Golf Scores

#1
Yesterday my buddy and I both shot 84, 12 over par. But although we had the same gross scores we noticed that we did not tie any single hole.

Hole Me Him
1 0 2
2 1 0
3 -1 2
4 1 0
5 1 0
6 0 1
7 0 1
8 0 3
9 2 -1
10 3 1
11 1 0
12 0 1
13 2 -1
14 0 1
15 0 1
16 1 0
17 0 2
18 1 -1
Total 12 12

No ties at all seemed very unlikely. What is the probability of that? I tried to estimate it using a Monte Carlo approach with Excel. I got started by simulating just 10 rounds. Tied holes for the 10 simulated rounds were 4,5,2,5,3,8,5,8,2,6. The results indeed suggest that the probability of no ties is quite low. But how low?

I would be interested in a formulaic solution to this problem. For simplicity, assume that each player always has the same set of hole by hole scores, totaling 12 over par, but that the hole by hole pattern of the scores can vary.

Thanks,
Jonart
 

hlsmith

Omega Contributor
#3
In general it would also be interesting to see if certain holes with comparable traits (short, hills, hazards) resulted in similar within player scores.
 

ArtK

New Member
#4
Jonart, I took the approach of using a Poisson PMF on a per-hole basis
where lamda is the average # of strokes. I squared each p(x) to find the
probability for two matched players, and summed the results of x = 1, 2, 3, ...
on up to 30. Here's the results:

lambda ---p of tie
2 ------- 0.188
3 ------- 0.164
4 ------- 0.143
4.66 -----0.132 *Your average
5 -------0.127
6 -------0.116
7 -------0.107

I dunno if this method is correct but it at least gives believable results:)

Art