seem to vary their choice, which leaves a considerably smaller (and possibly biased, though I haven’t thought through how) pool of matches.

  6. The thinking I always used was this: a top 50 player is more likely to win a service game than a return game (TA has 81.6% hold and 23.8% break for the top 50 against all opponents, with no player having a better break % than hold %). The first server will have equal or more service games than his opponent (more on sets with 6-3 and 6-1 endings, equal on all other scores [setting aside individual tie-break point serves]). So the equal service game sets should even out, but the first server should have an advantage in the sets where he ends with one more service game, thus skewing the sets won% his way.

    Also, think of how the individual scorelines (non-tiebreak) would have to occur. All sets with an even number of games could end with an equal number of minimum breaks from either side (7-5 1 break, 6-4 1 break, 6-2 2 breaks, 6-0 3 breaks), but a set with an odd number of games requires more breaks from the first returner than from the first server (6-3 needs a minimum of 2 breaks from the first returner, but a minimum of 1 from the first, server, 6-1 minimum of 3 from first returner, but only 2 from the first server). There’s no scenario that is easier for the first server.

    1. This is intuitively appealing, and I once went down the same road [1]. However, there’s simply no structural advantage to serving first.

      First of all, I’ve written both monte carlo simulations and a closed-form solution [2] to mathematically determine outcomes, and these don’t show any advantage.

      Intuitively, remember that to win, you need to either (a) reach and win a tiebreak, or (b) break serve more often than the other guy. Those are the only options. (a) isn’t relevant here.

      (b) reminds us that there is no advantage in serving *more* than the other guy in a single set. You still need at least one more break than the other guy gets. You only get the advantage of that extra service game in a (e.g.) 6-3 set if you’ve broken more than your opponent has.

      [1] [2] and

  7. I have a long shot theory:
    the favorite would like the match to be shorter (because he is likely to get another match the next day), and by serving first it could be shorter by 1 game. The underdog may even wish the match to be longer, in order to gain experience.

    1. one more or less game for following of tournament or career does make no difference at all though…
      They mainly choose to serve first because they know it s harder to handle the pressure serving at 4 5 down.

  8. Isn’t it a structural advantage that only the first server can win a set by breaking once (at 5:4) without the opponent having a chance of settling the score by re-breaking?

    Perhaps combined with the psychological effect of both players knowing about the “sudden death” effect of the tenth game, this should provide a real advantage.

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