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Analyzing the Serve

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                                                       Analyzing the Serve:
                                 Why Craig O’Shannessy’s Take is Off the Mark

    Craig O'Shannessy's blog of Nov. 5th, 2019 "Why Roger Federer Is The Best All-Round Spot Server" paints an incomplete picture of what makes up a great server. For convenience, his post appears at the end of this post.

    Let’s start with first principles. I think we would all agree that what a server is looking for is to maximize the probability of winning a point when serving. This includes (obviously!) both first and second serves. O’Shannessy’s analysis, however, only tells us about the effectiveness of the 6 locations (wide, body, T) of first serves in both boxes. It ignores two crucial components of effective serving: 1) What % of first serves goes in; and 2) How effective is a player’s second serve? At the risk of having you tune out (most readers don’t like math), here is the formula for calculating the probability (p) of winning a point on serve:
    p=x_1*y_1+(1-x_1 )*x_2*y_2                                where
    x_1 = probability that first serve is in
    x_2 = probability that second serve is in
    y_1 = probability of winning the point if first serve is in
    y_2 = probability of winning the point if second serve is in

    To see why O’Shannessy’s analysis leaves out much more than it includes, let’s take an extreme example. Let’s say that x_1 is .1. 1/10 is an absurdly low number of first serves to go in, but using this value serves to clearly demonstrate why simply looking at y_1 is incomplete. Let’s even use Berrettini’s Deuce Court T winning % of 82.5% (this is the highest percentage among all of the players and their six possible targets). This means that his first serve would be contributing to his probability of winning a point on serve by 8.25%. This absurdly low probability would leave Berrettini ranked outside of the Top 10 million for sure!

    Another way to say this is that O'Shannessy's analysis implicitly holds each of the other serving variables constant. This is almost certainly false. For example, his analysis would only be proximately correct if x_1 were equal both across the 6 different targets and across players. See my discussion below on the most likely higher % of first serves in when targeting the body.

     And, of course, his analysis takes no account of the second serve. I think you get the idea.
    
    Game theory predicts that servers will choose their targets so as to equalize their probabilities of winning across targets. This is based upon the idea that if a receiver knows with certainty what is coming, his return is much more likely to either go in and/or be stronger. Therefore, a good server must randomize among targets. 

    Since O’Shannessy does not provide us with the first serve percentages associated with each of the six targets for each of the players, it’s impossible to see if, in fact, our sample of professional players does play efficiently. My guess is that they do.

    Keep in mind that there are three ways of winning a point on serve: 1) Hitting an ace; 2) Getting an error on the return; or 3) Winning the point after a rally. The average for Wide and T serves are extremely close and substantially above those for Body serves in both boxes. At first glance, it might appear that Body serves are relatively inefficient. However, this is most likely not the case. Remember, there will not be any aces with the Body serve category. 

    What we can say is that Body serves are relatively safer to hit because they can only miss long or into the net. A Body serve cannot be missed wide. It would be interesting to see where these top players serve when the points are more important. An examination of choices made when facing break point could potentially be very illuminating.

O’Shannessy’s post follows for those of you who would like to see his piece.

Why Roger Federer Is The Best All-Round Spot Server
Nov052019
 
Craig O'Shannessy
Infosys ATP Beyond The Numbers shows that at the upcoming Nitto ATP Finals, opponents will have no safe zone when facing Roger Federer's serve. 
First serves are all about dropping heat and hitting spots, and there is no better return on investment for the Top 10 than going down the T in the Deuce Court.
An Infosys ATP Beyond The Numbers analysis of the current Top 10 uncovers who thrives the most at which first-serve location, and where the highest win percentages are located.
The six serve locations are wide, body and T in both the Deuce Court and Ad Court, with the data set coming from ATP Masters 1000 events, Nitto ATP Finals and Next Gen ATP Finals from 2011 to 2019.


The breakdown starts with the highest average win percentage location (Deuce Court T) and finishes with the lowest (Ad Court Body). It’s interesting to note that Roger Federer was the only player to feature in the top three at all six serve locations.
No. 1: Deuce Court T (Average Win % = 76.9%)
Only three players were able win north of 80 per cent at any of the six locations. Matteo Berrettini, who was ranked outside the Top 50 to begin 2019, boasts a new career-high ATP Ranking this week of No. 8, and out of all six serve locations, Berrettini had the highest win percentage at 82.5 per cent. He did it by going down the T in the Deuce Court.
Berrettini averaged hitting his first serve at 133 mph to this location, accumulating 82 aces and 83 unreturned serves.
The leading three players at this location:
M. Berrettini = 82.5%
R. Federer = 81.1%
S. Tsitsipas = 81.0%
No. 2: Ad Court Wide (Average Win % = 75.6%)
Russian sensation Daniil Medvedev led the Top 10 with winning first-serve points out wide in the Ad court, at 79.4 per cent.
He averages 123 mph with his first serve to this location, hitting 150 aces and having 168 first serves unreturned. Medvedev sits at his career-high ATP Ranking of No. 4, with four titles under his belt this season, including Masters 1000 crowns in Cincinnati and Shanghai.
The leading three players at this location:
D. Medvedev = 79.4%
R. Federer = 78.9%
S. Tsitsipas = 78.6%
No. 3: Deuce Court Wide (Average Win % = 75.3%)
Austrian Dominic Thiem is the leader with the wide slider in the Deuce Court, winning 78.4 per cent of first-serve points.
Thiem’s average first-serve speed to this location is 113 mph, which is considerably slower than the 121 mph he averages going down the T in the Deuce Court. This identifies that slice becomes more of a factor with the wide serve, carving the ball away from the returner.
The leading three players at this location:
D. Thiem = 78.4%
M. Berrettini = 77.3%
R. Federer = 77.2%
No. 4: Ad Court T (Average Win % = 73%)
Federer and Berrettini tied for the lead at this location, with both players winning 75.1 per cent of their first serves. Federer’s average first-serve speed is 117 mph, while Berrettini is considerably higher at 128 mph.
The leading three players at this location:
T1. R. Federer = 75.1%
T1. M. Berrettini = 75.1%
3. S. Tsitsipas = 75.0%
No. 5: Deuce Court Body (Average Win % = 65.4%)
It’s interesting to note that Thiem led the Top 10 with the wide and body serves in the Deuce court, two locations that are that side by side.
The leading three players at this location:
D. Thiem = 70.3%
R. Federer = 69.8%
R. Nadal = 66.3%
No. 6: Ad Court Body (Average Win % = 62.8%)
World No. 1 Novak Djokovic leads this category with a considerable 2.2 percentage-point lead over his nearest rival, winning 68.5 per cent of first serves at the body in the Ad Court.
Djokovic averages 116 mph to this location, which is faster than the 114 mph he averages going out wide and equal with when he goes down the T in the Ad court.
The leading three players at this location:
N. Djokovic = 68.5%
R. Federer = 66.3%
R. Nadal = 65.4%
Current Top 10: First Serve Win Percentage At All Six Serve Locations
(Bold = leader)
Ranking    Player    Deuce Wide    Deuce Body    Deuce T    Ad Wide    Ad Body    Ad T
1    N. Djokovic       74.9%              66.2%             76.2%          72.6%    68.5%      72.0%
2    R. Nadal           75.5%              66.3%             71.2%          74.3%    65.4%      74.0%
3    R. Federer        77.2%              69.8%             81.1%          78.9%    66.3%      75.1%
4    D. Medvedev    76.2%              61.5%             76.1%          79.4%    55.6%      74.1%
5    D. Thiem           78.4%              70.3%             75.9%          72.6%    62.8%     73.5%
6    A. Zverev          77.0%              63.4%             78.2%          73.9%    60.8%     74.4%
7    S. Tsitsipas       72.0%              64.0%             81.0%          78.6%    60.8%     75.0%
8    K. Khachanov   75.2%              63.4%             78.0%          78.2%    64.8%     69.7%
9    M. Berrettini      77.3%              66.2%             82.5%          77.1%    61.7%     75.1%
10    R. Bautista Agut    69.2%        62.4%             68.3%          70.4%    61.5%    67.1%
     Overall Average       75.3%        65.4%             76.9%          75.6%    62.8%    73.0%

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