## Measuring WTA Tactics With Aggression Score

Editor’s note: Please welcome guest author Lowell! He’s a prolific contributor to the Match Charting Project, and the author of the first guest post on this blog.

The Problem

Quantifying aggression in tennis presents a quandary for the outsider. An aggressive shot and a defensive shot can occur on the same stroke at the same place on the court at the same point in a rally. To know whether one occurred, we need information on court positioning and shot speed, not only of the current shot, but the shots beforehand.

Since this data only exists for a fraction of tennis matches (via Hawkeye) and is not publicly available, using aggressive shots as a metric is untenable for public consumption. In a different era, net points may have been a suitable metric, but almost all current tennis, especially women’s tennis, revolves around baseline play.

Net points also can take on a random quality and may not actually reflect aggression. Elina Svitolina, according to data from the Match Charting Project, had 41 net points in her match against Yulia Putintseva at Roland Garros this year. However, this was not an indicator of Svitolina’s aggressive play so much as Putintseva hitting 51 drop shots in the match.

The Match Charting Project does give some data to help with this problem however. We can use the data to get the length of rallies and whether a player finished the point, i.e. he/she hit a winner or unforced error or their opponent hit a forced error. If we assume an aggressive player would be more likely to finish the point and would be more likely to try to finish the point sooner rather than later in a rally, we can build a metric.

The Metric

To calculate aggression using these assumptions, we need to know how often a player finished the point and how many opportunities did they have to finish the point, i.e. the number of times they had the ball in play on their side of the net. To measure the number of times a player finished the point, we add up the points where they hit a winner or unforced error or their opponent hit a forced error. For short, I will refer to these as “Points on Racquet”.

To measure how many opportunities a player had to finish the point, we calculate the number of times the ball was in play on each player’s side of the net. For service points, we add 1 to the length of each rally and divide it by 2, rounding up if the result is not an integer. For return points, we divide each rally by 2, rounding up if the result is not an integer. These adjustments allow us to accurately count how often a player had the ball in play on their side of the net. For brevity, I will call these values “Shot Opportunities”.

If we divide Points on Racquet by Shot Opportunities we will get a value between 0 and 1. If a player has a value of 0, they never finish points when the ball is on their side of the net. If the player has a value of 1, they only hit shots that end the point. As the value increases, a player is considered more aggressive. For short, I will call this measure an “Aggression Score.”

The Data

Taking data from the latest upload of the Match Charting Project, I found women’s players with 2000 or more completed points in the database (i.e. all points that were not point penalties or missed points). Eighteen players fitted these criteria. Since the Match Charting Project is, unfortunately, a nonrandom sample of matches, I felt uncomfortable making assessments below a very large number of data points. Using 2000 or more data points, however, an overwhelming amount of data would be required to overcome these assessments, giving some confidence that, while bias exists, we get in the neighborhood of the true aggression values.

The Results

Below are the results from the analysis. Tables 1-3 provide the Aggression Scores for each player overall, broken down into serve and return scores and further broken down into first and second serves. They also provide differences between where we would expect the player to be more aggressive (Serve v. Return, First Serve v. Second Serve and Second Serve Return v. First Serve Return).

Table 1: Aggression Scores

```Name         Overall  On Serve  On Return  S-R Spread
S Williams     0.281    0.3114     0.2476      0.0638
S Halep       0.1818    0.2058     0.1537      0.0521
M Sharapova   0.2421    0.2471     0.2358      0.0113
C Wozniacki   0.1526    0.1788     0.1185      0.0603
P Kvitova     0.3306     0.347      0.309       0.038
L Safarova    0.2475    0.2694     0.2182      0.0512
A Ivanovic    0.2413     0.247     0.2335      0.0135
Ka Pliskova    0.256    0.2898     0.2095      0.0803
G Muguruza     0.231     0.238     0.2214      0.0166
A Kerber      0.1766    0.2044     0.1433      0.0611
B Bencic      0.1742    0.1784     0.1687      0.0097
A Radwanska   0.1473    0.1688     0.1207      0.0481
S Errani      0.1232    0.1184     0.1297     -0.0113
E Svitolina   0.1654    0.1769     0.1511      0.0258
M Keys        0.3017    0.3284     0.2677      0.0607
V Azarenka    0.1892    0.1988     0.1762      0.0226
V Williams    0.2251     0.247     0.1944      0.0526
E Bouchard    0.2458    0.2695     0.2157      0.0538
WTA Tour       0.209    0.2254     0.1877      0.0377```

Table 2: Serve Aggression Scores

```Name          Serve  First Serve  Second Serve  1-2 Spread
S Williams   0.3114       0.3958        0.2048       0.191
S Halep      0.2058       0.2298        0.1587      0.0711
M Sharapova  0.2471       0.2715        0.1989      0.0726
C Wozniacki  0.1788       0.2016         0.121      0.0806
P Kvitova     0.347       0.3924        0.2705      0.1219
L Safarova   0.2694       0.3079        0.1983      0.1096
A Ivanovic    0.247       0.2961        0.1732      0.1229
Ka Pliskova  0.2898       0.3552        0.1985      0.1567
G Muguruza    0.238       0.2906        0.1676       0.123
A Kerber     0.2044       0.2337        0.1384      0.0953
B Bencic     0.1784       0.2118        0.1218        0.09
A Radwanska  0.1688       0.2083        0.0931      0.1152
S Errani     0.1184       0.1254        0.0819      0.0435
E Svitolina  0.1769       0.2196         0.105      0.1146
M Keys       0.3284       0.3958        0.2453      0.1505
V Azarenka   0.1988       0.2257        0.1347       0.091
V Williams    0.247       0.3033        0.1716      0.1317
E Bouchard   0.2695       0.3043        0.2162      0.0881
WTA Tour     0.2254       0.2578        0.1679      0.0899```

Table 3: Return Aggression Scores

```Name          Serve  1st Return  2nd Return  Spread
S Williams   0.2476      0.2108      0.3116  0.1008
S Halep      0.1537      0.1399      0.1778  0.0379
M Sharapova  0.2358      0.2133      0.2774  0.0641
C Wozniacki  0.1185      0.1098       0.132  0.0222
P Kvitova     0.309      0.2676      0.3803  0.1127
L Safarova   0.2182      0.1778      0.2725  0.0947
A Ivanovic   0.2335      0.1952      0.3027  0.1075
Ka Pliskova  0.2095      0.1731      0.2715  0.0984
G Muguruza   0.2214      0.1888      0.2855  0.0967
A Kerber     0.1433      0.1127       0.191  0.0783
B Bencic     0.1687      0.1514       0.197  0.0456
A Radwanska  0.1207      0.1049      0.1464  0.0415
S Errani     0.1297      0.1131      0.1613  0.0482
E Svitolina  0.1511      0.1175      0.1981  0.0806
M Keys       0.2677      0.2322      0.3464  0.1142
V Azarenka   0.1762      0.1499      0.2164  0.0665
V Williams   0.1944      0.1586       0.255  0.0964
E Bouchard   0.2157      0.1757      0.2837   0.108
WTA Tour     0.1877      0.1609      0.2341  0.0732```

The first plot shows the relationship between serve and return aggression scores as well as the regression line with a confidence interval (note: since there are only 18 players in the sample, treat this regression line and all of the others in this post with caution).

The second and third plots show the relationships between players’ aggression scores on first serves and their aggression scores on second serves for serve and return points respectively as well as the regression lines with confidence intervals.

The fourth and fifth plots show the relationship between the spread of serve and return aggression scores between first and second serve and the more aggressive point for the player, i.e. first serve for service points and second serve for return points as well as the regression lines with confidence intervals.

We can take away five preliminary observations.

Sara Errani knows where her money is made. The WTA is notoriously terrible for providing statistics. However, they do provide leaderboards for particular statistics, including return points and games won. Errani leads the tour in both this year. She also uniquely holds a higher Aggression Score on return points than serve points. From this information, we can hypothesize that Errani may play more aggressive on return points because she has greater confidence she can win those points or because she relies on those points more to win.

Maria Sharapova is insensitive to context; Elina Svitolina is highly sensitive to context. She falls outside of the confidence interval in all five plots. More specifically, Sharapova consistently is more aggressive on return points, second serve service points and first serve return points than her scores for service points, first serve service points and second serve return points respectively would predict. She has also lower spreads on serve and return than her more aggressive points would predict.

This result suggests that Sharapova differentiates relatively little in how she approaches points according to whether she is serving or returning or whether it is first serve or second serve. Svitolina exhibits the opposite trend as Sharapova. Considering anecdotal thoughts from watching Sharapova and Svitolina, these results make sense. Sharapova’s serve does not seem to vary between first and second and we see a lot of double faults. Svitolina can vary between aggressive shot-making and big first serves and conservative play. Hot takes are not always wrong.

Lucie Safarova, meet Eugenie Bouchard; Ana Ivanovic, meet Garbine Muguruza. Looking at the plots, it is interesting to note how Safarova and Bouchard seem to follow each other across the various measures. The same is true for Ivanovic and Muguruza. A potential application of the aggression score is that it can point us to players that are comparable and may have similar results. Players with good results against Safarova and Ivanovic may have good results against Bouchard and Muguruza, two younger players whom they are much less likely to have played.

Serena Williams and Karolina Pliskova serve like Madison Keys and Petra Kvitova, but they are very different. Serena, Pliskova, Keys and Kvitova are all players that are known for their serves as their weapons. Serena and Pliskova have the third and fourth highest Aggression Scores respectively. However, they also have wide spreads on serve and return scores and they have much lower second serve service point scores than their first serve scores would predict, whereas Keys is about where the prediction places her and Kvitova is far more aggressive than her first serve points would predict.

While Serena is still a relatively aggressive returner, she rates lower on first serve return aggression than Maria Sharapova. Pliskova falls to the middle of the pack on return aggression. Kvitova and Keys, in contrast, are both very aggressive on return points. My hypothesis for the difference is that while Serena and Pliskova are aggressive players, their scores get inflated by using their first serve as a weapon and they are only somewhat more aggressive than the players that score below them. Kvitova and Keys, on the other had, are exceptionally aggressive players.

The WTA runs through Victoria Azarenka and Madison Keys. Oddly, the players who seemed to best capture the relationships between all of the aggression scores and spreads of aggression scores were Victoria Azarenka and Madison Keys. Neither strayed outside of the confidence interval and often ended up on the best-fit line from the regressions. They define average for the WTA top 20.

These thoughts are preliminary and any suggestions on how they could be used or improved would be helpful. I also must beseech you to help with the Match Charting Project to put more players over the 2,000 point mark and get more points for the players on this list to help their Aggression Scores a better part of reality.

## Is Serena Williams Taking Advantage of a Weak Era?

tl;dr: No.

Serena Williams is, without question, the best player in women’s tennis right now. She’s held that position off and on for over a decade, and it’s easy to make the case that she’s the best player in WTA history.

The longer one player dominates a sport, the tougher it is to distinguish between her ability level and the competitiveness of the field. Is Serena so successful right now because she is playing better than any woman in tennis history, or because by historical standards, the rest of the pack just isn’t very good?

As we’ll see, the level of play in women’s tennis has remained relatively steady over the last several decades. While there is no top player on tour these days who consistently challenges Serena as Justine Henin or peak Venus did, the overall quality of the pack is not much different than it has been at any point in the last 35 years.

Quantifying eras

Every year, a few new players break in, and a few players fade away. If the players who arrive are better than those who leave, the level of competition gets a bit harder for the players who were on tour for both seasons. That basic principle is enough to give us a rough estimate of “era strength.”

With this method, we can compare only adjacent years. But if we know that this year’s field is 1% stronger than last year’s, and last year’s field was 1% stronger than the year before that, we can calculate a comparison between this year’s field and that of two years ago.

Since 1978, the level of play has fluctuated within a range of about 10%. The 50th-best player from a strong year–1995, 1997, and 2006 stand out–would win 7% or 8% more points than the 50th-best player from a weak year, like 1982, 1991, and 2005. That’s not a huge difference. One or two key players retiring, breaking on to the scene, or missing substantial time due to injury can affect the overall level of play by a few percentage points.

The key here is that a dominant season in the mid-1980s isn’t much better or worse than a dominant season now. Perhaps Martina Navratilova faced a stiffer challenge from Chris Evert than Serena does from Maria Sharapova or Simona Halep, but that difference is at least partially balanced by a stronger pack beyond the top few players. Serena probably has to work harder to get through the early rounds of a Grand Slam than Martina did.

Direct comparisons

So, Serena’s great, and her greatness isn’t a mirage built on a weak era. Using this approach, how does she compare with the greats of the past?

Given an estimate of each season’s “pack strength,” we can rate every player-season back to 1978. For instance, if we approximate Serena’s points won in 2015 (based on games won and lost), we get a Dominance Ratio (the ratio of return points won to serve points lost) of 2.15. In layman’s terms, that means that she’s beating the 50th-ranked player in the world by a score of 6-1 6-1 or 6-1 6-2. The 2.15 number means she’s winning 115% more return points than that mid-pack opponent. If the pack were particularly strong this season, we’d adjust that number upwards to account for the level of competition.

Repeat the process for every top player, and we find some interesting things.

Serena’s 2.15–the second-best of her career, behind 2.19 in 2012–is extremely good, but only the 21st-ranked season since 1978. By this metric, the best season ever was Steffi Graf‘s 1995 campaign, at 2.42, with Navratilova’s 1986 and Evert’s 1981 close behind at 2.38.

Graf has seven of the top 20 seasons since 1978, Navratilova has four, and Evert has three. Venus’s 2000 ranks sixth, while Henin’s 2007 ranks tenth.

It seems to have become harder to post these extremely high single-season numbers. In the last ten years, only Serena, Henin, Sharapova, Kim Clijsters, and Lindsay Davenport have posted a season above 2.0. Serena has done so four times, making her the only player in that group to accomplish the feat more than once.

Best ever?

As we’ve seen in comparing Serena’s best seasons to those of the other greatest players in WTA history, it’s far from clear that Serena is the greatest of all time. Graf and Navratilova set an incredibly high standard, and since the greats all excelled in slightly different ways, against different peer groups, picking a GOAT may always be a matter of personal taste.

Assigning a rating to the current era, however, isn’t something we need to leave up to personal taste. I’m confident in the conclusion that Serena is not simply padding her career totals against a weak era. If anything, her own dominance–during an era when dominating the women’s game seems to be getting harder–is making her peers look weaker than they are.

## Ivo Karlovic and His Remarkable 10,466* Aces

Here’s the official story: This week, Ivo Karlovic crossed the much-heralded 10,000-ace milestone. Next up is the all-time record of 10,183 aces, held by Goran Ivanisevic.

Karlovic is one of the greatest servers in the game’s history, and he has in fact hit more than 10,000 aces. Ivanisevic was really good at serving, too, and he might even hold the all-time record. But when it comes down to the details in this week’s ATP press releases, all the numbers are wrong.

• The ATP doesn’t have any stats from before 1991. (Ivanisevic started playing tour-level matches in 1988.)
• ATP totals don’t include aces from Davis Cup matches, even though Davis Cup results are counted toward won-loss records and rankings.

I’ll add one more: There are plenty of other matches since 1991 with no recorded ace counts, too. By my count, we don’t have stats for 14 of Ivanisevic’s post-1991 matches. (They’re not on the official ATP site, anyway.) That doesn’t count Davis Cup, the Olympics (also no stats), and the now-defunct Grand Slam Cup.

If you like tracking records and comparing the best players from different eras, tennis might not be your sport. All of these problems exist for players who retired only recently, and some of the issues persist to the present day. And if you want to compare Federer or Ivanisevic with, say, Boris Becker or–it’s tough to write this without laughing–Pancho Gonzalez, you’re completely out of luck.

We’ll probably never find ace totals from all of the missing matches. But it seems silly to pretend we can identify the true record-holder and celebrate when these “records” are broken when we so obviously cannot.

Approximate* career* totals*

What we can do is estimate the number of missing aces for each of the top contenders. In Ivanisevic’s case, his 1988-90 seasons, combined with Davis Cup and other gaps in the record, total nearly 200 matches. Even if we can’t pinpoint the exact number of uncounted aces, we can come up with a number that demonstrates just how far ahead of Karlovic he currently stands.

To fill in the gaps, I calculated each player’s rate of aces per game for each surface for every season he played. For 1988-90, I used 1991 rates. (This post at First Ball In, which I discovered after writing mine, suggests that players improve their ace rates the first few seasons of their careers, so we should adjust a bit downward. That may be right. A 5% penalty for Goran’s 1988-90 knocks off about 60 aces from his total below.)

Once we crunch the numbers, we get an estimated 2,368 aces in Ivanisevic’s 195 “missing” matches. That gives him a career total of 12,551–a mark Karlovic couldn’t achieve until the end of 2017, if then.

But wait–Ivo has some missing matches, too! The gaps in his record only amount to 21 matches, mostly Davis Cup. The same approximation method adds 466 aces to his record, meaning he hit that 10,000th ace back in June, in his second-rounder against Alexander Zverev. Even with those nearly 500 “extra” aces, Ivanisevic’s record is almost surely out of reach.

What about Pete Sampras? Officially, Pete is fifth on the all-time list, with 8,858 aces. But like Goran, he played a lot of matches before record-keeping began in 1991. His ace record is missing nearly 200 matches, as well.

In Sampras’s case, we can estimate that he hit 1,815 aces that aren’t reflected in his official total. (In line with the caveat regarding Goran’s total above, we might want to knock that total down by 50 to reflect the possibility that he hit more aces in 1991 than in 1988-90.)

Making similar minor adjustments to the other members of the top five, Federer and Andy Roddick, here’s what the all-time list should look like, at least in general terms:

```Player      Official  Est Missing  Est Total
Ivanisevic     10183         2368      12551
Sampras         8858         1815      10673
Karlovic       10022          466      10488
Federer         9279          524       9803
Roddick         9074          694       9768
```

Coincidentally, Karlovic is officially within 200 aces of  Ivanisevic’s all-time record, and while he really isn’t anywhere near the record, he is that close our estimate of Sampras’s second-place total.

We can be confident that Ivo is a great server. But if we can’t be sure of his own ace total, mostly amassed in the last decade, it seems foolish to pretend that we’ll know when–or even if–he breaks the all-time record.