5.4.1 Results surface - ATP and WTA tournaments
Table 15: Results of all ATP and WTA tournaments sorted by surface
|
|
|
|
Grass
|
|
|
|
|
Gravel
|
|
|
Category
|
Proba-bility
|
|
Number of games
|
Mean return category
|
Standard deviation
|
T-test
|
|
Number of games
|
Mean return category
|
Standard deviation
|
T-test
|
1
|
1-5%
|
|
25
|
1,586
|
7,153
|
1,109
|
|
47
|
-1,000
|
0,000
|
0,000
|
2
|
5-10%
|
|
142
|
-0,444
|
2,716
|
-1,950
|
|
265
|
-0,506
|
2,560
|
-3,214
|
3
|
10-15%
|
|
169
|
-0,359
|
2,157
|
-2,165
|
|
382
|
-0,469
|
1,980
|
-4,627
|
4
|
15-20%
|
|
218
|
-0,157
|
2,046
|
-1,135
|
|
392
|
-0,058
|
2,120
|
-0,541
|
5
|
20-25%
|
|
218
|
-0,057
|
1,834
|
-0,456
|
|
595
|
-0,196
|
1,710
|
-2,783
|
6
|
25-30%
|
|
242
|
-0,057
|
1,595
|
-0,558
|
|
547
|
-0,184
|
1,520
|
-2,842
|
7
|
30-35%
|
|
266
|
-0,180
|
1,364
|
-2,151
|
|
667
|
-0,110
|
1,400
|
-2,036
|
8
|
35-40%
|
|
251
|
0,045
|
1,309
|
0,540
|
|
758
|
-0,069
|
1,280
|
-1,495
|
9
|
40-45%
|
|
261
|
-0,141
|
1,138
|
-2,008
|
|
683
|
-0,037
|
1,160
|
-0,832
|
10
|
45-50%
|
|
257
|
-0,038
|
1,055
|
-0,582
|
|
680
|
0,004
|
1,060
|
0,103
|
11
|
50-55%
|
|
182
|
-0,071
|
0,953
|
-1,001
|
|
429
|
-0,089
|
0,950
|
-1,932
|
12
|
55-60%
|
|
239
|
-0,073
|
0,866
|
-1,306
|
|
627
|
-0,106
|
0,870
|
-3,061
|
13
|
60-65%
|
|
275
|
0,008
|
0,776
|
0,169
|
|
770
|
-0,048
|
0,780
|
-1,704
|
14
|
65-70%
|
|
258
|
-0,102
|
0,722
|
-2,263
|
|
703
|
-0,071
|
0,710
|
-2,657
|
15
|
70-75%
|
|
270
|
-0,010
|
0,621
|
-0,274
|
|
695
|
-0,039
|
0,640
|
-1,606
|
16
|
75-80%
|
|
238
|
-0,081
|
0,589
|
-2,132
|
|
573
|
-0,013
|
0,550
|
-0,577
|
17
|
80-85%
|
|
212
|
-0,025
|
0,486
|
-0,756
|
|
580
|
-0,019
|
0,480
|
-0,976
|
18
|
85-90%
|
|
204
|
-0,053
|
0,432
|
-1,739
|
|
412
|
-0,039
|
0,420
|
-1,866
|
19
|
90-95%
|
|
221
|
-0,021
|
0,327
|
-0,972
|
|
436
|
-0,012
|
0,310
|
-0,830
|
20
|
95-100%
|
|
182
|
-0,029
|
0,235
|
-1,651
|
|
355
|
-0,006
|
0,190
|
-0,620
|
Total
|
|
|
4.330
|
-0,261
|
28,375
|
|
|
10.596
|
-3,067
|
20,690
|
|
|
|
|
|
Hard-court (i)
|
|
|
|
Hard-court (o)
|
|
Category
|
Proba-bility
|
|
Number of games
|
Mean return category
|
Standard deviation
|
T-test
|
|
Number of games
|
Mean return category
|
Standard deviation
|
T-test
|
1
|
1-5%
|
|
1
|
-1,000
|
0,000
|
0,000
|
|
49
|
-1,000
|
0,000
|
0,000
|
2
|
5-10%
|
|
76
|
-0,214
|
2,998
|
-0,623
|
|
551
|
-0,519
|
2,338
|
-5,208
|
3
|
10-15%
|
|
132
|
-0,030
|
2,645
|
-0,132
|
|
591
|
-0,331
|
2,196
|
-3,667
|
4
|
15-20%
|
|
222
|
-0,331
|
1,847
|
-2,674
|
|
686
|
-0,182
|
2,039
|
-2,333
|
5
|
20-25%
|
|
304
|
-0,080
|
1,805
|
-0,777
|
|
863
|
-0,197
|
1,702
|
-3,392
|
6
|
25-30%
|
|
358
|
-0,200
|
1,508
|
-2,509
|
|
936
|
-0,198
|
1,513
|
-4,008
|
7
|
30-35%
|
|
366
|
-0,082
|
1,413
|
-1,113
|
|
1.009
|
-0,108
|
1,397
|
-2,453
|
8
|
35-40%
|
|
398
|
-0,060
|
1,279
|
-0,932
|
|
985
|
-0,104
|
1,262
|
-2,581
|
9
|
40-45%
|
|
384
|
-0,062
|
1,156
|
-1,047
|
|
1.115
|
-0,110
|
1,144
|
-3,209
|
10
|
45-50%
|
|
349
|
0,065
|
1,058
|
1,141
|
|
1.014
|
-0,107
|
1,048
|
-3,251
|
11
|
50-55%
|
|
343
|
-0,050
|
0,955
|
-0,974
|
|
837
|
-0,055
|
0,955
|
-1,658
|
12
|
55-60%
|
|
345
|
-0,160
|
0,868
|
-3,432
|
|
994
|
-0,035
|
0,861
|
-1,284
|
13
|
60-65%
|
|
401
|
-0,051
|
0,786
|
-1,310
|
|
1.160
|
-0,030
|
0,781
|
-1,323
|
14
|
65-70%
|
|
389
|
-0,077
|
0,717
|
-2,122
|
|
1.036
|
-0,025
|
0,702
|
-1,163
|
15
|
70-75%
|
|
371
|
-0,034
|
0,633
|
-1,025
|
|
988
|
-0,043
|
0,636
|
-2,104
|
16
|
75-80%
|
|
360
|
-0,011
|
0,551
|
-0,384
|
|
916
|
-0,001
|
0,544
|
-0,042
|
17
|
80-85%
|
|
329
|
-0,047
|
0,501
|
-1,710
|
|
942
|
-0,011
|
0,473
|
-0,746
|
18
|
85-90%
|
|
217
|
-0,009
|
0,390
|
-0,341
|
|
649
|
-0,008
|
0,388
|
-0,551
|
19
|
90-95%
|
|
175
|
-0,042
|
0,355
|
-1,582
|
|
729
|
-0,039
|
0,345
|
-3,051
|
20
|
95-100%
|
|
88
|
-0,024
|
0,241
|
-0,950
|
|
636
|
-0,010
|
0,197
|
-1,252
|
Total
|
|
|
5.608
|
-2,503
|
21,707
|
|
|
16.686
|
-3,113
|
20,521
|
|
Graph 4: Development of the mean return of ATP and WTA tournaments per surface
Table 16: Mean return in category 1-7 and 15-20 per surface
Year
|
Mean return category 1-7
|
Mean return category 15-20
|
Grass
|
-0,150
|
-0,036
|
Gravel
|
-0,233
|
-0,023
|
Hard-court (i)
|
-0,151
|
-0,028
|
Hard-court (o)
|
-0,239
|
-0,019
|
As said before, the favorite longshot bias is based on underdogs and favorites, so categories 1-7 (underdogs) and category 15-20 (favorites) are the most important. In table 12 a quick overview of the returns per surface is added. Looking at table 16 we see at every surface a lower return in the underdogs categories compared to the favorites, which can be a indication for the existence of a favorite longshot bias.
If we compare the t-values in the years with the t-values of section 5.1 and 5.2, we see a lot more insignificant results. Especially the results of gravel and hard-court (i) are insignificant. Because of those insignificant t-values (-2 < t < 2) we can doubt about the existence of a favorite longshot bias at those surfaces. It is interesting to test the ATP and WTA tournaments separately, because this might lead better t-values. With better t-values the doubt about the existence of a favorite longshot bias could disappear. In 5.4.2 we test the data per surface for ATP and WTA tournaments separately.
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