All else equal, increasing your first serve speed is a good thing … so how useful is it? Earlier this week, I published some generic numbers, but those are far too crude to answer this question.

To get a better answer, we need to see what happens when specific players serve a little faster or slower. Sometimes, players dramatically mix up serve speed (as with slice serves wide), but most of the time, each player stays within a fairly limited range defined by his own power and skill.

The algorithm I’ve employed is fairly complicated, so I’ll give you the results first.

It appears that most players, if they increased their average serve speed by one mile per hour, would win 0.2% more first service points. That’s not many–it’s not even one point in every match. But every little bit helps, and according to my win probability models, winning 0.2% more first serve points can increase your chance of winning an even match from 50% to just short of 51%. Except possibly at the extremes, that continues to be the case for 2 MPH, 3 MPH, and greater increases–so a 5 MPH increase takes that 50/50 match and turns it into a 54/46 contest.

(One assumption here is that all players respond to increases in serve speed the same way. I’m sure that’s not true, but at this stage it’s a necessary assumption.)

The effect of a speed increase is even greater on ace and service winner rates. Each additional MPH on a player’s serve increases his ace rate by about 0.4%, and his service winner rate by about 0.5%.

Now for the algorithm and some caveats.

**Process**

The algorithm was designed to control (to the extent possible) for different types of serving and playing styles, as well as the different average speeds to the deuce and ad court, as well as to different directions (wide, body, and T).

I used only US Open data, to avoid differences between surfaces and between the speed guns used at different events. I used data only from the 18 players who had more than 150 first-serve points tracked by Pointstream. For each of those players, I found their average first-serve speed for each of six directions: wide, body, and T to the deuce and ad courts. Then, I randomly selected 150 of their first-serve points, and for each point, noted the difference between the point’s serve speed and the player’s average in the relevant court/direction.

Thus, every one of 2700 points was labeled 0 (average for that player/court/direction), or +1 (one mph above average), or -4, and so on. That results in large pools of points with each label. Many of the pools were too small for useful analysis, so I grouped them in sets of five: (-2, -1, 0, +1, +2), (-1, 0, +1, +2, +3), and so on. The pools, then, were useful from about -15 to +15.

From there, I looked at each of several stats (points won, aces, service winners) for each pool, and compared the rates from one pool to the next. The results were somewhat erratic–in some instances, an additional mph results in aces or points won going down, but over the set of 31 pools, they generally went up. The numbers presented above are the averages of each one-mph change.

**Caveats**

It’s not a very big sample, especially when separating serves into pools of 0, +1, +2, and so on.

One issue with the dataset is that the 18 servers were usually winning–that’s how they got enough first serves to merit inclusion. Thus, the average returner in the dataset is below average. That isn’t necessarily a bad thing–perhaps below-average returners respond to changes in serve speed the way above-average returners do–but without more data, it’s tough to know.

Another concern is what the numbers really tell us below about 5 mph slower than average. The algorithm operates on the assumption that a 120 mph serve is the same as a 121 mph serve, only slower. Comparing 120 and 121, that’s probably true. But comparing 120 and 108–for the same player, serving in the same direction–it probably isn’t. The 108 mph isn’t a simulation of what would happen if the player wasn’t as good; it’s probably a strategic choice, likely accompanied by some spin.

That said, the algorithm doesn’t directly compare 120 and 108, it compares 108 and 109, and perhaps in the aggregate, there is something useful to be gleaned from comparing a strategic spin first serve to an identical serve one mph faster. In any event, limiting the range to between -10 and 10, or even -7 and 7, doesn’t change the results much.

Finally, the sample is completely inadequate to tell us what happens at the extremes. The average player appears to improve his chances by adding another bit of speed, but does John Isner? There may be a ‘sweet spot’ where a player can get maximum gains from an additional 1, 5, or 10 mph on his first serves, but beyond which, the gain is more limited.

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