I'm becoming less enchanted with the idea that larger scoring spreads of total scores always indicates less luck. There are some fluky things about it, and it needs hundreds of rounds of data to even hope to work.

I still like the basic concept of looking at how "well" a course allocated the scores it gave out, and comparing that to how well random assortments of those scores would have worked.

To measure how well a given sorting of scores worked, I'm now looking at the correlation of a single hole's scores to the total scores from all other holes.

For Pro Worlds, I looked at the total score from the first two rounds on each hole, now well that total correlated with the other holes, and how well that total did compared to all the two-round totals that would have come from scrambling the scores on that hole.

The way Brewster Ridge #10 handed out its scores was better than only 17.9% of all random assortments. At the other extreme, Fox Run #16 handed out its scores in a way that was better 99.8% of all random assortments.

Looking closer, we can see that BR #10 generally gave out lower two-round-total scores to players who scored higher on other holes, with a correlation of negative 9.7%. Random ways of handing out scores would not have a preference as to who gets higher scores, so they would cluster around zero correlation.

FR#16 generally gave out higher two-round-total scores to the players who got higher scores on other holes, with a correlation of positive 27.5%. Usually, random allocations don'’t generate much correlation, so this hole beat random allocations 99.8% of the time.

If all the holes were allocating scores randomly, we would expect that some holes would fall toward the bottom of this measure, and some toward the top. However, 25 of the 32 holes had a positive correlation. There is only about a 1% chance of that happening if scores are only being allocated randomly.