Changes to Handicapping System for Next Year

[Libbing]

OK, just ran a similar Excel file:
1) 500 one-on-one series of 20 matches (so 1000 rounds; recalcing changed answer by 1% or less every time, so sample is valid)
2) Handicap formula with the 96% factor, rating 71.5, slope 128; using the average of the best 50% of each of the 20 round series of matches
3) I did not round or truncate any scores (just used the actual decimals for all calcs)
4) did this with stroke play with no accounting for adjusting scores / maxing scores per hole (I think this makes it even worse for the high HC)
Results:
a) baseline; both players shoot the exact score every time: Low HC shooting 72 every round wins 100% of the time vs a high HC shooting 82 every time; this is due to the 96% factor
b) same differential; Low HC shoots between 72-77; High HC shoots between 82-87; Low HC wins 56% of the time
c) higher differential for high handicapper; Low HC shoots 72-77; high HC shoots 82 - 92; Low HC wins 65% of the time (that is pretty much the same outcome as the simple grid that predicted 66% to the low HC)
d) really high differential for high handicapper; Low HC shoots 72-77; high HC shoots 82 - 102; Low HC wins 70% of the time

So, low handicapper is better off due to the 96% factor and due to a lower deviation in scores.

[BC MIST]

(1) By definition, that rating should plot the impact of those design features across a broad spectrum of players to derive that MX+B formula.
(2)On the second point, handicap strokes are designed to be given out on the most difficult holes first.

(1) Courses are rated based on the performance of TWO golfers, the "scratch" golfer and the "bogey" golfer, as defined in the RCGA Handicap manual. The slope is a measure of relative difficulty for golfers who are not scratch and is calculated by multiplying the difference in course ratings of the two golfers by 5.381.

(2) Strokes are not allocated based on the degree of difficulty of a hole. Unfortunately, most golfers still believe that the #1 handicapped hole is the most difficult hole, but this is not true. Your #1 hole is the hole on which the higher handicapped golfer NEEDS a stroke. For example, a couple of years ago I took hundreds of scores from our weekly Men's Night and determined average score per hole for the ten lowest handicapped golfers (average handicap of 3) and the worst 10 golfers (average handicap of 22). The averages were then subtracted and the holes ranked by the difference. #6 Premiere, a sub 500 yard par 5, averaged 4.86 for the better players, but averaged 7.03 for the weaker ones. It was the easiest hole for the good players and the hardest for the poorer ones. It had the greatest difference of any hole on that course, making it the #1 handicapped hole because it is the hole on which the high handicapped player NEEDS a stroke.
The par 3's, generally speaking, are the more difficult holes on courses for both types of golfers, as the average approach shot is normally longer than the average par 4. However, the par 3's will have a higher handicap number, because there is less chance of "bogey" golfer making a large number.

[mjf]

So, low handicapper is better off due to the 96% factor and due to a lower deviation in scores.

So... if the purpose of this whole activity was to put the higher handicappers on an equal footing with lower handicappers, why not simply get rid of the 96% factor?

[jvincent]

I think Libbing's assertion that the 0.96 factor is what is causing the lower handicap to do better is not really looking at the whole picture.

My analysis looked at a random set of results that were calculated using the handicap formula and integer numbers for scores. It's important to use integers because that's how golf is scored.

In a stroke play competition I think having the low handicaps win slightly more than 50% is "right" in a net event. They are more consistent and as such should win more but not so much more as to be unfair. A 56% win rate satisfies that condition IMHO.

Match play might end up being a completely different story since the effect of big numbers are less penal on the high handicap golfer. I should be able to whip something together tonight for match play.

[Libbing]

(1) Courses are rated based on the performance of TWO golfers, the "scratch" golfer and the "bogey" golfer, as defined in the RCGA Handicap manual. The slope is a measure of relative difficulty for golfers who are not scratch and is calculated by multiplying the difference in course ratings of the two golfers by 5.381.

(2) Strokes are not allocated based on the degree of difficulty of a hole. Unfortunately, most golfers still believe that the #1 handicapped hole is the most difficult hole, but this is not true. Your #1 hole is the hole on which the higher handicapped golfer NEEDS a stroke. For example, a couple of years ago I took hundreds of scores from our weekly Men's Night and determined average score per hole for the ten lowest handicapped golfers (average handicap of 3) and the worst 10 golfers (average handicap of 22). The averages were then subtracted and the holes ranked by the difference. #6 Premiere, a sub 500 yard par 5, averaged 4.86 for the better players, but averaged 7.03 for the weaker ones. It was the easiest hole for the good players and the hardest for the poorer ones. It had the greatest difference of any hole on that course, making it the #1 handicapped hole because it is the hole on which the high handicapped player NEEDS a stroke.
The par 3's, generally speaking, are the more difficult holes on courses for both types of golfers, as the average approach shot is normally longer than the average par 4. However, the par 3's will have a higher handicap number, because there is less chance of "bogey" golfer making a large number.

Good clarifications. But I think the points still hold (the MX+B formula is intended to plot performance across golfers; they use a scratch golf and a bogie golfer to approximate that. I didn't realize that's how they did. I had given them too much credit assuming they'd use a bigger pool. Given that the resulting line is used for everyone, they assume that differential holds throughout the range of talents.

In terms of the difficulty of holes, totally agree with you. Rather than saying "hardest holes", we should say "hardest holes for a higher handicap player vs a lower handicap player)"; but that's too many words. I'll stick to "hardest holes"!. Again though, my point holds in that it only works as designed when there is a one on one match. When you get a three man bet going the strokes between the worst two golfers are usually not handed out correctly (middle handicap usually gives strokes to the high handicap on the wrong holes; but fixing that means you have to keep track of 3 different matches rather than one).

[Libbing]

I think Libbing's assertion that the 0.96 factor is what is causing the lower handicap to do better is not really looking at the whole picture.

My analysis looked at a random set of results that were calculated using the handicap formula and integer numbers for scores. It's important to use integers because that's how golf is scored.

In a stroke play competition I think having the low handicaps win slightly more than 50% is "right" in a net event. They are more consistent and as such should win more but not so much more as to be unfair. A 56% win rate satisfies that condition IMHO.

Match play might end up being a completely different story since the effect of big numbers are less penal on the high handicap golfer. I should be able to whip something together tonight for match play.

To be clear, I think the lower handicapper has an advantage because of the .96 AND, MORE IMPORTANTLY, because I am assuming that lower handicappers on average have lower absolute deviations of scores (note that the absolute deviation is important, not the percent deviation). If you take the deviation difference (lower HC has less deviation) as a given, and you assume that scores are evenly distributed across the range of scores (not necessarily a safe assumption), then this is simple math on both the .96 and the calculation. I don't see any question about it.

Now for the reality check which might lessen but not negate the answer. Not all high handicappers have higher absolute deviations in scores than lower handicappers. I've known 8 handicappers that have a slightly tighter range than a 4 HC. I don't think that is the norm. But who knows - it would be interesting to get data on that. The other issue with the whole random number generator is that 20 scores computed randomly with a given range might not represent an actual golfer. I'm guessing there is some kind of bell curve that could impact these answers. Not sure whether it would or not, but it might.

So, the system rewards consistency and talent. Shocker. That's not a bad thing, but it doesn't mean I'm going to put a lot of money on the system assuming it's expected to result in a 50/50 chance of wining (unless, of course, I'm playing someone that is wilder than me).

In terms of whole numbers, assuming random outcomes and random slopes / ratings, using whole numbers vs decimals should not have an impact (high or low handicap I would think would have equal exposure to getting more or less scores shaved off). But I'll run it and see. Would be surprised if my answer changed more than a couple of percent.

In any event, I think we've concluded that there is an advantage to the better golfer. Just a matter of degree from there.

[jvincent]

The other issue with the whole random number generator is that 20 scores computed randomly with a given range might not represent an actual golfer. I'm guessing there is some kind of bell curve that could impact these answers. Not sure whether it would or not, but it might.

For an individual golfer, I'm pretty sure the scores would not be truly random. However, since this is supposed to apply across the entire population of golfers, it should be random.

I think I've figured out how to simultaneously calculate results for both stroke and match play so I will give that a shot tonight. I'm curious what it will look like.

This brings us back full circle to why was the change made?

My analysis suggests that for stroke play competitions the new system is worse for the high handicap golfer, which is opposite of what was supposed to happen. Maybe the result will be different for match play?

[Libbing]

I think it is more fair for match play because ballooned holes don't matter as much for the high deviation player. We've all been in those rounds where you hit a par on one hole and a 9 on the next. That happens more frequently with higher handicappers.

I reran my numbers truncating the index and rounding the handicap. Increased the amount by which it favored the better player by another 1%.

[BC MIST]

This brings us back full circle to why was the change made?

My analysis suggests that for stroke play competitions the new system is worse for the high handicap golfer, which is opposite of what was supposed to happen. Maybe the result will be different for match play?

If the high handicap player is more likely to have a higher differential total, and as a consequence a higher course handicap, while the LH player's total does not change, how can the new ESC be worse for the weaker player?

[Libbing]

BC - I agree. The new rules help the higher handicapper because on average it allows higher scores over par to be recorded for handicap determination. For example, for a 15 handicapper, the max score for determining handicap on a par 3 was a 5; the new max is a 7. So, for determining a player's index, a 15 handicapper will be allowed to post 2 additional strokes on that hole, thus recording a a worse total score and thus giving them a higher index and thus more strokes in a compeitition.

Most of the recent back and forth here has been whether the system favors high vs low rather than new vs old system. I still think the system is more equitable in match play than stroke play.

[jvincent]

If the high handicap player is more likely to have a higher differential total, and as a consequence a higher course handicap, while the LH player's total does not change, how can the new ESC be worse for the weaker player?

Good question. I'm not 100% confident in my methodology at this point, which is why I want to do an actual hole by hole calculation. That way I can calculate HDCPs for both the new and old system and compare stroke vs match play results from a single, consistent set of data.

Almost finished it last night. Need to do some RTFMing on Excel and a few more tweaks.

[bentgrass]

As someone who is interested in the math behind handicaps and the probabilities of winning competitions between players of different abilities and consistency, I find the site www.popeofslope.com to be a good reference. Here is a link to a page describing the rationale of the 96% "bonus for excellence" factor and the effect on the probabilities of a lower handicap player beating a higher handicap player (53% for a 1 stroke difference in handicaps, 60% for 6 stroke difference):

http://www.popeofslope.com/magazine/...xcellence.html

[adanac]

Good question. I'm not 100% confident in my methodology at this point, which is why I want to do an actual hole by hole calculation. That way I can calculate HDCPs for both the new and old system and compare stroke vs match play results from a single, consistent set of data.

Almost finished it last night. Need to do some RTFMing on Excel and a few more tweaks.

Interesting that you think some randomly generated scores for two fictitious players can be a suitable substitute for 100,000 actual scores by real players. Seems you are simply trying to "prove" your own point of view. Just sayin'.

[jvincent]

Have you read the whole thread?

My assertion is that the study was flawed because the results are biased by using scores from only one course. If they had used results from several different courses then the results would have been better randomized and as such more statistically valid.

If a truly random (i.e. genereated) set of data gets the same results then I have no issue. If they don't, then the original study needs to be questioned.

Sorry, but I spent too much time in math classes to let bad statistical methods like this slide.

[adanac]

Yes, I've read the entire thread. The USGA uses the same method of equitable stroke control, and have for several years. Are you suggesting that their evaluation is flawed also?
What do you see as the end result of your exercise?

[jvincent]

Yes, I am saying it is flawed. Even Dean Knuth, the guy at the USGA who created the slope based system, says that the current USGA system is flawed. See the following quote from him.

In fact, there are more substantial errors already present in the Handicap System through Equitable Stroke Control. While ESC works well for the single digit handicapper, it penalizes double-digit handicappers who have limits of 7s and 8s on their cards. That's too much on par threes, but not enough on par fives. So more errors can come from ESC limits than the effect of any driver, conforming or nonconforming.

I am trying to decide where the analysis done by the RCGA that says the new system is more fair to higher handicap golfers is correct or not using a proper, i.e. truly random, set of scores. Go ask any stats professor if a data sample taken at one golf course is valid when applied generally to handicaps that must cover ALL golf courses and see what answer you get.

[AAA]

One of the reasons why the UK has not taken on slope is because it has been found to be seriously flawed at around the 17 handicapper.

It seems Australia are having problems with introducing the USGA system and slope. In the mid range the current handicaps simply don't tie up. I don't know the detail but that seems to be the gist.

[adanac]

Yes, I am saying it is flawed. Even Dean Knuth, the guy at the USGA who created the slope based system, says that the current USGA system is flawed. See the following quote from him.



I am trying to decide where the analysis done by the RCGA that says the new system is more fair to higher handicap golfers is correct or not using a proper, i.e. truly random, set of scores. Go ask any stats professor if a data sample taken at one golf course is valid when applied generally to handicaps that must cover ALL golf courses and see what answer you get.

Again, what outcomes do you expect from your theoretical exercise? Have you discussed your concern with the RCGA personnel involved with handicapping?
Just askin' to see where you're goin'.

[Kilroy]

What's wrong with him doing this to satisfy his own thurst for knowlege? It's one thing to have an opinion, it's quite another when you have done the math to back up that opinion.

[adanac]

What's wrong with him doing this to satisfy his own thurst for knowlege? It's one thing to have an opinion, it's quite another when you have done the math to back up that opinion.

Whose math and whose opinion is better? In my opinion, it's always better to use real scores from real golfers (and the more data the better) than randomly-generated (not really random from the description) numbers from fictitious players. Again in my opinion, scores made by real players are not random.
We also have to recognize that no system of handicapping is perfect, in spite of everyone's best efforts. There are, and always will be, anomalies.

Now I've worked up a real thirst.

[jvincent]

Again, what outcomes do you expect from your theoretical exercise? Have you discussed your concern with the RCGA personnel involved with handicapping?
Just askin' to see where you're goin'.

I'm doing it just to see if the RCGA made the correct decision. I know based on past discussions with them that they won't change their mind on this so contacting them is of little value.

What I find ironic is that the man who created the current USGA handicap system believes it is flawed, has suggested a reasonable alternative, and it has not been adopted by the USGA. For the RCGA to fall in line (intentional use of words) with the USGA given this is typical. I would not be surprised if the USGA was putting pressure on the RCGA.

[jvincent]

Whose math and whose opinion is better? In my opinion, it's always better to use real scores from real golfers (and the more data the better) than randomly-generated (not really random from the description) numbers from fictitious players. Again in my opinion, scores made by real players are not random.

The only reason for taking a large sample of golfers is to get randomized data. That's presumably why they studied scores for three years.

However, by NOT randomizing the golf course used for the data collection, there is GUARANTEED to be a bias in the results.

If I generate random data based on a probability distribution of score relative to par and use that to evaluate the proposed handicap system then I can be sure that there is no bias to my results.

As you point out, even that system won't be "perfect" because every course has a built in bias in the results because some holes are tougher than others and the way handicap strokes are allocated matters. However, I stand by the statement that it will be better than a system which is derived from a single course's data.

[adanac]

The only reason for taking a large sample of golfers is to get randomized data. That's presumably why they studied scores for three years.

However, by NOT randomizing the golf course used for the data collection, there is GUARANTEED to be a bias in the results.

If I generate random data based on a probability distribution of score relative to par and use that to evaluate the proposed handicap system then I can be sure that there is no bias to my results.

As you point out, even that system won't be "perfect" because every course has a built in bias in the results because some holes are tougher than others and the way handicap strokes are allocated matters. However, I stand by the statement that it will be better than a system which is derived from a single course's data.

A couple more questions:
Don't you think that the consultant statistician from Simon Fraser University would have pointed out faults/limitations in the methodogy if there were any?
Does the existing system of ESC in Canada provide perfect results?

[jvincent]

I assume that he was the one that came up with the parameters for the study, or that he was somehow limited to one course.

As to whether the old RCGA ESC system is perfect, I don't think any handicapping system can be perfect. Also, it depends on what you are trying to achieve.

Is the goal to make stroke play competitions between specific handicap ranges more fair? Or is it to make match play competitions more fair?

I would agree with the original premise that having the same ESC limit for a 1 handicap and and 18 handicap is not correct. I think that a BETTER way to have handled this would be to reduce the ranges for the ESC limits to be in increments of 9 strokes but still have the limits be relative to par. That is what Dean Knuth was proposing.

I think a system based on that would be more equitable in the long term.

[adanac]

From post no. 12 in this thread, where BC MIST quotes Matt Mackay of RCGA:

"In the spring of 2011, the RCGA Handicap & Course Rating Committee met to discuss the status of the current ESC method. The committee analyzed some small-sample data and determined that there would be merit in commissioning further statistical research based on a larger sample of scores.

Professor Tim B. Swartz (Simon Fraser University) was requested to perform an analysis on an extensive set of full golf rounds recorded by members of the Coloniale GC (Alberta) from 1996-1999. This analysis compared the current RCGA ESC method with the current USGA ESC method. His analysis concluded that the current RCGA ESC method causes differences in Handicap Factor that are not commensurate with the difference in ability. This is most acute for golfers in the higher half of each range of handicaps within the ESC table. Put simply, it did not make great sense to treat a 1 handicap the same as an 18 handicap (maximum hole score of 2 over par) when their abilities are so different. By reducing the size of handicap ranges (they will become increments of 9) that problem is mitigated. The new ESC provides a more even distribution across a wide range of handicaps.

Apart from the statistical merits of the new ESC, there are some other benefits:
-Using maximum numbers for all handicap ranges other than 0-9 makes the ESC procedure easier to understand and apply (ie. I am a 12 Course Handicap so my max score on any hole is a 7)

-Using maximum numbers also mitigates the common issue of courses not allocating the proper par to certain holes, as per RCGA yardage/par guidelines

-Currently, in a head to head match, the lower handicap player has a slightly better than 50% chance of winning. The new ESC will bring that closer to 50/50.

-It brings an RCGA Handicap Factor and USGA Handicap Index into mathematical equivalency, which is important considering the number of ‘snowbirds’ playing golf in the USA during the winter months.

While those in the 1-9 handicap range will feel no impact, handicaps on the whole will rise to some degree, most notably for people in the higher handicap ranges. But don't expect your handicap to balloon...remember that only your best 10 differentials from your most recent 20 rounds are calculated, so most often those rounds with high hole scores will not even be part of the handicap calculation."

AAA mentioned the Australian handicapping changes -
http://admin.golfaustralia.org.au/si...180-source.pdf

[jvincent]

OK, let's address the specific points that Matt made.

Put simply, it did not make great sense to treat a 1 handicap the same as an 18 handicap (maximum hole score of 2 over par) when their abilities are so different. By reducing the size of handicap ranges (they will become increments of 9) that problem is mitigated. The new ESC provides a more even distribution across a wide range of handicaps.

No disagreement about going to increments of 9.

-Using maximum numbers for all handicap ranges other than 0-9 makes the ESC procedure easier to understand and apply (ie. I am a 12 Course Handicap so my max score on any hole is a 7)

Excuse me? How is max = 7 easier to understand than max = triple?

-Using maximum numbers also mitigates the common issue of courses not allocating the proper par to certain holes, as per RCGA yardage/par guidelines

Red herring. How many holes have you played where par is set incorrectly? Besides, if the course is rated properly this should be taken into account in the rating.

-Currently, in a head to head match, the lower handicap player has a slightly better than 50% chance of winning. The new ESC will bring that closer to 50/50.

Just read this closely for the first time. He says match, so I assume the goal is to make MATCH play results closer to 50/50. Equity in stroke play competitions is not the goal.

-It brings an RCGA Handicap Factor and USGA Handicap Index into mathematical equivalency, which is important considering the number of ‘snowbirds’ playing golf in the USA during the winter months.

Pressure from the USGA?

[adanac]

OK, let's address the specific points that Matt made.



No disagreement about going to increments of 9.



Excuse me? How is max = 7 easier to understand than max = triple?



Red herring. How many holes have you played where par is set incorrectly? Besides, if the course is rated properly this should be taken into account in the rating.



Just read this closely for the first time. He says match, so I assume the goal is to make MATCH play results closer to 50/50. Equity in stroke play competitions is not the goal.



Pressure from the USGA?

You hadn't read this before (you asked if I had read the thread)? It seems that you have more axes to grind than just the calculation methods. Sorry to hear about them.
I sincerely doubt that there is any pressure whatsoever from the USGA - they have more important things to do than worry about handicapping in Canada.

[jvincent]

I had read it before, I just missed the one point about it applying to a match.

I have no axe to grind. Rightly or wrongly I don't accept things blindly just because somebody says so without adequate justification, especially in an area where I have some knowledge/experience.

The flaws in the handicapping system are a regular discussion on this and other golf boards. Sorry if you don't think they should be discussed.

[adanac]

I had read it before, I just missed the one point about it applying to a match.

I have no axe to grind. Rightly or wrongly I don't accept things blindly just because somebody says so without adequate justification, especially in an area where I have some knowledge/experience.

The flaws in the handicapping system are a regular discussion on this and other golf boards. Sorry if you don't think they should be discussed.

Not sayin' they shouldn't be discussed, just sayin' that others have constuctive views and actions.

Here's an idea to resolve the imperfections - let's play straight up! Net best ball, but no strokes.

Carry on as you wish.

[jvincent]

I never said that other suggestions weren't welcome or constructive.

I'm trying to prove (or disprove) the statements made by the RCGA based on a statistical model. I have no vested interest in the results nor do I know how it will turn out. That's the reason for doing the experiment.