For some time, I have believed that par 3’s in APBA are more difficult to one-putt than par 4’s or par 5’s. I reasoned that it has to be harder to get the ball closer to the pin on a par 3, since there aren’t really any short approach shots involved (a few 100-yard par 3’s notwithstanding).
I didn’t test this hypothesis directly, but I did the next best thing. I looked at whether the number of putts varies as a function of the hole’s par value. In other words, are there significantly more putts on par 3’s than par 4’s or par 5’s?
TL;DR – No. I looked at 18,450 holes of APBA Golf (1,025 rounds) and found no correlation between the number of putts per hole and that hole’s par value (-0.001). Overall, there were an average of 1.57 putts/hole. For par 3’s, that average was only marginally higher at 1.59, not enough to mean anything. Interestingly, the amount of variability of putts among par 3’s, 4’s, and 5’s was virtually the same (SD =0.56 in all three cases). Here is a summary of my findings.
I also looked at whether higher scores on holes were associated with more putts. Not surprisingly, they were. There was a 0.416 correlation between the number of putts on a hole and the hole score. I don’t have other things to compare it to (yet), but bad putting alone would seem to be a fairly strong factor in driving up scores.
Not only that, but bad putting has an even greater effect on how you shoot relative to par. There was a 0.504 correlation between the number of putts per hole and scores relative to par.
Several factors can account for why a given golfer’s putting numbers may be higher than average besides just being a bad putter. He may have trouble scrambling, such that his first putt is often from a long way off with little chance of going in. Or, he may be great at reaching greens in regulation–but not getting the ball close to the hole.
Taken together, these results indicate that, on average, putting accounts for more than one-and-a-half strokes per hole or roughly 28.3 putts per round. Obviously, these numbers will vary slightly based on the player and course involved. But, in general, putting difficulty does not appear to be related to a hole’s par value.
The PGA tour average for the last 3 years is 1.61 or so. I think your 1.57 is in the ball park of that average. For a board game, your APBA putting results seem pretty realistic to me. Also, like most people, I’m guessing that the data you collected comes from the All Time Greats (ATGs) and other top-rated players, who might be better putters on average than today’s set of tour pros–many of whom may never even get a card. These are just theories, mind you.