Course rating tells scratch golfers how difficult the course will be; slope rating tells bogey golfers how difficult it will be.
To put it another way: USGA Course Rating tells the best golfers how hard a golf course actually plays; USGA Slope Rating indicates how much harder the course plays for "regular" (meaning not among the best) golfers.
The minimum slope rating is 55 and the maximum is 155 (slope does not relate specifically to strokes played as course rating does). When the slope rating system was first put into effect, the USGA set the slope for an "average" golf course at 113; however, not many 18-hole golf courses have slope ratings that low. Some do, but the real-world average is higher than 113. (However, a slope of 113 is still used in certain calculations within the handicap system.)
Like course rating, slope rating is calculated for each set of tees on a course, and a course may have a separate slope rating on certain tees for women golfers.
The most important role of slope is leveling the playing field for players of different skill levels. For example, let's say Player A and Player B average 85 strokes each for 18 holes. But Player A's average is established on a very difficult course (say, a slope rating of 150), while Player B's average is established on a much easier course (say, a slope rating of 105). If handicaps were simply estimates of golfers' average scores, then these two players would have the same handicap index. But Player A is clearly the better golfer, and in a match between the two Player B would clearly need some strokes.
Slope rating allows the handicap index to reflect these factors. Because he plays on a course with a higher slope rating, Player A's handicap index will be lower than Player B's (when it is calculated using the slope ratings), despite the fact that they both average scores of 85. So when A and B get together to play, B will get those extra strokes he needs.
Slope rating also allows golfers to go to different golf courses and adjust their handicap index up or down depending on how difficult each course plays (this is the "course handicap" mentioned above).
Slope is primarily used in the United States, but golf associations in other countries are beginning to adopt slope or similar systems.
Why is it called "slope"?
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