Hardcourt (i)
|
Proba-bility
|
Number of Games
|
Mean return categorie
|
Standard deviation
|
T-test
|
|
Hardcourt (o)
|
Proba-bility
|
Number of Games
|
Mean return categorie
|
Standard deviation
|
T-test
|
Category
|
|
Category
|
1
|
1-5%
|
1
|
-1,000
|
0,000
|
0,000
|
|
1
|
1-5%
|
42
|
-1,000
|
0,000
|
0,000
|
2
|
5-10%
|
70
|
-0,147
|
3,117
|
-0,394
|
|
2
|
5-10%
|
349
|
-0,414
|
2,546
|
-3,039
|
3
|
10-15%
|
118
|
-0,182
|
2,464
|
-0,802
|
|
3
|
10-15%
|
328
|
-0,385
|
2,117
|
-3,294
|
4
|
15-20%
|
198
|
-0,306
|
1,882
|
-2,287
|
|
4
|
15-20%
|
361
|
-0,255
|
1,960
|
-2,475
|
5
|
20-25%
|
272
|
-0,119
|
1,778
|
-1,100
|
|
5
|
20-25%
|
441
|
-0,288
|
1,617
|
-3,740
|
6
|
25-30%
|
311
|
-0,244
|
1,476
|
-2,915
|
|
6
|
25-30%
|
480
|
-0,235
|
1,485
|
-3,470
|
7
|
30-35%
|
316
|
-0,085
|
1,411
|
-1,066
|
|
7
|
30-35%
|
529
|
-0,137
|
1,382
|
-2,275
|
8
|
35-40%
|
344
|
-0,053
|
1,281
|
-0,760
|
|
8
|
35-40%
|
563
|
-0,085
|
1,269
|
-1,593
|
9
|
40-45%
|
335
|
-0,030
|
1,162
|
-0,465
|
|
9
|
40-45%
|
619
|
-0,046
|
1,158
|
-0,980
|
10
|
45-50%
|
297
|
0,095
|
1,058
|
1,546
|
|
10
|
45-50%
|
563
|
-0,109
|
1,051
|
-2,460
|
11
|
50-55%
|
291
|
-0,057
|
0,955
|
-1,013
|
|
11
|
50-55%
|
427
|
-0,022
|
0,959
|
-0,484
|
12
|
55-60%
|
299
|
-0,164
|
0,869
|
-3,266
|
|
12
|
55-60%
|
538
|
-0,042
|
0,861
|
-1,137
|
13
|
60-65%
|
350
|
-0,073
|
0,790
|
-1,731
|
|
13
|
60-65%
|
658
|
-0,080
|
0,791
|
-2,582
|
14
|
65-70%
|
331
|
-0,094
|
0,721
|
-2,378
|
|
14
|
65-70%
|
565
|
-0,056
|
0,711
|
-1,856
|
15
|
70-75%
|
324
|
-0,029
|
0,631
|
-0,841
|
|
15
|
70-75%
|
544
|
-0,013
|
0,624
|
-0,476
|
16
|
75-80%
|
312
|
-0,005
|
0,546
|
-0,147
|
|
16
|
75-80%
|
470
|
0,009
|
0,539
|
0,343
|
17
|
80-85%
|
294
|
-0,029
|
0,488
|
-1,031
|
|
17
|
80-85%
|
490
|
0,006
|
0,459
|
0,299
|
18
|
85-90%
|
194
|
-0,010
|
0,391
|
-0,347
|
|
18
|
85-90%
|
338
|
0,011
|
0,366
|
0,550
|
19
|
90-95%
|
153
|
-0,033
|
0,343
|
-1,186
|
|
19
|
90-95%
|
395
|
-0,032
|
0,335
|
-1,872
|
20
|
95-100%
|
82
|
-0,029
|
0,249
|
-1,050
|
|
20
|
95-100%
|
414
|
-0,017
|
0,210
|
-1,691
|
Total____4.892'>Total
|
|
4.892
|
|
|
|
|
Total____1.500'>Total
|
|
9.114
|
|
|
|
Table 18: Results of all WTA tournaments sorted by surface
Proba-bility__Number_of_Games'>Grass
|
Proba-bility
|
Number of Games
|
Mean return categorie
|
Standard deviation
|
T-test
|
|
Gravel
|
Proba-bility
|
Number of Games
|
Mean return categorie
|
Standard deviation
|
T-test
|
Category
|
|
Category
|
1
|
1-5%
|
5
|
-1,000
|
0,000
|
0,000
|
|
1
|
1-5%
|
5
|
-1,000
|
0,000
|
0,000
|
2
|
5-10%
|
48
|
-0,359
|
3,202
|
-0,776
|
|
2
|
5-10%
|
86
|
-0,746
|
1,658
|
-4,171
|
3
|
10-15%
|
53
|
-0,127
|
2,480
|
-0,374
|
|
3
|
10-15%
|
132
|
-0,469
|
1,986
|
-2,715
|
4
|
15-20%
|
82
|
-0,165
|
2,041
|
-0,732
|
|
4
|
15-20%
|
136
|
0,047
|
2,223
|
0,246
|
5
|
20-25%
|
89
|
-0,050
|
1,839
|
-0,258
|
|
5
|
20-25%
|
218
|
-0,258
|
1,648
|
-2,315
|
6
|
25-30%
|
97
|
0,035
|
1,636
|
0,212
|
|
6
|
25-30%
|
177
|
0,022
|
1,636
|
0,181
|
7
|
30-35%
|
82
|
-0,030
|
1,434
|
-0,193
|
|
7
|
30-35%
|
187
|
-0,119
|
1,388
|
-1,171
|
8
|
35-40%
|
86
|
0,147
|
1,329
|
1,026
|
|
8
|
35-40%
|
229
|
-0,047
|
1,281
|
-0,551
|
9
|
40-45%
|
83
|
-0,004
|
1,174
|
-0,035
|
|
9
|
40-45%
|
201
|
0,086
|
1,175
|
1,038
|
10
|
45-50%
|
88
|
-0,136
|
1,046
|
-1,217
|
|
10
|
45-50%
|
187
|
0,033
|
1,065
|
0,424
|
11
|
50-55%
|
56
|
-0,050
|
0,959
|
-0,391
|
|
11
|
50-55%
|
127
|
-0,116
|
0,953
|
-1,374
|
12
|
55-60%
|
84
|
-0,027
|
0,869
|
-0,285
|
|
12
|
55-60%
|
179
|
-0,081
|
0,867
|
-1,250
|
13
|
60-65%
|
89
|
-0,045
|
0,792
|
-0,531
|
|
13
|
60-65%
|
217
|
-0,111
|
0,794
|
-2,061
|
14
|
65-70%
|
90
|
-0,149
|
0,732
|
-1,935
|
|
14
|
65-70%
|
214
|
-0,146
|
0,730
|
-2,928
|
15
|
70-75%
|
81
|
-0,100
|
0,658
|
-1,370
|
|
15
|
70-75%
|
199
|
-0,013
|
0,627
|
-0,292
|
16
|
75-80%
|
93
|
-0,137
|
0,614
|
-2,154
|
|
16
|
75-80%
|
177
|
-0,065
|
0,580
|
-1,499
|
17
|
80-85%
|
88
|
-0,018
|
0,484
|
-0,346
|
|
17
|
80-85%
|
218
|
-0,022
|
0,479
|
-0,693
|
18
|
85-90%
|
75
|
-0,040
|
0,422
|
-0,812
|
|
18
|
85-90%
|
135
|
-0,041
|
0,425
|
-1,135
|
19
|
90-95%
|
73
|
-0,045
|
0,361
|
-1,060
|
|
19
|
90-95%
|
150
|
-0,009
|
0,307
|
-0,365
|
20
|
95-100%
|
58
|
-0,005
|
0,190
|
-0,214
|
|
20
|
95-100%
|
106
|
-0,007
|
0,198
|
-0,373
|
Total____716'>Total
|
|
1.500
|
|
|
|
|
Total
|
|
3.280
|
|
|
|
Hardcourt (i)
|
|
|
|
|
|
Hardcourt (o)
|
|
|
|
|
|
Proba-bility
|
Number of Games
|
Mean return categorie
|
Standard deviation
|
T-test
|
|
|
Proba-bility
|
Number of Games
|
Mean return categorie
|
Standard deviation
|
T-test
|
Category
|
|
Category
|
1
|
1-5%
|
0
|
0,000
|
0,000
|
0,000
|
|
1
|
1-5%
|
7
|
-1,000
|
0,000
|
0,000
|
2
|
5-10%
|
6
|
-1,000
|
0,000
|
0,000
|
|
2
|
5-10%
|
202
|
-0,700
|
1,920
|
-5,179
|
3
|
10-15%
|
14
|
1,247
|
3,726
|
1,253
|
|
3
|
10-15%
|
263
|
-0,264
|
2,294
|
-1,868
|
4
|
15-20%
|
24
|
-0,543
|
1,551
|
-1,715
|
|
4
|
15-20%
|
325
|
-0,100
|
2,124
|
-0,848
|
5
|
20-25%
|
32
|
0,243
|
2,024
|
0,680
|
|
5
|
20-25%
|
422
|
-0,101
|
1,783
|
-1,162
|
6
|
25-30%
|
47
|
0,090
|
1,696
|
0,366
|
|
6
|
25-30%
|
456
|
-0,159
|
1,542
|
-2,205
|
7
|
30-35%
|
50
|
-0,067
|
1,440
|
-0,331
|
|
7
|
30-35%
|
480
|
-0,076
|
1,415
|
-1,180
|
8
|
35-40%
|
54
|
-0,106
|
1,278
|
-0,609
|
|
8
|
35-40%
|
422
|
-0,128
|
1,253
|
-2,106
|
9
|
40-45%
|
49
|
-0,282
|
1,093
|
-1,804
|
|
9
|
40-45%
|
496
|
-0,190
|
1,123
|
-3,773
|
10
|
45-50%
|
52
|
-0,108
|
1,052
|
-0,742
|
|
10
|
45-50%
|
451
|
-0,105
|
1,047
|
-2,123
|
11
|
50-55%
|
52
|
-0,014
|
0,959
|
-0,103
|
|
11
|
50-55%
|
410
|
-0,088
|
0,950
|
-1,881
|
12
|
55-60%
|
46
|
-0,137
|
0,873
|
-1,060
|
|
12
|
55-60%
|
456
|
-0,027
|
0,862
|
-0,660
|
13
|
60-65%
|
51
|
0,097
|
0,750
|
0,926
|
|
13
|
60-65%
|
502
|
0,034
|
0,765
|
1,003
|
14
|
65-70%
|
58
|
0,020
|
0,691
|
0,224
|
|
14
|
65-70%
|
471
|
0,011
|
0,689
|
0,342
|
15
|
70-75%
|
47
|
-0,063
|
0,649
|
-0,661
|
|
15
|
70-75%
|
444
|
-0,079
|
0,649
|
-2,568
|
16
|
75-80%
|
48
|
-0,054
|
0,583
|
-0,641
|
|
16
|
75-80%
|
446
|
-0,011
|
0,550
|
-0,404
|
17
|
80-85%
|
35
|
-0,198
|
0,588
|
-1,989
|
|
17
|
80-85%
|
452
|
-0,031
|
0,488
|
-1,338
|
18
|
85-90%
|
23
|
-0,003
|
0,395
|
-0,037
|
|
18
|
85-90%
|
311
|
-0,029
|
0,410
|
-1,264
|
19
|
90-95%
|
22
|
-0,109
|
0,430
|
-1,184
|
|
19
|
90-95%
|
334
|
-0,048
|
0,357
|
-2,447
|
20
|
95-100%
|
6
|
0,037
|
0,008
|
11,000
|
|
20
|
95-100%
|
222
|
0,005
|
0,168
|
0,407
|
Total
|
|
716
|
|
|
|
|
Total
|
|
7.572
|
|
|
|
In tables 19 and 20 below the mean return in the underdog categories (1-7) and in the favorite categories (15-20) are given. At every surface, except hard-court (i), you see that the return on favorites is higher than on underdogs, which can be an indication for a favorite longshot bias. At hard-court (i) in ATP and WTA tennis the return in categories 1 to 7 is higher than in the categories 15-20, which can be an indication for a reverse favorite longshot bias.
Table 19: Mean return in category 1-7 and 15-20 over the years at ATP tournaments
Year
|
Mean return category 1-7
|
Mean return category 15-20
|
Grass
|
-0,178
|
-0,022
|
Gravel
|
-0,243
|
-0,020
|
Hard-court (i)
|
-0,178
|
-0,283
|
Hard-court (o)
|
-0,021
|
-0,006
|
Table 20: Mean return in category 1-7 and 15-20 over the years at WTA tournaments
Year
|
Mean return category 1-7
|
Mean return category 15-20
|
Grass
|
-0,101
|
-0,062
|
Gravel
|
-0,212
|
-0,027
|
Hard-court (i)
|
0,041
|
-0,081
|
Hard-court (o)
|
-0,187
|
-0,035
|
As said in section 5.4.1 we wanted to test the results over the years for ATP and WTA tournaments separately, with the goal of getting more t-values that are significant. Looking at the t-values in table 17 and 18, we see that they are actually becoming more insignificant.
By separating between ATP and WTA tournaments, the same as in section 5.3.2 happens; the results becoming more insignificant. When we put all the data together, the results are looking fine and significant, but when we split them apart, the results show a whole other point of view. This is not in line with the literature of Forrest & Mchale, 2007 and Cain et al, 2003. Only at hard-court (o) tournaments in ATP tournaments, we see significant t-values. In addition, table shows a higher return at favorites than underdogs in hard-court (o) tournaments. Based on those results we can say that there is a favorite longshot bias in hard-court (o) ATP tournaments.
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