User:Bwestgate23/Tournament Play vs. Head-to-Head

Tournament Play Versus Head-to-head Competition
In general, a single handicapping system will not lead to equality in all types of competitions; for example, head-to-head matches, first place in a tournament, or top 25% in a tournament. The USGA's "average best" method is designed to give all players an equal chance at first prize in a tournament. Using this system, however, a weaker golfer will typically be at a disadvantage in a head-to-head match, or for a top 25% finish in a tournament, unless he is given more strokes than his handicap would dictate.

These issues arise because weaker golfers tend to have wider distributions (higher variance) of scores than stronger golfers. For example, consider the stylized score densities in Figure 1. Golfer A is stronger (average score 80) and also has a narrower distribution, golfer B is weaker (average score 90) and has a wider distribution. In reality, score distributions are discrete, not continuous, and also not typically symmetric like this, but the results given here remain valid.



In head-to-head play (2 competitors), the fairest handicapping method would be to align the averages (mean or median) of the two distributions, as in Figure 2, in this case by giving the weaker golfer 10 strokes. Then both competitors would have an equal chance of winning the match.

However, tournament play is very different. Consider a tournament with many golfers of skills A and B. Under the handicap of Figure 2, the B golfers would have a significant advantage to win the top prize in the tournament, because it is much more likely for a B golfer to have a very low net score. To remedy this, handicaps could be readjusted to align the 1st percentiles (for example) of the two distributions, as in Figure 3. In this case, golfer types A and B would have a roughly equal chance at shooting their "best" score and winning the top prize. However, if there are many prizes awarded in the tournament (for example, to the top 25% of golfers), the A golfers would now have a significant advantage to win those prizes, because the bulk of the A distribution is now to the left of the B distribution.