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How Likely was that Last Score?

You have come to a strange course and are playing with a new foursome, and as the game starts you take up a friendly wager with one of the other golfers. Looking to be in his early forties and wearing a straw hat and long white pants, he gives you a smile as he tells you his course handicap: "I'm a twelve, but I've been playing a lot worse lately." The required number of strokes is given, and your foursome tees up on the first hole.

During the round, you begin to doubt that your newfound friend in the straw hat is really a twelve handicap. Your doubt is strengthened when he takes off his shoes and socks, steps into a stream running across the fourteenth hole, and hits the ball out of the water onto the green. Your friend ends up with a 77 and wins the bet - big time.

You begin to wonder: Is this guy really a 12? What are the chances that, as a 12, he can shoot a 77? Is this something you could ever figure out?

Given the statistical nature of the golf handicap, this is something you can figure out, and we have reproduced a graph below to help you with the calculation:
Course Handicaps

We also reproduce the information in tabular format, which may be easier for some to use:

Net Course Handicap
Differential 0 - 5 6 - 12 13 - 21 22 - 30 30+
055555
-110101087
-22322211310
-35751432315
-4151121874022
-53792761747235
-679053632313060
-723491200552229101

The graph and table may seem a bit intimidating at first, but both are quite easy to use. The first step is to find your course handicap along the bottom of the graph (or top of the table). The second is to calculate what differential line you are (or net differential row, in the case of the table). The differential lines are the horizontal lines that run from 0 to negative 10 up the right side of the graph. Your differential line is calculated using the following formula:

(SCORE - RATING) x (113/SLOPE) - COURSE HANDICAP


Where Score is your score on the round, Rating is the course rating, Slope is the slope of the course, and Handicap is your current handicap. For example, if your course handicap was 15, and you shot an 82 on a course with a rating of 72 and a slope of 130, your differential would be (82-72) x (113/130) - 15 = -6.

You then follow the differential line horizontally until the position on the graph marked by your handicap. The vertical position of the differential line at that point corresponds to the odds of shooting the score (e.g. 5 to 1, 80 to 1 or 500 to 1). Also note that the scale is not linear, but that the distance from 1 to 10 is the same as from 10 to 100. You can find more specific odds by looking at the tick marks on the side of the graph, which show the levels for 2-9, 20-90, & 200-900.

On the table, you would look at the cell the corresponds to the row of your net differential line and the column of your course handicap. The number contained in that cell is the odds of shooting that score. For example, if your course handicap was 10, and you shot a 75 on a course with rating of 70 and slope of 120, your net differential would be (75-10) x (113/120) - 10 = -5. If you looked that up in the table you would see the number was 276, corresponing to a 1 in 276 (or 0.3%) chance of shooting that round. Not impossible, but not likely either.

Some people ask why for a differential of 0 the odds are still about 5 to 1? The explanation lies in the fact that your handicap is calculated with your best scores, so that you will need an above average day to have a score low enough to reach your handicap differential.

Let's go back to the example mentioned at the beginning of this discussion. Assume the rating and the slope of the course you played was 72 and 113, respectively. If the man in the straw hat, with a handicap of 12, shoots a 77 on such a course, the differential is calculated as (77-72) x (113/113) - 12 = -7. Find the differential line of -7 on the graph and follow it until you reach the vertical marked by a handicap of 12. This point is at the top of the graph, and corresponds to odds of approximately 1000 to 1, or about 0.1%. Was your competitor lucky or just too good for his handicap? You decide.
From Dean Knuth, the Pope of Slope
Beating your handicap by three strokes or more twice in tournaments becomes such a rare event that Section 10-3 of the USGA handicap system automatically reduces the player's USGA handicap index. Less than 1 percent of the golfers are reduced under that procedure, so it is an uncommon event, except by the sandbaggers of the links. However, it is true that the size of the handicap index does affect the probability of making a low net score.






















 
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