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The Slope and Rating II: Calculations

One of the most important components in the calculation of your handicap is the rating and slope of the course that you play. The slope and rating numbers are used to measure a course's difficulty. The rating represents the average score a scratch golfer (handicap of 0) would shoot on the course, and the slope represents the increased level of difficulty a bogey golfer (handicap of 18) would face as compared to a scratch golfer. For more information about the basics of the rating and slope please see the first Rating and Slope article in this section.

So how does a course end up with a rating of 72.1 and slope of 134 versus a rating of 68 and slope of 115? Actually, the calculation is not at all what you would expect, and in the article below we shed light on the mystery.

Course Rating

Most golfers picture the course rating as being calculated by a group of scratch golfers who play the course, and turn in their scorecards to an official who takes the average. It may surprise you, but no actual playing is involved in the calculation of the course rating. The rating is solely a yardage formula with some slight adjustment for obstacles. This is because yardage should have the greatest effect on the game of a scratch golfer. Woods on the right or water in front of the tee do not bother a scratch golfer very much. But, the difference in trying to make a birdie from 120 yards versus 160 yards can be quite significant. For their calculations, the USGA employs an imaginary ideal scratch golfer who drives the ball 250 yards (225 of carry, 25 of roll), can hit his/her second shot 220 yards (200 and 20), tends to draw the ball and is strong at all phases of the game.

The Scratch Yardage Rating is the simple calculation, as it is essentially the course yardage divided by 220 plus 40.9. This rating may be adjusted for several factors, including whether a ball will roll longer or shorter than 25 yards, the number of elevated or dogleg holes, prevailing wind and altitude, etc. In essence, any factor that will alter the scratch golfer profile (to hit farther or shorter than 250 yards) will affect the Scratch Yardage Rating.

The Scratch Obstacle Rating is considerably more complex to calculate. Each rater receives a form with 11 boxes for each hole (that's 198 boxes in total). Into each box is entered a number representing an obstacle value.The standard is 4. A lower value means the difficulty posed by, say, trees, is less than standard. A 10 means the hole is etched into a jungle. The obstacles for each hole considered include: topography, fairway, recoverability & rough, out of bounds, water hazards, trees, bunkers, the green target, green surface, and a psychological factor. Each of these is weighted and the 18-hole sum of weighted values is multiplied by 0.11. Raters then subtract 4.9 to determine the Scratch Obstacle Rating.

The sum of the Scratch Yardage Rating and Scratch Obstacle Rating becomes the Course Rating.

Let's take a simplified example of a 6000 yard course (with no adjustments) that has average-type obstacles on every hole. The Scratch Yardage Rating would be 6000/220 + 40.9 = 68.2. The calculation of the Scratch Obstacle Rating is complex, but in this case would emerge around 3.0. Thus, the Course Rating would be calculated as 71.2.
Yardage versus Obstacle Ratings
While over 95% of the rating comes from the yardage, the swing in course rating often comes from the obstacles. For example, if the course suddenly became 400 yards longer, the Scratch Yardage Rating would incrase from 68.2 to 70.0, or 2.6%. In contrast, if our average course obstacles (rated 4) became much more difficult (rated 8) our Scratch Obstacle Rating would increase from 3.0 to 10.9, or over 250%.

Course Slope

So, for the slope, do we at least send bogey golfers out to play and compare their scores to the course rating? No. The USGA has created a model bogey golfer as well. The USGA's bogey golfer is meant to represent a golfer with a Handicap Index of 17.5 to 22.4. They can hit tee shots an average of 200 yards and can reach a 370 yard hole in two shots.

Similar to the course rating, the slope is made up of a Bogey Yardage Rating and a Bogey Obstacle Rating. The Bogey Yardage Rating is once again based on yardage, but uses a different formula. This time, it is equal to the course yardage divided by 160, plus 50.7. The Bogey Obstacle Rating is based on the same 11 factors, only they are weighted differently for each hole. The sum of the factors for all 18 holes is then multiplied by 0.26 and then 11.5 is subtracted. Note that obstacles are now much more significant because the 0.26 used is two and a half times as much as the 0.11 factor used for the Scratch Obstacle Rating.

Once again the Bogey Yardage Rating and Bogey Obstacle Rating are added together to create the Bogey Rating. But there is still one more calculation to go. The difference between the Bogey Rating and the Course Rating is multiplied by 5.381, and the result is the slope (i.e. [BR-CR]*5.381=slope). Why 5.381? Using this number as a multiplying factor will produce Slope Ratings of 113 when the differential between the Bogey Rating and Course Rating is 21.0 (The expected difference in score on an average course between our model scratch golfer and bogey golfer with handicap between 17.5 and 22). A Slope of 113 (actually 1.13) also is the empirically derived regression value of scores played on standard American golf courses. So it all ties together.

Let's revisit our 6000 yard course, this time with our bogey golfer in mind. The Bogey Yardage Rating is 6000/160+ 50.7, or 88.2. The same average obstacles now become a Bogey Obstacle Rating of 7.2. Together, the Bogey Rating is 95.4, 24.2 points higher than our Course Rating of 71.2. 24.2 Multiplied by 5.381, our slope is calculated as 130.

A lot of number crunching to be sure, but still this process is not an exact science. What it does do, though, is bring the handicap system to a new level of accuracy across handicaps.

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