PGA Travelers (Cromwell, CT): What will be the TOURNEY-WINNING SCORE?
93% are choosing "20 under par or better." Statistical analysis indicates, however, far greater likelihood of "19 under par or worse."
The leaderboard looks like this:
For the winner to be 20 under par or better, Goydos needs -4 (66), Perry -5 (65), etc...
How likely is that?
Through yesterday, 240 rounds were played by those who made the weekend cut. This is the distribution:
| 61 | 1 | | | 62 | 0 | | | 63 | 4 | | | 64 | 6 |
| 65 | 19 | | | 66 | 36 | | | 67 | 43 | | | 68 | 46 |
| 69 | 24 | | | 70 | 32 | | | 71 | 11 | | | 72 | 7 |
| 73 | 6 | | | 74 | 1 | | | 76 | 1 | | | 78 | 1 |
If we leave out the scores of the 8 golfers cut after yesterday's round, this is the distribution and the percentages:
| score | # | percent | | | score | # | percent |
| 61 | 1 | 0.5% | | | 62 | 0 | 0.0% |
| 63 | 4 | 1.9% | | | 64 | 6 | 2.8% |
| 65 | 19 | 8.8% | | | 66 | 33 | 15.3% |
| 67 | 41 | 19.0% | | | 68 | 43 | 19.9% |
| 69 | 20 | 9.3% | | | 70 | 29 | 13.4% |
| 71 | 10 | 4.6% | | | 72 | 7 | 3.2% |
| 73 | 3 | 1.4% |
The overall mean is 67.7 with a standard deviation of 2.14. Below is the actual distribution of round scores (blue) for those who made the final cut, as well as a normalized statistical distribution (red):
Based on the normalized function, Goydos has a 21% of scoring 66 or better, Perry a 10.3% chance of scoring 65 or better, and Toms a 4.2% of scoring 64 or better.The chances of scoring a 63 or better is 1.4%, 62 or better 0.4%, and 61 or better 0.4%.
If we put them all together, there is only a 35.6% of someone shooting 20 or under for the tournament.
With typically tougher pin placements on the final day, that number drops still further.
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Now it may be that the leaders have better than average chance of shooting the necessary low scores. That might be the case (marginally) for Perry and Tom, but probably not for Goydos. If anything, a more likely distribution for him would include the scores of those who did not make the cut, as he has missed the cut this year more often than he has made it.
All told, this pick has almost a 2:1 likelihood of panning out, far better than the great majority of SftC picks, and certainly far better than any other afternoon offerings.
I don't think your analysis quite works. Mathematically, everything seems legit, but I think the application is incorrect. You've combined the entire field of golfers to get the probabilities of obtaining a particular score. In doing so you've limited your analysis to the average golfer when the field is made of below average and above average golfers. For example, you say there's a probability of .019 of any golfer to receive a score of 63. While that is true for any golfer, I would certainly say that the probability of Goydos' shooting a 63 is far greater than .019 since he's already already done it 2 of 3 rounds. Thoughts?
ReplyDeleteI just noticed your post. Thanks for posting. You may be correct, especially in retrospect, having lost the proposition.
ReplyDeleteI still think though that my odds were approximately correct. I'm not sure I agree with you about Goydos. Most statisticians dismiss the idea of the "hot hand" in basketball and other sports, attributing it instead to normal statistical variation (although i don't believe anyone has ever studies golf streaks). Where the analysis was deficient is that it's clear that Perry is not the average golfer. Still, I believe his performance that Sunday was highly unlikely.