problem with handicap system

Wow, you are right. I just wrote a little index and score database spreadsheet, so I've been studying the formulas. It seems a pretty straightforward error, what is their defense?

For others not up on the issue, here's the problem: In figuring the differential of a score, you first get the difference between your score and the course rating. So if you shot an 80 on a 72 rated course, that's a diff of 8. But that 8 doesn't mean much for the non-scratch golfer, because the course rating of 72 is only for scratch golfers . That's where the slope comes in. The slope is a number derived from the difference between the course rating (for the scratch golfer) and the bogey rating (every course has a bogey rating, bet you didn't know that). So, if a course has a slope of 130 (harder than the standard 113), your diff of 8 becomes a diff of 6.95 (8*113/130), thus lowering your score for the purpose of making a meaningful comparison to the scratch golfer. If the slope was easier, it would raise your score. The problem occurs for scores lower than the course rating. Let's say instead of shooting 80 on the 72 rated course, you shoot 68. That's a diff of -4. Ok, so as in the previous example, if the slope is 130, you apply the formula and end up with a diff of -3.48. That's odd, instead of lowering your score for the harder course, you just raised it! That's not right. But wait -- why apply the slope at all? The slope is only to adjust the score for the worse-than-scratch player, by definition. It makes no sense to apply it to a better than scratch player. For any score at the course rating or better, the diff should not be adjusted at all ! I think Reid argues that it should be adjusted, but in the opposite way. That's not correct because slope only has meaning for the worse-than-scratch golfer, by definition (slope derived from the bogey rating). For Reid to be right, you'd have to have a "pro rating", which would be a reverse slope. The so-called bonus-for-excellence (actually, penalty-for-suckiness) does work correctly for the plus handicappers, as Reid mentioned. (Reid, where is your article published?)

Erik, I think you mis-read my post. You say that the 96% bonus works correctly. Well, so did I. That was just a separate point at the end of the main discussion.

The main point is that the differential is calculated with a slope adjustment, which lowers the score for scores greater than the course rating, when the slope is greater than 113. But it increases the score for a score better than the course rating. That is logically inconsistent, firstly, and secondly, makes no sense when one considers the rationale for course rating and bogey rating. Your statement that a line will extend through the origin is interesting, but doesn't address the points I brought up.

Is that why it is called slope? I wondered about that, and it seems to make sense. Thanks :)

Yes Shindig. It comes from the "slope" of the line on a Cartesian coordinate system (like the x,y graphs you used in high school).
Here is a rough (ie not rigorous explanation) of why its called "slope".
A scratch golfer will average approximately (lets ignore the .96 factor for now) 72 in his 10 best scores of his last 20 rounds on a course (call it "Average Acres) rated at 72 and of average severity (more on this later). A 20 handicapper will average 92 in his 10 best of his last 20 on the same course. Now when they go to Oakmont (an extremely difficult, severe course) the scratch golfer's score will increase roughly in accordance with the increase in course rating (I would guess Oakmont is rated at about 78 from the tournament tees but I don't know). The scratch golfer is supposed to be able to average 78 in his ten best of his last 20 scores. In contrast, the 20 handicapper cannot average 98 in his ten best of his last 20 because the severity of Oakmont will injure his scoring ability far more than it will the scratch golfer's. He may average 120 in his ten best of his last 20. Now here is where the word "slope" comes in... Think back at the Cartesian coordinate system (the X-Y graph). As you go out to higher and higher handicappers (to the right on the X-axis), their ability to shoot "what they are suppose to be able to shoot" (based on their handicap and the course ratings) lessens. In other words it is harder for a 20 handicapper to play to his handicap at Oakmont than at "Average Acres". The line on the graph is very steep for Oakmont because as you go to the right on the X-axis and plot the player's acores, all the points are going to be high above 98 (around 120). Thus Oakmont has a high "slope" rating. (Draw a line through the middle of those points and through 0,0 and that line will have a slope (Y = mX +B, where m is the slope and B is the y-intercept (at Average Acres, B= 72)). Now over at Average Acres the slope Rating will be 113 (a number chosen to be average so that there is a standard to which all other courses can be compared and so that you won't get the sticky problem of having negative slopes). Our 20 handicapper's scores (his ten best of his last 20 I mean) will plot nicely around this average slope line (which will go up in accordance if you will (the slope value will be exactly 1) with the increase in the handicap of the player you are plotting SO THE 20 HANDICAPPER'S TEN BEST OF HIS LAST 20 WILL PLOT AROUND 92). Now lets go over to "Easy Acres " and plot some scores from this very flat, no hazards, no rough, short course with no forced carries. The scratch golfer will still shoot the course rating here according to the theory but the 20 handicapper will benefit from the "lack of severity" of this course and his best ten of his last 20 scores will average below 92. Maybe something like 86... THE TEN BEST SCORES WILL PLOT AROUND 86... In such a case the slope of the line will be less than 1 and the slope rating for Easy Acres will be less than the standard average of 113. It might have a slope rating of 100 or 92 or something.
In english now instead of math language... The severity of Oakmont hurts the bogey golfer much more than the scratch golfer because the scratch golfer is so good that he avoids many of the severe characteristics of the course. So his score won't go up AS MUCH AS THE BOGEY GOLFER'S WILL when they play Oakmont.
That's all there is to it!

To Will from a few posts ago... My mathematical analysis is in my book. The .96 bonus for excellence is handled correctly as both you and Erik stated in your posts. In an old thread at THESANDTRAP.COM, someone had it backwards.

Will: The USGA's response was of the 2+2=5 variety.
I would love to sit down with the person who came up with the slope idea. He or she must be brilliant. The concept is correct. The formula is flawed, however.

My opinion on why it is flawed? Its because the formula moves the plus handicapper's index in the wrong direction for scores shot on courses of high slope rating. I already posted that. Oh I see why you're making that comment... Go see Will's post. He asked me where the article was. I didn't mention it because I told you that I wouldn't ask people to refer to the book anymore and I haven't.
Please see my other posts on problems with chipping and pitching and problems with putting. I'm helping a lot of people (I hope)
Should the yellow line really be labeled "Handicap Index" in your graph? It looks like it should be labeled "Course X"

My understanding is this:

If you shoot above the course rating, and the course has a slope higher than 113, your score differential _decreases_ from the actual value, leading to a lower handicap. Under the slope system, a hypothetical course of sufficient difficulty could reduce a score of 82 to 72.

The math works the same way for scores below the course rating. If you shoot 62 on a course with a slope rating higher than 113, the slope calculation _decreases_ the differential from, say, 10, to some number closer to zero. Which means that for an expert, plus-handicap golfer, their rounds on _lower_ slope rated courses look better than those on higher slope rated courses.

Big Lex:
That's precisely why its wrong. A score on a lower slope rated course shouldn't look better than the same score on a higher rated course.
PS did you go to Washington and Lee? My two best childhood friends went there. Great school and Great Lacrosse team.

That's what I meant. Its the average course- the one with a slope rating of 113. It (as you know well) has a slope of 1 as do all courses of rating 113. So it should be labeled "Course 3 (slope 113). Handicap index is the x axis.

I know this doesn't apply to 99.99% of golfers. But my point is, hey, why not do it right? As it is now, two guys (A and B) shoot 65 every day at their home courses. one guy's(A) course has a slope rating of 135. The other guy's (B) has a slope rating of 100. The handicaps come out to be +5.6 for A and +7.6 for B.
B should give A 2 strokes if they were to have a match?? C'mon. (A's the better player!)

making a +4 into a +3.5 because the course has a high slope rating is not ok because it is easier for a + handicapper to beat a scratch golfer on a more severe course (higher slope rating). In other words it is easier for Phil Mickelson to beat a scratch golfer at Oakmont than at some rinky dink course. Alot easier. So he should have to give more not less strokes were they to have a match. So if he plays at Death Valley (72/155) and shoots 68's all the time he should have a handicap of more than +4 (more "plus", not less).

You and I of all people should not be disagreeing on this.

That's exactly the problem. For the plus handicapper, the scores on harder courses should be adjusted to reflect the increased difficulty of the course, just like it does for the duffer.

It's really very simple. Scores for all non-scratch golfers, for hard courses, should be adjusted lower. Scores for all non-scratch golfers, for easy courses, should be adjusted higher. Why would you adjust the score of a plus-handicapper to be better if he's playing an easier course? The whole purpose of the adjustment is to compensate for the difficulty of the course, not magnify the difference.

Erik, you are saying that a fellow who shoots 4 under on a 140 slope course should get strokes from a guy who shoots 4 under on a 120 slope course. Put that way, you can see the problem.

Glad to hear you agree with my original post, your last paragraph is completely correct.

So. I've made my point that the current formula is wrong.
Everyone sees that now.

How you decide to fix it is another thing but consider this... If I shoot 68 every day at Pine Valley (slope 153 from the back) and you shoot 68 every day at Easy Acres (same course rating) . You will be giving me strokes when we go to another course to play a match. I'll take that bet every time. If you ignore the slope modifier, we play even. Guess what? I'll still beat you more often than you will beat me because it takes more skill to shoot 68 at Pine Valley than at Easy Acres.

Throw away the slope system for + handicappers? That's one of the options for sure. So is the "no plus system " I proposed in my (dare I mention it?) book. But if you choose to use the slope system, you have to make the matches fair because that is the SPIRIT of the handicapping concept- so that golfers of varying abilities can have a fair match.
Bottom line: The current USGA system is not fair in its present state. That's what I've been saying in this thread for 5 days, guys.

I'm glad we can at least agree that the slope shouldn't be used to determine plus handicaps. And, by extension, that we agree with Reid's original posing of the handicap problem. Whew, glad that's over.

I'm from Australia and here we don't even use a slope rating.

What we do is we have a set course rating, for example at my course it is 74 and then we have a Calculated Course Rating for every comp day. This CCR is found by taking the net score of the player that comes in at 12.5% of the comp. This means that in a competition of 100 players, the CCR would be the net score of the player who finished 13th.

If that 13th best player shot a net 75 then the CCR would be 75. If on the same day I shot 75 of the stick then I would have played to 0. My handicap is 7 so I would have had a net 68 on a course with a rating of 75.

We then work out our handicaps for the next round by multiplying the number of shots we were under out handicaps by another number (0.2) which I will explain in more detail later and then we subtract that number from our exact handicap.

Playing off a 7 handicap I lose 0.2 from my handicap for every shot I am under the CCR. If I had shot a net 68 with a CCR of 75 then that would be
7 * 0.2 = 1.4. My exact handicap is 6.6 so it would then become 5.2.

The amount of shots that you lose for every shot you are under the CCR changes depending on your handicap.

27+ = 0.5
20-26 = 0.4
13-19 = 0.3
5-12 = 0.2
4- = 0.1

If you play over the CCR on a given day then you add 0.1 to your handicap.

I feel that this system works better than the slope rating because it still makes it easier for higher handicapers but it also works for scratch and plus handicap golfers.

This is a great thread! I had some email conversations with Erik yesterday, and he has won me over, in part, to his way of thinking. The reason is something that hasn't been discussed in great detail yet in this thread.

We have to get specific about what the concept of slope is intended to accomplish.

Slope is a system intended to compensate for the fact that certain course design elements affect golfers of different skill levels by varying degrees. Example: a forced carry of 150 yards from a men's tee. Any male (other than juniors or seniors) with an index of probably 10 or less has virtually zero problem with this; for 999 out of 1000 shots he hits here, the forced carry will not penalize him.

With respect to this specific design feature, he is equivalent to a scratch or better golfer . A scratch or +3 guy isn't any less penalized by this feature than he is.

But of course the higher handicap players will be penalized by this feature, to varying degrees depending on their skill level.

The slope system is intended to compensate for this sort of thing, and other features like it, to more accurately level the playing field for handicap competitions than can be done by course rating alone (which is essentially a measure of effective playing length of a course).

So, the question becomes, what design elements define the slope rating? In my example, if slope rating were based 100% on the number of forced carries of 150 yards or less, then obviously there should be no slope correction for determining handicap for players of index 10 or lower (golfers with average best score differentials of about 10 or less from the rating).

If the aggregate design features which factor into slope are thought to affect golfers to at least some degree up to the point of a scratch golfer, then obviously we should stop adjusting for slope when we get to the scratch level (avg. score differentials of zero or below).

This is what Erik suggests, and I agree...on the condition that the slope elements truly pertain only to golfers with hcp higher than scratch. Whether they do or not is another question, one that perhaps the creator of the system would be willing to answer. It's actually an empiric question, when you think about it.

I am not totally convinced that at a certain point the difficulty of a golf course becomes the same for all golfers. The slope system suggests this and may be designed as such, but it's hard to believe that Winged Foot from the tips doesn't pose certain challenges and risks that effect a scratch index, club pro, but do not affect David Toms.

You could argue that a utopian system would accurately adjust for all such design elements.

Anyway, I'm convinced that if the intent of the slope system was to compensate up to a certain point, then the system should be dropped beyond that point.

I'm also convinced that it is definitely wrong for the system to continue to function and have a paradoxical, opposite effect on competition at plus handicap levels.