5.3.1 Results over the years - ATP and WTA tournaments
After looking at the difference between men and women in the previous section, this section will show results over the last 5 years separately.
Table 9: Results of all ATP and WTA tournaments sorted by year (2009-2013)
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2009
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2010
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2011
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Category
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Proba-bility
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Number of games
|
Mean return category
|
Standard deviation
|
T-test
|
|
Number of games
|
Mean return category
|
Standard deviation
|
T-test
|
|
Number of games
|
Mean return category
|
Standard deviation
|
T-test
|
1
|
1-5%
|
|
11
|
-1,000
|
0,000
|
0,000
|
|
5
|
-1,000
|
0,000
|
0,000
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24
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-1,000
|
0,000
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0,000
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2
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5-10%
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191
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-0,315
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2,850
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-1,525
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166
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-0,779
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1,642
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-6,112
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187
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-0,627
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2,066
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-4,147
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3
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10-15%
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282
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-0,276
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2,193
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-2,110
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|
242
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-0,225
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2,364
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-1,481
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264
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-0,387
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2,162
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-2,905
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4
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15-20%
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319
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-0,052
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2,137
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-0,432
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277
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-0,248
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1,958
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-2,109
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306
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-0,042
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2,154
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-0,345
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5
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20-25%
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392
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-0,183
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1,728
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-2,099
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421
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-0,107
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1,781
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-1,236
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387
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-0,187
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1,722
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-2,132
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6
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25-30%
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412
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-0,231
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1,490
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-3,153
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|
442
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-0,147
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1,542
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-2,008
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434
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-0,150
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1,547
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-2,022
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7
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30-35%
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|
389
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-0,057
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1,425
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-0,785
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|
468
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-0,168
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1,367
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-2,653
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495
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-0,199
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1,352
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-3,274
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8
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35-40%
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444
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-0,124
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1,254
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-2,090
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469
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-0,112
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1,261
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-1,923
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504
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-0,051
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1,281
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-0,894
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9
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40-45%
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472
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-0,058
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1,155
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-1,087
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483
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-0,065
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1,154
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-1,230
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480
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-0,098
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1,146
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-1,880
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10
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45-50%
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490
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-0,015
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1,058
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-0,320
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449
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-0,097
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1,046
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-1,970
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446
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-0,059
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1,055
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-1,187
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11
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50-55%
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385
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-0,049
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0,955
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-1,014
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399
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-0,084
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0,954
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-1,751
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325
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-0,107
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0,949
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-2,038
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12
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55-60%
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474
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-0,130
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0,867
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-3,270
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427
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-0,037
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0,864
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-0,889
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422
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-0,014
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0,860
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-0,345
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13
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60-65%
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530
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-0,047
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0,786
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-1,378
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529
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-0,037
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0,783
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-1,076
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486
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-0,041
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0,783
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-1,151
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14
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65-70%
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441
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-0,042
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0,706
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-1,259
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456
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-0,042
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0,706
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-1,274
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515
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-0,070
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0,715
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-2,211
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15
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70-75%
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408
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-0,033
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0,633
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-1,043
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475
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-0,028
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0,630
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-0,961
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489
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-0,004
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0,619
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-0,159
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16
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75-80%
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401
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-0,003
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0,545
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-0,126
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438
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-0,016
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0,554
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-0,590
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447
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-0,003
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0,546
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-0,123
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17
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80-85%
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424
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-0,007
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0,469
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-0,290
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415
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-0,040
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0,495
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-1,662
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398
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-0,027
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0,485
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-1,123
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18
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85-90%
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296
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-0,066
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0,442
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-2,567
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309
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-0,011
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0,393
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-0,486
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302
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-0,024
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0,404
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-1,036
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19
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90-95%
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352
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-0,044
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0,353
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-2,359
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293
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-0,044
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0,353
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-2,134
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314
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-0,039
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0,347
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-2,016
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20
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95-100%
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215
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-0,016
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0,218
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-1,062
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209
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-0,004
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0,186
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-0,342
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237
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0,002
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0,162
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0,176
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Total
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7.328
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-2,748
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21,264
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7.372
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-3,291
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20,032
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7.462
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-3,129
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20,357
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2012
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2013
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Category
|
Proba-bility
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Number of games
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Mean return category
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Standard deviation
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T-test
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|
Number of games
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Mean return category
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Standard deviation
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T-test
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1
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1-5%
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43
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-0,485
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3,380
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-0,942
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39
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0,090
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4,754
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0,118
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2
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5-10%
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264
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-0,448
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2,580
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-2,823
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226
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-0,330
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2,911
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-1,706
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3
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10-15%
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256
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-0,387
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2,130
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-2,914
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230
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-0,463
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2,057
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-3,410
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4
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15-20%
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304
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-0,314
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1,880
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-2,915
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312
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-0,197
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2,021
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-1,721
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5
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20-25%
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393
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-0,037
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1,830
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-0,405
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387
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-0,307
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1,608
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-3,759
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6
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25-30%
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395
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-0,234
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1,480
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-3,152
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400
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-0,134
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1,556
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-1,725
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7
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30-35%
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478
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0,010
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1,450
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0,158
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478
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-0,139
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1,383
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-2,193
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8
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35-40%
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480
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-0,099
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1,260
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-1,722
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495
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0,028
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1,305
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0,478
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9
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40-45%
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491
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-0,184
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1,120
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-3,636
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517
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-0,024
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1,164
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-0,462
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10
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45-50%
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415
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-0,050
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1,060
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-0,955
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|
500
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0,010
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1,058
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0,220
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11
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50-55%
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342
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0,000
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0,960
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0,004
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340
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-0,079
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0,956
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-1,527
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12
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55-60%
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402
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-0,101
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0,870
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-2,336
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480
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-0,104
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0,868
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-2,628
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13
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60-65%
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517
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0,016
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0,770
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0,484
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544
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-0,064
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0,790
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-1,902
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14
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65-70%
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491
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-0,014
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0,700
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-0,447
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483
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-0,108
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0,723
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-3,277
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15
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70-75%
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465
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-0,099
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0,660
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-3,258
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487
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-0,019
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0,627
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-0,681
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16
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75-80%
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404
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-0,029
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0,560
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-1,055
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397
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-0,026
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0,559
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-0,910
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17
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80-85%
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|
417
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-0,038
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0,490
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-1,580
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|
409
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0,008
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0,455
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0,375
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18
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85-90%
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|
274
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-0,003
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0,380
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-0,131
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|
301
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-0,010
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0,394
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-0,452
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19
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90-95%
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|
323
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-0,009
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0,310
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-0,534
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|
279
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-0,008
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0,305
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-0,417
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20
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95-100%
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|
320
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-0,013
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0,200
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-1,168
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280
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-0,027
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0,232
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-1,966
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Total
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7.474
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-2,518
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24,070
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7.584
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-1,902
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25,727
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In the tables above, the pattern of the less negative return in the higher categories and the higher negative return in the lower categories still emerges.
Graph 3: Development of the mean return of ATP and WTA tournaments in the last 5 years (2009-2013)
Graph 3 shows the line of the mean returns per year. It is hard to see which favorite longshot bias is the strongest, but in every year there the line goes upwards.
In category 1 in 2013 there is a positive return of €0,090. In this category there are 39 matches and one match is won by an underdog which gives a high return and therefore the mean return is positive. Also category 8, 10 and 17 of 2013 matches will give you a positive return.
The favorite longshot bias is based on underdogs and favorites, which means we have to look at category 1 (underdogs) and category 20 (favorites). In table 10 a quick overview of the returns is added. In every year, except of 2013, the return in category 20 is higher than in category 1. Based on these facts, you might be able to conclude that, a favorite longshot bias exists in every year, except of 2013.
Table 10: Mean return in category 1-7 and 15-20 over the years
Year
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Mean return category 1-7
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Mean return category 15-20
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2009
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-0,178
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-0,027
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2010
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-0,221
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-0,025
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2011
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-0,235
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-0,015
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2012
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-0,204
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-0,231
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2013
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-0,037
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-0,014
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Looking at table 10, we see that for every year the underdog categories generate a lower mean return than the favorite categories, except of 2012. Based on those numbers, you might be able to conclude that, a favorite longshot bias exists in every year, except of 2012.
It is hard to look if the trend is becoming stronger over the years. If you look at the categories 1-7 the return gets lower till 2011 and from there the return gets higher. In the favorite categories the return till 2011 becomes higher, but in 2012 there is a very low result of -0,231. The results are not showing a clear trend over the years.
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. Because of those insignificant t-values (-2 < t < 2) we can doubt about the existence of a favorite longshot bias. 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 5.3.2 we test the data over the years for ATP and WTA tournaments separately.
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