# Second Serve +1 = 3

Knowing that even following a second serve, the majority of points in men’s professional tennis are contested in the 0-4 shot range, what are some of the ways in which players could go about increasing their effectiveness in these short rallies? As a server, you want to maximize the number of “1” and “3” shot rallies in that 0-4 range, i.e. the rally lengths that lead to you winning the point (remember that rallies of an odd length mean a point for the server, while rallies of an even length lead to a point won by the returner). Are there any particular areas of the service box you should target more often with your serve? Furthermore, let’s say you’d prefer your first stroke after the return to be a forehand. How does that change the equation?

Once again, I decided to use the dataset of all individual points played in the 2020 US Open men’s singles matches, compiled by Jeff Sackmann. Specifically, I wanted to focus on points starting with the second serve, and a rally length of 3. (The few lines of code needed for the article can be found here.)

Second Serve Rally Lengths, 2020 US Open Men’s Singles

There are two reasons why I think this particular scenario is important. The first is simply that it was the most frequently occurring rally length in dataset (see above). The second reason is slightly more tactical. If I wanted to maximize the rally length of 1 after a second serve, that means I don’t want the serve to come back. I need to either hit it harder, with more spin, risk more, or be more unpredictable with its location. On the other hand – maximizing the rally length of 3 – I want the serve to come back. I just want it to come back to where I want it, so I can do damage with my “+1.” I don’t need for the serve to be the dagger and take a lot of risk with it; I only need it to set up the rest of my game.

Let’s start with the 30,000ft view. Overall, there were 6,541 second serve points in the dataset, for which the serve direction was tagged. The direction was assigned one of five values: Wide, Body-Wide, Body, Body-Center, and Center. It’s important to mention that the 6,541 points are both deuce and ad points combined, as well as righty and lefty servers combined. Here are the direction percentages for all second serve points:

Second Serve Directions: Overall

We can learn two things from the table: one, the body serve reigns supreme. When we combine all three of the body serve categories, we see that more than 7 out of every 10 second serves were aimed at the body of the opponent. The body serve is especially effective when the returner wants to take the return early, or on the rise – right around the baseline or inside it. It will lose some of its bite when the returner stands 2+ meters behind the baseline and has time to move and make space for the return. Second, the players are apprehensive about opening up the court for the opponent, going wide with their second serve only about 10% of the time.

With that general overview of the second serve direction patterns, let’s zoom in on the second serve patterns that yielded the rally length of 3 most often. There were 1,577 second serve rallies of length 3 in the datatset, tagged with the corresponding serve direction. The breakdown is as follows:

Second Serve Directions: Rally Length = 3

Looking at both of the above tables combined, it doesn’t seem that serving into one particular area of the box resulted in more 3 stroke rallies than expected; the percentages are all basically the same. The biggest difference was in the “Center” location, where players directed 17.05% of their second serves, but that location yielded about 15% of three stroke rallies. That 2% difference is probably due to the fact that after a second serve down the center, both the server and returner are positioned near the middle of the court, not dissimilar to what you would see in the warmup. It is harder to generate any attacking angles from that part of the court, and we’re likely to see a longer baseline rally as a result.

If there aren’t any obvious areas of the box to serve into to increase the likelihood of the 3 stroke rally by themselves, are there any areas that increase my chances, as a server, that my “+1” will be a particular stroke? I would argue that the majority of players would prefer that first stroke after the serve to be a forehand.

Short of watching every point and tagging the first stroke hit by the server following the return, we’ll need to use a proxy. If a specific rally in the dataset ended with a winner, the point is tagged with either a ‘F’ or a ‘B’ – forehand or backhand – based on the type of shot that resulted in the winner. What we have below are second serve points, of rally length 3, that ended with a forehand winner. Overall, there were 373 of those points in the dataset, with the distribution as follows:

Second Serve Directions: Rally Length = 3, Winner = ‘F’

The thing that stands out in this table is the column with the “Wide” serve direction. In the tables above, we saw that about 10.5% of all second serves were hit into the wide section of the box, and 11% of all second serve 3 stroke rallies started with a wide second serve. But when looking at second serve 3 stroke rallies finishing with a forehand winner, that number jumps to over 17%.

Obviously looking at a small subset of points – the ones ending with a winner – has its limitations. For example, we are not considering rallies that ended with a forced error by the returner on stroke number 4. However, I think that there is something to pay attention to even with the relatively small sample size.

We saw from the data how infrequent second serves out wide are – only about 11% of second serves were hit out wide in the dataset. I would guess the percentage would be even smaller than that in just the deuce side of the court. In the ad side, the kick out wide tends to be the easiest topspin serve for a right handed server to hit, and the wide “slider” in the ad is the bread and butter of lefties. So if a player decides to hit a second serve wide in the deuce, he often catches the opponent by surprise, resulting in a weaker return. And on that weaker return, the server has time to move around his backhand if he needs to, and get on offense with his forehand. Moreover – just by the geometry of the court – it is harder to direct a return from the wide section of the deuce side into the ad side of the server: the net is higher, and the court is shorter that way. As a result, the return will probably come back through the middle, or cross court – allowing the server to “cheat” that way in preparation for his +1.

If you are a player yourself, or maybe coaching a player, and you would like to increase the chances of crushing a forehand following your second serve, don’t forget about the wide target. Especially in the deuce side.