"Interesting" Hole Handicap Allocation Analysis

[DaveLeeNC]

There are two ways to determine hole handicaps per the USGA

 

1) "Match Play" approach where the #1 handicap hole would typically be the hole with the largest scoring differential between the low handicap group and the high handicap group

 

2) "Stroke Play" approach where the #1 handicap hole would typically be the hole that is the hardest (against par) across the field.

 

And there are two ways to allocate strokes in a 2 person match play event

 

1a) Lower handicap player gets no strokes and the higher handicap player gets the # of strokes that his/her course handicap is higher than his/her lower handicap opponent. We'll call this the right way.

 

2a) Each player 'just gets his strokes' so the players play 'even' on holes where they each get a stroke (which would typically be the lower hole handicap holes). We'll call this the convenient way, although 'the wrong way' would be equally descriptive.

 

But the question was asked 'if your hole handicaps are allocated using approach #2 above just how wrong is it is you allocate strokes using 2a) instead of 1a)?

 

Conveniently I had done the hole handicaps on a couple of our courses and still had that data. I could easily recalculate hole handicaps using both 1) and 2) methodologies. So I applied technique 1a) to two hypothetical matches (4 course handicap against 12 course handicap, and 12 course handicap against 20 course handicap) and called this 'the correct result'.

 

Then I used the hole handicaps per 2) and compared the results (where a stroke is actually given) for both allocation methodologies ( 1a and 2a ). I was able to do this for 2 courses. What I found was that using 1a), the results were that 50% of the holes where a stroke was given matched the 'correct result' (using 1 and 1a). Using 2a) 25% of the holes where a stroke was given matched the 'correct result'.

 

Being a numbers guy I found this interesting.

 

FWIW.

 

dave

 

ps. The value in this exercise in our case is related to the fact that (in this particular event) a player's strokes is independent of the players opponent - something that is only determined by the status of the event after 9 holes where, within a foursome, the next 9 holes are two match play events (first 9 winner/winner, loser/loser). Our scorecards are automatically marked by hole with your course handicap strokes. Folks get used to following that, we are old, and don't change our ways easily :-)

[PJ72]

I think my brain just exploded.

[larrybud]

I suspect if you did this over a long period of time with a lot of real-world data, you'll find a small percentage difference using the proper method if the hole handicaps were developed by comparing difference between scratch and bogey golfer.

[DaveLeeNC]

[quote name='larrybud' timestamp='1411661406' post='10182013']
I suspect if you did this over a long period of time with a lot of real-world data, you'll find a small percentage difference using the proper method if the hole handicaps were developed by comparing difference between scratch and bogey golfer.
[/quote]

Larry, could you elaborate on what you are saying here? I don't know exactly what 'proper method' refers to. And I don't know what the term 'small percentage difference' refers to (difference between what and what?).

I just didn't understand - sorry.

dave

[larrybud]

Given that: Hole handicaps are generally assigned for match play, where instead of absolute score being used to determine the hardest hole, the difference between scratch and bogey golfer is used. Which is why hole handicap assignments are often confusing for players (i.e. "why is the third hole only a handicap of 16? it's such a hard hole!!").

Now, if you had scores from 1,000 matches, and you figured out the outcomes two ways:
1) using # of strokes in the [b]difference [/b]of the two players (which is the correct way of doing things) vs
2) giving [b]full handicaps[/b], (which essentially gives the worse player strokes on hole which aren't the biggest diff between bogey and scratch golfers)

I think you will find that #2 would be an advantage to the better player (call him the "A" player vs "B" player). I don't have any statistical analysis to back up my claim, but here the reason I believe it would be so:
1) the A player already has an advantage on each hole
2) the A player will now have an even bigger advantage on the "hard" holes (the holes which has the biggest diff between bogey and scratch player).
3) Yes, he will have more of a disadvantage on the easier holes, but because the "B" player is less consistent, the B player has a bigger chance of wild hole scores even on the "easier" holes.

[D^2]

http://www.usga.org/ourexpertsexplain.aspx?id=21474844134

[DaveLeeNC]

[quote name='larrybud' timestamp='1411669601' post='10182987']
Given that: Hole handicaps are generally assigned for match play, where instead of absolute score being used to determine the hardest hole, the difference between scratch and bogey golfer is used. Which is why hole handicap assignments are often confusing for players (i.e. "why is the third hole only a handicap of 16? it's such a hard hole!!").

Now, if you had scores from 1,000 matches, and you figured out the outcomes two ways:
1) using # of strokes in the [b]difference [/b]of the two players (which is the correct way of doing things) vs
2) giving [b]full handicaps[/b], (which essentially gives the worse player strokes on hole which aren't the biggest diff between bogey and scratch golfers)

I think you will find that #2 would be an advantage to the better player (call him the "A" player vs "B" player). I don't have any statistical analysis to back up my claim, but here the reason I believe it would be so:
1) the A player already has an advantage on each hole
2) the A player will now have an even bigger advantage on the "hard" holes (the holes which has the biggest diff between bogey and scratch player).
3) Yes, he will have more of a disadvantage on the easier holes, but because the "B" player is less consistent, the B player has a bigger chance of wild hole scores even on the "easier" holes.
[/quote]

Actually this is a very interesting 'math optimization problem' (what is the optimum handicap allocation that would best level the field when players of differing ability compete in match play). Unfortunately this is a factorial complexity problem (pretty much as bad as it gets in the world of complexity). But since you are limited to only 18 hole matches, it could be a most interesting optimization problem that I could maybe just solve by brute force.

I have data on around 800 scores on two different courses so, in principle, I could find "the right answer" for those courses. IN PRINCIPLE :-)

dave

[DaveLeeNC]

[quote name='D^2' timestamp='1411673869' post='10183429']
[url="http://www.usga.org/ourexpertsexplain.aspx?id=21474844134"]http://www.usga.org/...?id=21474844134[/url]
[/quote]

That is an interesting article PARTICULARLY given our own course situation.

Several years ago our handicap committee chair observed that we had no idea where the hole handicaps came from on the six courses that we were dealing with. So we decided to 'do it right' and re-establish the hole handicaps in a proper manner using the match play perspective (the USGA preferred methodology).

At this point it is VERY important to point out how our club tends to work. Our club tends to have 'team matches' where (for example) each team is a foursome and the (again as an example) 2 best scores (after strokes) of the foursome on each hole was the team score. There were lots of game variations but this was a typical weekly competition.

So we re-did the hole handicaps and the negative outcry from the membership (which I totally agreed with, BTW) was immediate and overwhelming. Prior to the re-do of the hole handicaps, 'net par' had a kind of meaning (it tended to mean staying even against the field). With the new hole handicaps you had no clue. I''ll give you a good example which would be holes #10 and #15 on course No. 3 at our club.

Hole #10 is a EXTREMELY difficult hole. It is a dogleg left par 4 (where the dogleg occurs about 175 yards out) and your second shot (even after a perfect drive) leaves you with a severely L-R sloping lie). It is kind of the hole from hell for low and high handicappers alike. And (per match play perspective) ended up with a hole handicap of 10 or something like that.

Then on this same course is hole #15. It is a very short par 5 (dogleg left) where low handicappers viewed it as a driver/hybrid to the green hole. High handicappers encountered this cross bunker maybe 90 yards short of the green which made it a really tough hole for them. So this hole became the #1 handicap hole on the course.

So me, as a mid-single digit handicap player encountered the following in the club competitions where I played (note that these WERE NOT match play things).

1) I did not get a stroke on what is (for me) the 2nd hardest hole (against par) across the 108 holes that I played at our club

2) I did get a stroke on what is (for me) the absolute EASIEST hole (against par) across the 108 holes that I played at our club

For the competitions that were the norm for our club this was not a useful way to allocate strokes.

dave

[Newby]

[quote name='DaveLeeNC' timestamp='1411675376' post='10183601']what is the optimum handicap allocation that would best level the field when players of differing ability compete in match play)
[/quote]

Some years ago the English and Scottish Golf Unions (together withthe USGA I believe) analysed thousands of matchplay results.
They found that with 3/4 difference (which was the CONGU recommendation at the time), the lower handicapper won 61% of the time. With full difference (now the CONGU rule), the lower handicapper won 55% of the time.
They estimate that to get to 50/50, the higher handicapper would have to be increased to 120% of his playing handicap before taking the difference.

[DaveLeeNC]

[quote name='Newby' timestamp='1411679077' post='10183949']
[quote name='DaveLeeNC' timestamp='1411675376' post='10183601']what is the optimum handicap allocation that would best level the field when players of differing ability compete in match play)
[/quote]

Some years ago the English and Scottish Golf Unions (together withthe USGA I believe) analysed thousands of matchplay results.
They found that with 3/4 difference (which was the CONGU recommendation at the time), the lower handicapper won 61% of the time. With full difference (now the CONGU rule), the lower handicapper won 55% of the time.
They estimate that to get to 50/50, the higher handicapper would have to be increased to 120% of his playing handicap before taking the difference.
[/quote]

Newby, very interesting and 'on point' information - thanks.

dave

[edwjmcgrath]

Dave, I'm familiar with 1.) the match play method for determining hole handicaps and 1a.) the method for determining who gets strokes in match play.
That's the only way I've ever seen it done. Where do you find support for anything else?

[Newby]

[quote name='edwjmcgrath' timestamp='1411695582' post='10185283']
Dave, I'm familiar with 1.) the match play method for determining hole handicaps and 1a.) the method for determining who gets strokes in match play.
That's the only way I've ever seen it done. Where do you find support for anything else?
[/quote]

Ed
The USGA, Golf Australia and CONGU all have slightly different 'formulae' for 1). I have never seen anything other than 'difference' for 1a).

[DaveLeeNC]

[quote name='edwjmcgrath' timestamp='1411695582' post='10185283']
Dave, I'm familiar with 1.) the match play method for determining hole handicaps and 1a.) the method for determining who gets strokes in match play.
That's the only way I've ever seen it done. Where do you find support for anything else?
[/quote]

Ed, section 17-5 of the USGA Handicap Manual describes method 2).

Method 2a) has no 'support' that I am aware of.

dave

[larrybud]

The only reason to allocate hole handicaps relative to par is for Stableford, and that isn't played much in the States.

Allocating hole handicaps for stroke play would only have an effect in a playoff situation for stroke play.

[edwjmcgrath]

I was on the committee that did this for our course recently. We made liberal use of section 17-1 Committee Discretion.
While we used the numbers as a guideline, we did not just use the numbers blindly.
We did not make one of our easiest holes the #1 handicap as the numbers suggested.
We avoided making the first hole a low handicap since it is a playoff hole.
We avoided making 9 and 18 low handicaps since matches may be over before players got to use their stroke.
We imagined matches not only between low and high handicappers, but also the more common match between players of similar ability.
Then we tweaked the rankings to try to make the best tradeoff, all things considered.

I agree that method 2a has no support.

[DaveLeeNC]

[quote name='larrybud' timestamp='1411732514' post='10187507']
The only reason to allocate hole handicaps relative to par is for Stableford, and that isn't played much in the States.

Allocating hole handicaps for stroke play would only have an effect in a playoff situation for stroke play.
[/quote]

In our case it also had a huge effect on the satisfaction of our membership, for reasons previously stated.

dave

[TheCityGame]

[b]DaveLeeNC[/b]-- how did you simulate your hypothetical matches? I've always wondered about a proper way to simulate scores on each hole, but I don't have good information on the distributions. . .which sort of brings me to a larger point. . .

If the USGA had ANY interest in being open with their handicap data, smart people would get a chance to properly answer any questions we've thought up, and some that we haven't.

We could figure out answers to [b]DaveLeeNC's [/b]experiment for every course.

We could figure out what slope & rating should be at every course, every tee.

We could explain to the USGA once and for all that plus handicaps shouldn't have lower differentials at harder courses.

I figure they know that opening up the data would open them up to tons of criticism, and probably people complaining about match results going back as far as the data. They know that courses would get re-rated and re-sloped which would change handi's and tick people off, and lots of other stuff.

In the long run, good things happen when you make your data available.

[larrybud]

[quote name='TheCityGame' timestamp='1411734264' post='10187649']
We could figure out what slope & rating should be at every course, every tee.

We could explain to the USGA once and for all that plus handicaps shouldn't have lower differentials at harder courses.
[/quote]

What data do you want, or think they have?

Let's say there was a database of hole by hole scoring for every player for a given course that we had access to. How do you plan on calculating a course rating from that?

[TheCityGame]

[quote name='larrybud' timestamp='1411736558' post='10187837']
[quote name='TheCityGame' timestamp='1411734264' post='10187649']
We could figure out what slope & rating should be at every course, every tee.

We could explain to the USGA once and for all that plus handicaps shouldn't have lower differentials at harder courses.
[/quote]

What data do you want, or think they have?

Let's say there was a database of hole by hole scoring for every player for a given course that we had access to. How do you plan on calculating a course rating from that?
[/quote]They certainly have every score that's been reported to GHIN and GolfNet since. . .forever? With each of those scores, they have a slope and a rating AND a course.

To get "my" slopes/ratings from that basically you'd have to create a "baseline" scratch rating at any course you want.

You could easily see if the scratch rating at course X was accurate based on your baseline scratch golfer's scores at course X. You'd need to do something similar for the slope for courses.

This would require a lot of "cross-pollination", if you will. You need enough rounds from golfers travelling to do this, but with millions of golfers in the USGA system, and lots of years of data, this shouldn't be too hard.

There's a slight "chicken & egg" problem with baselining a scratch golfer, but no more so than currently exists. And, at least people working with the data would be upfront about it.

At the very least, I would expect that "my" system would more accurately capture a slope than USGA employees walking a course and assigning one point for a bunker, one point for a pond, etc etc.

If there were enough hole-by-hole scores in the system, you could get a good look at the assignment of handicap holes, also. Check their accuracy, see how they've changed through time.

Having data like this would also allow us to get a better grasp on the frequency of exceptional scores (I believe Knuth's frequencies are wrong), better identify sandbaggers. I'd really like to get a handle on golfer variability, and hole score variability at courses.

There's really so much people could do with the data if we had it. I kind of keep waiting for one of these websites (OOB Golf, or Stracka, or something) to put something out like this.

[Newby]

[quote name='larrybud' timestamp='1411732514' post='10187507']
The only reason to allocate hole handicaps relative to par is for Stableford, and that isn't played much in the States.

[/quote]

A mathematical simulation was done taking hundreds of actual scores and assigning handicap stroke/stoke indices at random. The variation in resultant stableford points was negligible. Swings and roundabouts at work.

[larrybud]

[quote name='TheCityGame' timestamp='1411739648' post='10188061']
[quote name='larrybud' timestamp='1411736558' post='10187837']
[quote name='TheCityGame' timestamp='1411734264' post='10187649']
We could figure out what slope & rating should be at every course, every tee.

We could explain to the USGA once and for all that plus handicaps shouldn't have lower differentials at harder courses.
[/quote]

What data do you want, or think they have?

Let's say there was a database of hole by hole scoring for every player for a given course that we had access to. How do you plan on calculating a course rating from that?
[/quote]They certainly have every score that's been reported to GHIN and GolfNet since. . .forever? With each of those scores, they have a slope and a rating AND a course.

To get "my" slopes/ratings from that basically you'd have to create a "baseline" scratch rating at any course you want.

You could easily see if the scratch rating at course X was accurate based on your baseline scratch golfer's scores at course X. You'd need to do something similar for the slope for courses.

This would require a lot of "cross-pollination", if you will. You need enough rounds from golfers travelling to do this, but with millions of golfers in the USGA system, and lots of years of data, this shouldn't be too hard.

There's a slight "chicken & egg" problem with baselining a scratch golfer, but no more so than currently exists. And, at least people working with the data would be upfront about it.

At the very least, I would expect that "my" system would more accurately capture a slope than USGA employees walking a course and assigning one point for a bunker, one point for a pond, etc etc.

If there were enough hole-by-hole scores in the system, you could get a good look at the assignment of handicap holes, also. Check their accuracy, see how they've changed through time.

Having data like this would also allow us to get a better grasp on the frequency of exceptional scores (I believe Knuth's frequencies are wrong), better identify sandbaggers. I'd really like to get a handle on golfer variability, and hole score variability at courses.

There's really so much people could do with the data if we had it. I kind of keep waiting for one of these websites (OOB Golf, or Stracka, or something) to put something out like this.
[/quote]

I'm sure i could write a screen scraper app to pull down scores from the GHIN, but I was leading you towards the chicken & egg problem. :-)

I'm not a member of the GHIN, they have an option to enter hole by hole scores?

[TheCityGame]

[quote name='larrybud' timestamp='1411758259' post='10189853']
[quote name='TheCityGame' timestamp='1411739648' post='10188061']
[quote name='larrybud' timestamp='1411736558' post='10187837']
[quote name='TheCityGame' timestamp='1411734264' post='10187649']
We could figure out what slope & rating should be at every course, every tee.

We could explain to the USGA once and for all that plus handicaps shouldn't have lower differentials at harder courses.
[/quote]

What data do you want, or think they have?

Let's say there was a database of hole by hole scoring for every player for a given course that we had access to. How do you plan on calculating a course rating from that?
[/quote]snip
[/quote]

I'm sure i could write a screen scraper app to pull down scores from the GHIN, but I was leading you towards the chicken & egg problem. :-)

I'm not a member of the GHIN, they have an option to enter hole by hole scores?
[/quote]Currently, I don't think GHIN lists courses. And, you might be able to add hole by hole, but I don't think it's searchable. I'm golfNet, so I don't know all of GHIN. But, I'm really talking about ALL the data.

There's SO MUCH more information out there. What if you were able to cross-reference scores with GPS data and weather data and get an idea of how scores vary at particular courses as the weather changes? Not just for general interest, but to make adjustments to people's handicaps?

I thought that the UK used a "how the course was playing that day" adjustment. We could easily have something like that. That 75 you put up in the wind when the course average was 3 strokes higher that day? Sorry Charlie. . .it's going in as a 72.

As to the chicken & egg. . .except for being able to historically match up "scratch" golfers, it really doesn't make a difference. As a matter of fact, I'd just start over and make touring pros 0 handicaps and go from there.

[Truman]

I don't think local governing bodies are interested in the hole rating, only the course rating. At least that's the case with ours. They will help with the data analysis once it's collected, if you need it. Once we did the statistics we did not add add a human bias, we let the rating match the standard deviation. We felt that makes it easier to explain to members.