Cory in dc
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AtLarge posted some stats over on AZBilliards, so I did some math (Mike Page verified my calculations). I thought this group might be interested in one or both.
Originally Posted by AtLarge View Post
Eight days of One-Pocket:
Orcollo - Chohan
July 2017
Day 1: 3 - 10
Day 2: 11 - 10
Day 3: 15 - 10
Day 4: 9 - 10
4-Day Total: 38 - 40
Oct. 2017
Day 1: 10 - 7
Day 2: 10 - 6
Day 3: 10 - 8
Day 4: 10 - 12
4-Day Total: 40 - 33
8-Day Total: 78 - 73
Commentary by Cory in DC
You could this as Tony winning 3 out of 8 days of play. If they are dead even, meaning the probability of winning is 50/50, then the odds of Tony winning exactly 3 of 8 days are 22% (and the probability of winning 3 or fewer days if it's actually even is 36.3%). The odds of him winning exactly 4 of 8 are 27%. So, (1) Tony's odds of winning 3 of 8 days are too close to (2) Tony's odds of winning 4 of 8 days to statistically reject the null hypothesis that Tony and Dennis are even.
You could also view it by the game. Out of 151 trials, if the odds are in fact 50/50, then Tony's chance of winning between 70 and 75 games (i.e., coming close but not ahead) are about 33.6%. You still can't definitively reject the null hypothesis that Tony and Dennis are even.
It is still more likely than not that Dennis is better than Tony given the available data (so don't take the above to mean I'll bet on Tony at even odds), but we need more data to be statistically definitive. I.e., a rematch.
Cory
Originally Posted by AtLarge View Post
Eight days of One-Pocket:
Orcollo - Chohan
July 2017
Day 1: 3 - 10
Day 2: 11 - 10
Day 3: 15 - 10
Day 4: 9 - 10
4-Day Total: 38 - 40
Oct. 2017
Day 1: 10 - 7
Day 2: 10 - 6
Day 3: 10 - 8
Day 4: 10 - 12
4-Day Total: 40 - 33
8-Day Total: 78 - 73
Commentary by Cory in DC
You could this as Tony winning 3 out of 8 days of play. If they are dead even, meaning the probability of winning is 50/50, then the odds of Tony winning exactly 3 of 8 days are 22% (and the probability of winning 3 or fewer days if it's actually even is 36.3%). The odds of him winning exactly 4 of 8 are 27%. So, (1) Tony's odds of winning 3 of 8 days are too close to (2) Tony's odds of winning 4 of 8 days to statistically reject the null hypothesis that Tony and Dennis are even.
You could also view it by the game. Out of 151 trials, if the odds are in fact 50/50, then Tony's chance of winning between 70 and 75 games (i.e., coming close but not ahead) are about 33.6%. You still can't definitively reject the null hypothesis that Tony and Dennis are even.
It is still more likely than not that Dennis is better than Tony given the available data (so don't take the above to mean I'll bet on Tony at even odds), but we need more data to be statistically definitive. I.e., a rematch.
Cory