# Seeking to Measure Quality of Performance A Bignacca by luckboy

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```									Seeking to Measure the Quality of Tennis Performance
By Alberto Brignacca (National Coach Tennis Federation, Italy) How many times have we heard tennis coaches, commentators, fans and even players say of a recently concluded contest: “What a great match…”? Sometimes, of course, we hear the opposite statement as well. It is common to think that the higher the ranking of the players the better the quality of the match, but we know this is not always the case. The question then is: Is there a system that, u sing available statistical data, can provide a numeric and therefore objective measure of the quality of tennis players’ performances in a given match? This issue is of great interest if, for example, we consider the opportunity to build databases that permit comparisons between different levels of play, i.e. performances of the pros and of the players that aspire to that level, such as top juniors. If we all agree with the assumption that the efficacy and quality of a player’s game is directly related to the ability to execute winning patterns of play – and likewise that poor performance results from a tendency to commit too many unforced errors – we can affirm that the quality of performance can be measured by analyzing these two variables. The methods expressed here represent two ways to treat the same issue, even if they differ in important aspects that will be underlined. 1. The winners/errors ratio method. This method, proposed recently by Josef Brabenec, has the benefit of simplicity because it just tabulates players’ winners and errors in a given match. In other words, when player A wins a given number of points in a match, these points are considered to be the simple sum of his/her winners plus the opponent’s errors. The same tally is carried out with player B. If we take as an example the 2005 US Open Men’s Singles final, in which Roger Federer defeated Andre Agassi 6-3, 2-6, 7-6, 6-1, we note that Federer won 132 points and hit 69 winners and 72 errors. Agassi won 106 points and hit 34 winners and 63 errors. As we can see, the sum of Federer’s winners and Agassi’s errors equals the total points won by Federer and vice versa.
US OPEN 2005 MEN'S SINGLES FINAL
PLAYER POINTS WON WINNERS TOTAL ERRORS UNFORCED ERRORS WINNER:ERROR RATIO

FEDERER AGASSI

132 106

69 34

72 63

37 28

1:1.04 1:1.85

The ratio in the last column is an indicator of the number of errors committed for every winner hit. Of course, a lower number means few errors and therefore better performance. In this match, Federer hit 1 winner for every 1.04 errors, while Agassi had a 1:1.85 ratio. Using this method, we see that the total winner/error ratio for
Seeking to Measure the Quality of Tennis Performance. A. Brignacca Italy)

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both players combined was 1:1.31, a calculation that can be used to evaluate the overall quality of the match and compare it with other matches. The problem with this method is that both forced and unforced errors are treated the same. From a match analysis point of view, this can be misleading; and in fact the author warns about this, recommending that the strokes preceding the eventual winner or error be analyzed. 2. The aggressive margin method This method (which comes from a methodological proposal by Bill Jacobson, creator of a match-analysis software program) is based on the idea that errors are not the same and should be divided into those that are forced and unforced. It separates errors that have been made following an opponent’s successful pattern of play and errors that are independent of those patterns. From a technical point of view, this method is more accurate than the one based on a simple tallying of winners and errors, even if it presents some significant problems in terms of interpretation and practicality. This method treats an opponent’s winner and a forced error caused by the opponent’s play in the same way (the sum is indicated as “points won with forcing shots”). Calculating a player’s so-called “aggressive margin” is a little more complicated than the simple data gathering of the first method and is expressed as a percentage. The formula is as follows: points won with forcing shots minus unforced errors are divided by total points played to come up with a number that indicates the ability of the player to take control of the points, while making few errors. Its goal is to take into account the modern play er’s need to be both aggressive and stingy with the amount of unforced errors he/she commits. In the same match considered before, we see that Federer’s aggressive margin was better than Agassi’s, with the Swiss able to end the point with a winning play almost half the time (43%) and only make 1.5 unforced errors for every 10 points played (15%). The difference between these two percentages (28.2%) was his aggressive margin.
US OPEN 2005 MEN'S SINGLES FINAL
PLAYER POINTS WON WINNERS TOTAL ERRORS UNFORCED ERRORS
POINTS WON WITH FORCING SHOTS

AGGRESSIVE MARGIN

FEDERER AGASSI

132 106

69 34

72 63

37 28

104 69

28.2% 17.2%

3. Pros and cons The winners/errors ratio method:
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PROS – simplicity of the method, consistency during data collection phase. CONS – not making a distinction between forced and unforced errors leads to distortion in drawing technical and tactical conclusions The aggressive margin method: PROS – ability to take into account the right technical attitude (control of the points) CONS – treating a player’s winners and his/her opponent’s forced errors in the same way requires the data collector have excellent technical judgment so that the statistics are accurately compiled and the results are consistent from one match to another. 4. Comparisons using available data It can be interesting to use the data available from the singles matches of pros and juniors during the 2005 Slam tournaments. Data has been collected from the tournaments’ websites and the table that follows shows the distribution of matches.
2005 SLAM TOURNAMENTS
MEN'S SINGLES WOMEN'S SINGLES BOY'S SINGLES GIRLS' SINGLES

AUSTRALIAN OPEN ROLAND GARROS WIMBLEDON US OPEN

127 123 126 89

126 127 127 88

63 63 39 8

63 63 39 9

If we consider the following t bles, it is clear that there is a strong correlation a between the players’ victories in the matches and his/her better performance (using the two methods) relative to the losing opponent. From a technical point of view, however, the second method seems to provide better results if we consider the levels of play and the different surfaces. For example, if we consider the French Open, played on red clay, we see that the more conservative style of play adopted by players is clearly shown by the aggressive margin method, but not as well by the winners/errors method.
WINNING PCT. OF PLAYERS WITH BETTER WINNER/ERROR RATIO GRAND SLAM TOURNAMENTS 2005 TOURNAMENT MEN'S SINGLES WOMEN'S SINGLES BOY'S SINGLES GIRLS' SINGLES

AUSTRALIAN OPEN ROLAND GARROS WIMBLEDON US OPEN

93.7% 86.1% 94.4% 90.0%

92.0% 92.9% 85.8% 89.7%

82.5% 95.2% 92.3% n/a

83.8% 84.1% 76.9% n/a

Seeking to Measure the Quality of Tennis Performance. A. Brignacca Italy)

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WINNING PCT. OF PLAYERS WITH BETTER AGGRESSIVE MARGIN GRAND SLAM TOURNAMENTS 2005 TOURNAMENT MEN'S SINGLES WOMEN'S SINGLES BOY'S SINGLES GIRLS' SINGLES

AUSTRALIAN OPEN ROLAND GARROS WIMBLEDON US OPEN

96.8% 94.3% 96.0% 98.7%

96.8% 96.0% 97.6% 93.6%

96.8% 100.0% 97.4% n/a

100.0% 96.8% 94.8% n/a

AVERAGE WINNER/ERROR RATIO GRAND SLAM TOURNAMENTS 2005
TOURNAMENT MEN'S SINGLES winning player losing player WOMEN'S SINGLES winning player losing player BOY'S SINGLES winning player losing player GIRLS' SINGLES winning player losing player

AUSTRALIAN OPEN ROLAND GARROS WIMBLEDON US OPEN

1:1.74 1:1.74 1:1.56 1:1.66

1:3.28 1:2.67 1:2.50 1:2.62

1:2.06 1:2.04 1:1.90 1:2.07

1:4.35 1:3.75 1:3.38 1:5.43

1:2.38 1:2.04 1:1.98 n/a

1:3.51 1:3.98 1:3.52 n/a

1:2.76 1:2.14 1:2.41 n/a

1:5.96 1:3.76 1:3.68 n/a

AVERAGE AGGRESSIVE MARGIN GRAND SLAM TOURNAMENTS 2005
TOURNAMENT MEN'S SINGLES winning player losing player WOMEN'S SINGLES winning player losing player BOY'S SINGLES winning player losing player GIRLS' SINGLES winning player losing player

AUSTRALIAN OPEN ROLAND GARROS WIMBLEDON US OPEN

22.5% 10.7% 29.0% 22.1%

11.0% -0.8% 21.9% 12.0%

14.0% 6.8% 25.2% 17.0%

0.3% -6.9% 12.2% 1.5%

14.3% 8.9% 23.1% n/a

4.7% -3.4% 12.8% n/a

9.4% 6.8% 19.2% n/a

-8.0% -5.3% 7.1% n/a

Both methods clearly show that if a player plays better than his/her opponent then he/she will win most of the time (sounds obvious, doesn’t it?), but the aggressive margin method seems to more accurately identify which of the two players’ performance was superior. If we consider the same matches, the aggressive margin method was for each category a better predictor of which players would win the matches. In two categories (Roland Garros Boys Singles and Australian Open Girls Singles) its accuracy rate was 100%; and indeed the only times the player with the better aggressive margin was not the winner were instances where the matches had unusual score-lines, for example 1-6, 7-5, 7-5. 5. Conclusions – Which method is best? In conclusion, it seems that the aggressive margin method is best at describing with just one number the quality of the players’ performance. It has been already noted that this method considers the difference between points won and opponents’ unforced errors as “points won with forcing shots” and this may not be accepted by everybody. However, the method’s strength is its recognition that the points a player loses when the opponent does not hit a clean winner are not necessarily errors.
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The following statistics from Pete Sampras’ epic win over main rival Andre Agassi in the 2001 U.S. Open quarterfinals also serve as a good means of comparing the two methods. Like in the other examples, the aggressive margin method was better at summarizing the quality of the match since it revealed that Sampras and Agassi both had a high ratio of points won with forcing shots relative to unforced errors, something rarely achieved by two players in the same match. It also showed that there were more than 8 winning plays every 10 points played.
US OPEN 2001 MEN'S SINGLES QUARTERFINAL
PLAYER POINTS WON WINNERS TOTAL ERRORS UNFORCED ERRORS
POINTS WON WITH FORCING SHOTS

AGGRESSIVE MARGIN

WINNER/ ERROR RATIO

SAMPRAS AGASSI

176 162

80 55

107 96

40 19

157 122

34.6% 30.5%

1.34 1.75

In addition – and this can be the subject of another study – the aggressive margin method can be useful for players (and their coaches) that want to reach the next level of play, as it shows clearly the balance between aggressive and more defensive play. We know that the higher the level the more players must develop their aggressive side, while still also keeping unforced errors to a minimum. Because the aggressive margin indicator summarizes performance in both of those areas, it can be used as a measure of a player’s competence and improvement. 6. Bibliography
Brabrenec J., A Different Look at the 2005 US Open, ITF Coaching & Sport Science Review, Issue 37, December 2005, pages 10-11. Jacobson B., Computennis Topics Notebook, Sports Software, Inc., 1993. Brignacca A., Candusso A., Strazza A., “Analisi statistica dei fattori maggiormente condizionanti l’esito dei match” (Project Work 2° Corso per Tecnici Nazionali della Federazione Italiana Tennis con valore di allenatore di quarto livello europeo), Scuola dello Sport C.O.N.I, 2005.

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