Index calculation: A question of mathematics

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Rule 33-4 says the Committee must publish a handicap stroke table.

Firstly, let me say I’m not one to get hung up on pedantic calculation, because ultimately it means very little for overall Stableford or Par calculation. However, the way my club’s Committee has gone about it has me perplexed.

The person in charge collected player scores and worked out hole averages, which is fine. But then to determine the index, he consulted a mathematician and was advised the appropriate methodology was to work out the percentage by which the average score exceeded the hole’s par.

Thus a par-3 with an average of 3.9 received a percentage of 130%, whereas a par-5 with an average of 6.2 received a percentage of 124%. Thus the par-3 was considered harder and received a lower index than the par-5, even though the average score for the par-5 was 0.3 more strokes over par.

This seems a bit crazy. Why would you mathematically use a percentage rather than just an “over-par” score? Surely the average player is concerned that he needs 0.3 strokes more on a certain hole compared to another?

Trentham Golf Club
http://www.trenthamgolf.com.au

 

Without thinking about it too deeply, using an ‘over-par’ score doesn’t cater for the fact that higher markers do blow out the most on par 5s (triples, quads and higher) whereas lower markers make their scores here, but are still just birdies with the occasional eagle.

Couple this with the higher proportion of higher markers in clubs would mean lower markers getting strokes on par 5s and not on par 3s, where they need them more. Not much fun picking up on a hard par 3 just because double bogey can’t score.

This percentage system would somewhat alleviate this, but it should be used with a differing set of indexes for 18-36 handicaps to ensure such markers get two strokes on par 5s before two on a par 3.

 

 

Publish
I disagree with you on one point. Its not a bit crazy its a whole lot crazy.

I collect the Stroke round scores for our holes and when we are changing cards we review the indexing. If there is significant change we alter the indexes. These are entirley based on the difference over par.

Steb
You surely are not seriously advocating two indexes. As a captain there are players every week who have trouble applying their handicap to one index, add another in there and then players on the cusp will be toally confused.

 

Radar, a number of courses use a separate index for 18-36. I used to be a member at Bathurst golf club, which has two long par 3s rated in their top 5. It’s really not that confusing.
http://www.bathurstgolf.com...

I agree with Steb that the scores racked up by high handicappers can totally distort the index. As a junior I played at a course in the Adelaide hills, where the 7th hole is a slightly downhill 150m par 3 with a water carry of about 125m. It had quite a large, flat green which was quite easy to putt on. But because a lot of higher handicappers hit a lot of balls into the water, when they averaged out the scores to work out the index, it came out at number 4. The fact that a 4 handicapper got a shot on the hole was ridiculous. (By comparison, the 9th hole was 145m, with a more difficult green, but was rated 17)

 

@Radar, yes, people do have trouble with one index, but I’d suggest it’s easier for a 35 marker to understand he gets two shots on a 5/34 index than a 17 index. No calculation necessary, it’s right in front of them. But I’m guessing here, I’ve never asked anyone.

 

 

Libba

Fair enough I do remember seeing this on a couple of courses, but does it really need to be so.
For Bathurst as an example. If the holes are so different for the men how come the ladies only have one index, their handicaps go out to 45. Surely their hight handicap blow outs would skew it even more?

Steb

Good point It may in fact make it easier.

In the end it makes very little difference as each player will find some holes harder than others will and vis vera. Index is only a guesstimate at difficulty

 

While I have played the odd course with a double index, they are so rare that nearly everyone is comfortable with a single index. It would seem to be more trouble than it’s worth.

When I’ve been involved with index calculations, I’ve just used the actual stroke figures, but I can see some logic in the percentage idea.

A couple of other possible considerations:
  • using ‘statistical mean’ – cutting out the extremities of the number ranges so you’re only using the middle 80% of scores.
  • making some effort to spread the index evenly over the course so that most players get half their shots on each nine.

Have fun with it.

 

I’ve always thought that it is a case of Roundabouts & swings. Stableford is all about the final score after 18 holes. sure a long marker might get 2 shots on a Par 3 making it easy for him to score on that hole. But somewhere on the course is another hole where he does not get 2 shots that will even up the Equation.
OB I like your Idea. Our indexes are worked out Evens on the front nine. Odds on the back. Gives a nice even spread of shots & in reality they are probably pretty accurate.

 

Would have been better consulting a statistician.

For a a decent sized sample of data, the statistician should be able to determine the standardised average for each hole. Using the above method, the percentage above the hole’s par does not take into account population sizes for each group of grades. They can also factor in the results of A, B and C grader’s performance on each hole whilst taking into account the population size of each group and then you would have a more accurate picture of what the real difficulty indices should be in play for the course.

Ghetto train – get on it.
Bandit express.

Winner C grade OOM #3 Patterson River.

 

Too much effort for something that really doesn’t apply to any particular person on the course. An old 18 marker will find different holes difficult to a young 18 marker, a left hander 18 different to right hander 18, a short gamer 18 different to a long gamer 18.

I don’t particular like optimising for the majority if the minority get shafted, I’d rather see everyone suboptimal.

 

 

Isn’t stroke index difficulty only of potential significance in stableford?
In match play is should be about relative significance (incidentally I though Oz had a separate index for matchplay).

In normal strokeplay the handicap strokes are subtracted at the end.

What other rules are we not playing by?

 

Only comps like par and stableford that have a point system. The calculation of the indices is a whole lot of trouble that don’t really affect things by a whole lot.

Ghetto train – get on it.
Bandit express.

Winner C grade OOM #3 Patterson River.

 

Isn’t stroke index difficulty only of potential significance in stableford?
In match play is should be about relative significance (incidentally I though Oz had a separate index for matchplay).

In normal strokeplay the handicap strokes are subtracted at the end.

.

Spot on AAA. The Stroke index has no impact on Matchplay which has its own Index, so really where players get 1 or 2 strokes has little impact on the final score in a Single stableford event. It might give a slight advantage to longer markers in a 4 BBB stableford but even that would be of little significance.

 

I would say it’s more likely to affect a par round eg. making a birdie on a hole where you get a shot will only give you a plus, as opposed to 4 stableford points or a ‘nett eagle’ in a stroke round. (ie in a par round, there is no difference on that hole between making a birdie and a par, whereas there is a difference between a birdie and a par on a hole where you do not get a shot)

 

England Golf or CONGU did some theoretical work using thousands of randomly (computer) generated SIs, scores and handicaps and determined that it was ‘swings and roundabouts’ as far as stableford was concerned.
I don’t know about par/bogey but would guess it was much the same.

What other rules are we not playing by?

 

But:

a) there are holes such as long par 3s and 4s that all golfers agree are hard. These should receive low indices so players can play the hole as their ability dictates without having to play risky golf just to get a point. People want due reward, not fake reward. A wipe or single point is a confidence killer, 3+ points is a confidence booster. Golf is all confidence.

b) a course with an easy back 9 but equally distributed indices across the whole 18 now gives the higher marker a much better chance of winning on countback, simply because of the index allocation.

 

 

As always. Nothing works well for all clubs & Indexing should be & is performed on an individual club basis. What works for some will not be accurate for others.

 

I appreciate the comments here, but realistically we have to have one compromised index that allows for differences in play between high and low handicappers (e.g. performances on par-3s vis-a-vis par-5s), and nothing will be perfect.

However, I’m still pondering ‘percentage’ versus ‘strokes’, because I can’t see how a percentage is relevant to the golfer out on the course.

Take two holes at Trentham:

  • The 2nd is a 157m par-3, with a hole average across the year of 3.97 strokes. For ‘percentage’, this is 132.26% and ranks the hole as Index 5. For ‘strokes over par’, it is 0.97 and the hole is ranked Index 13.
  • The 9th is a 458m par-5, with a hole average across the year of 6.40 strokes. For ‘percentage’, this is 128.05% and ranks the hole as 11th, for ‘strokes over par’, it is 1.40 and the hole is ranked Index 4.

Which hole is harder and should allow a stroke to the “average player”? The one that is 132% as opposed to 128%, or the one that averages about 1 stroke over par as opposed to the one that averages 1.4 strokes over par?

Notes:

1. While the par for the course is 70, the sum of the hole averages is roughly 90, meaning the “average golfer” is about a 20 handicapper.

2. All the hardest holes (based on ‘strokes above par’) are the longest par-4s and the longest par-5, which shows that length is a strong predictor of difficulty regardless of handicap. Low handicappers (0-8) would receive a stroke on these holes regardless.

Trentham Golf Club
http://www.trenthamgolf.com.au

 

England Golf or CONGU did some theoretical work using thousands of randomly (computer) generated SIs, scores and handicaps and determined that it was ‘swings and roundabouts’ as far as stableford was concerned.


I agree with that. For any given set of 18 hole scores, you could apply any indexes you like and the Stableford points would be near enough to the same.

However, people feel the need for the index to be ‘fair and reasonable’ so I guess we’re stuck with countless hours of pointless analysis to please that perception.

Trentham Golf Club
http://www.trenthamgolf.com.au

 

The USGA handicap manual suggests that the handicap indexes be calculated by comparing individual hole scores from lower handicappers to individual hole scores by higher handicappers, disregarding “par”. The hole with index 1 would be the hole where the higher handicapper most needs a stroke to get a halve with the lower handicapper (obviously in match play). There are other considerations included also, but that’s the main criterion.

 

When all is said and done, it doesn’t matter that much. If you are going to score 36 stableford points it really doesn’t matter much which holes you get your shots on, but …

Another way to look at the issue is that to an 8 handicap player, it doesn’t matter which hole is rated number 1. What matters most is which holes are rated 8 and 9 because he gets a shot on one hole and not the other.

The most accurate ratings may well come from analysis of players around the relevant handicap.

Truth is important even if it hurts sometimes

 

Let’s face it, for those with a handicap of scratch, 18 or 36, the index doesn’t matter one iota. It is most significant for those on 9 or 27 and it is for those players that some effort should be made to spread the joy evenly.

 
Let’s face it, for those with a handicap of scratch, 18 or 36, the index doesn’t matter one iota. It is most significant for those on 9 or 27 and it is for those players that some effort should be made to spread the joy evenly

I agree, but go a bit further and say that when considering which hole to rate number 9, the scores of 8, 9 and 10 handicappers are the most relevant.

Mind you, the guy on 14 could be expected to be pretty interested in which holes are rated 14 and 15 as well.

Truth is important even if it hurts sometimes

 

The more I have thought about this, and having been a member of clubs to use the different systems, the more I like the idea of separate indexes 1-18 and 19-36.
So after borrowing ideas from previous posts, how about use the scores from players with handicaps up to 9 to rate the 9 hardest holes (players with handicaps between 9 and 18 will get a shot on all of these holes anyway).
Then use the scores from players with handicaps 10-18 to rate holes with those indexes (players with lower handicaps won’t get any shots on these holes so their scores don’t matter)
Then use the scores from players with handicaps 19 and above to determine the 19-36 indexes, which takes Steb’s point about higher markers tending to fare worse on longer holes, compared to lower markers (and the 1-18 index is meaningless to them anyway, so they won’t be affected by how lower handicapped players perform on these holes).
Of course, this might require a club to employ half a dozen statisticians as full-time handicappers, but I’m sure this is just a minor detail.

 

Perhaps a better idea would be to keep hole by hole stats for individual players so that each player would have his own indeces which could change over time

What other rules are we not playing by?

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