Are Two First Serves Ever Better Than One?

Italian translation at settesei.it

It’s one of those ideas that never really goes away. Some players have such strong first serves that we often wonder what would happen if they hit only first serves. That is, if a player went all-out on every serve, would his results be any better?

Last year, Carl Bialik answered that question: It’s a reasonably straightforward “no.”

Bialik showed that among ATP tour regulars in 2014, only Ivo Karlovic would benefit from what I’ll call the “double-first” strategy, and his gains would be minimal. When I ran the numbers for 2015–assuming for all players that their rates of making first serves and winning first-serve points would stay the same–I found that Karlovic only breaks even. Going back to 2010, 2014 Ivo was the only player-season with at least 40 matches for whom two first serves would be better than one.

Still, it’s not an open-and-shut case. What struck me is that the disadvantage of a double-first strategy would be so minimal. For Karlovic (and others, mainly big servers, such as Jerzy Janowicz, Milos Raonic,and John Isner), hitting two first serves would only slightly decrease their overall rate of service points won. For Rafael Nadal and Andy Murray, opting for double-first would reduce their rate of service points won by just under two percentage points.

Here’s a visual look at 2015 tour regulars (minimum 30 matches), showing the hypothetical disadvantage of two first serves. The diagonal line is the breakeven level; Ivo, Janowicz, and Isner are the three points nearly on the line.

Since some players are so close to breaking even, I started to wonder if some matchups make the double-first strategy a winning proposition. For example, Novak Djokovic is so dominant against second serves that, perhaps, opponents would be better off letting him see only first serves.

However, it remains a good idea–at least in general–to take the traditional approach against Djokovic. Hypothetically, two first serves would result in Novak raising his rate of return points won by 1.2 percentage points. Gilles Simon and Andy Murray are in similar territory, right around 1 percentage point.

Here’s the same plot, showing the disadvantage of double-first against tour-regular returners this season:

There just aren’t any returners who would cause the strategy to come as close to breaking even as some big servers do.

The match-level tactic

What happens if a nearly-breakeven server, like Karlovic, faces a not-far-from-breakeven returner, like Djokovic? If opting for double-first is almost a good idea for Ivo against the average returner, what happens when he faces someone particularly skilled at attacking second serves?

Sure enough, there are lots of matches in which two first serves would have been better than one. I found about 1300 matches between tour regulars (players with 30+ matches) this season, and for each one, I calculated each player’s actual service points won along with their estimated points won had they hit two first serves. About one-quarter of the time, double-first would have been an improvement.

This finding holds up in longer matches, too, avoiding some of the danger of tiny samples in short matches. In one-quarter of longer-than-average matches, a player would have still benefited from the double-first strategy. Here’s a look at how those matches are distributed:

Finally, some action on the left side of the line! One of those outliers in the far upper right of the graph is, in fact, Ivo’s upset of Djokovic in Doha this year. Karlovic won 85% of first-serve points but only 50% of second-serve points. Had he hit only first serves, he would’ve won about 79% of his service points instead of the 75% that he recorded that day.

Another standout example is Karlovic’s match against Simon in Cincinnati. Ivo won 81% of first-serve points and only 39% of second-serve points. He won the match anyway, but if he had pursued a double-first strategy, Simon could’ve caught an earlier flight home.

Predicting double-first opportunities

Armed with all this data, we would still have a very difficult time identifying opportunities for players to take advantage of the strategy.

For each player in every match, I multiplied his “double-first disadvantage” (the number of percentage points of serve points won he would lose by hitting two first serves) with the returner’s double-first disadvantage. Ranking all matches by the resulting product puts combinations like Karlovic-Djokovic and Murray-Isner together at one extreme. If we are to find instances where we could retroactively predict an advantage from hitting two first serves, they would be here.

When we divide all these matches into quintiles, there is a strong relationship between the double-first results we would predict using season-aggregate numbers and the double-first results we see in individual matches. However, even if the most double-first-friendly quintile–the one filled with Ivo serving and Novak returning–there’s still, on average, a one-percentage-point advantage to the traditional serving tactic.

It is only at the most extreme that we could even consider recommending two first serves. When we take the 2% of matches with the smallest products–that is, the ones we would most expect to benefit from double first–26 of those 50 matches are one in which the server would’ve done better to hit two first serves.

In other words, there’s a ton of variance at the individual match level, and since the margins are so slim, there are almost no situations where it would be sensible for a player to hit two first serves.

A brief coda in the real world

All of this analysis is based on some simplifying assumptions, namely that players would make their first serves at the same rate if they were hitting two instead of one, and that players would win the same number of points behind their first serves even if they were hitting them twice as often.

We can only speculate how much those assumptions mask. I suspect that if a player hit only first serves, he would be more likely to see streaks of both success and failure; without second serves to mix things up, it would be easier to find oneself repeating mechanics, whether perfect or flawed.

The second assumption is probably the more important one. If a server hit only first serves, his ability to mix things up and disguise serving patterns would be hampered. I have no idea how much that would affect the outcome of service points–but it would probably act to the advantage of the returner.

All that said, even if we can’t recommend that players hit two first serves in any but the extreme matchups, it is worth emphasizing that the margins we’re discussing are small. And since they are small, the risk of hitting big second serves isn’t that great. There may be room for players to profitably experiment with more aggressive second serving, especially when a returner starts crushing second serves.

Ceding the advantage on second-serve points to a player like Djokovic must be disheartening. If the risk of a few more double faults is tolerable, we may have stumbled on a way for servers to occasionally stop the bleeding.