Standard deviation of the winner’s score
Standard deviation isn’t precisely a measurement of difficulty so much as a measure of exceptionality. Still, a look at the degree to which the winner was able – or unable – to distance himself from the field may tell us something about how easy (or difficult) the winner at least found the layout to be.
Here’s the table showing the average standard deviation performance for each winner at each course. In each case the winner’s score is compared with the four-round field average. A higher standard deviation – 3.0 or above – indicates a relative romp. A standard deviation below about 2.0 suggests that player performance was compressed…suggesting a tougher course. Between 2.25 and 2.75 would be a “normal” spread.
Courses are listed from smallest to largest standard deviation, which is to say from most to least competitive. Because golf is a game where less is more, winners’ standard deviations are always negative.
Average winner’s standard deviation
Winged Foot -2.20
Oakland Hills -2.24
Shinnecock Hills -2.39
Pebble Beach -2.93
As a group, these courses tend to compress the field; only Pebble produces winners who separate themselves from their competitors by more than a “normal” distance.
No course homogenizes a field quite like Merion…but Winged Foot comes close. Of its five champions, only Zoeller (and Norman) in 1984 stood apart. Their sub-par scores came in 2.74 standard deviations better than the field average. When Jones won in 1929, he managed only a -2.13 standard deviation spread, one of the smallest of his championship resume. Casper only reached -2.06 in 1959, Irwin’s 1974 win registered -2.17 and Oglivy topped out at a modest -1.90 in 2006.