Here is a link to the USGA Handicap Manual (Appendix E): http://www.usga.org/content/usga/home-page/Handicapping/handicap-manual.html#!rule-14410
This is a table that shows the probabilities of golfers of differing handicap index ranges returning “scores” (“net handicap differentials”). It’s a little hard to understand at first (and the math is based on USGA formulas), but it’s also very instructive.
It shows (among other things):
* Lower index players are generally more likely to shoot slightly above or below 0 differential than higher index players.
* But when it gets to taking it REALLY low (say -5, for instance), the higher index is more likely to do this than the lower index. A 30 or more index can do it once every 53 rounds. A 10 to 14.9 will do it once every 102 rounds. But a less than 0.0 will do it only once every 502 rounds.
SO…looking at Jim’s situation above (with an 11.8 index), he can expect to shoot “even” once every 4.7 rounds and “one under” once every 7.6 rounds.
And, likewise, multiplying these “probabilities” over FOUR rounds, the chances of being “even” for all four would be 487:1. The chances of being “one under” for all four rounds is 3,336:1.
PLEASE NOTE (however): As the WA committee is quick and correct to point out, this table, handicap calculations and handicap examinations are based NOT on par, but on COURSE RATINGS and differentials. Since we play shorter courses here, our course ratings are almost always LESS than par. If par is 72 but the course rating is 69, our “even” net handicap differential round will actually be (about) three UNDER par.
That’s why, for instance, when you look at flight scores on Thursday night, you may see flight winners with scores of (let’s say) four under par cumulative for the four rounds. Chances are very good that because they played courses with lower course ratings, their scores were actually HIGHER than the course ratings. As the committee explains, it’s all about DIFFERENTIALS (NOT PAR).