Defensible Math? Applying probabilities to Junk Points

[TomeeGee]

I have been trying to establish guidelines for handicap scoring "junk points" (birdies, eagles, and albatrosses) in our golf tournament. For years we have discounted the scores for points earned with handicap (b*stard birdies, etc). Natural vs Handicap were 5/3 Birdie, 10/7 Eagle and 15/12 Albatross. I've tried to find guidance and justification for these amounts and percentages on the USGA site and others with no results. 

What I have done is look at the USGA "handicap allowance" on some games to protect the high handicap golfer from running away with the competition. But that applies to Stableford, group games and not match play. However, there isn't any guidance for applying a "penalty" amount to junk points over the lower handicap golfer.

I found this USGA "probability chart" for the odds of golfer hitting below their handicap index by handicap (https://bit.ly/3wVHgqs). Using that chart as a guide, I have tried to determine the percentage likelihood of achieving -1, -2, or -3 on any given hole by handicap.

I can't upload the excel, but here's a screen grab: enter image description here

I added the color and the converting to percentages. Comparing handicaps 5.9 or less up to 21.9, there is little to no statistical difference in the likelihood of hitting -1.0 to -1.9 against your index (for the purpose of discussion, I’ll call that the “birdie zone.” Next level, the “eagle zone” the odds are very slight. Only a difference of .41% between these same handicap ranges. The “albatross zone” spreads only slightly more… .58%.

The drop off comes when the handicap goes over 22. The difference between low and high is for Birdie, 2.5% (4.29% for handicap greater than 31). Eagle 3.34% (5.65% for higher than 31) and Albatross 2.6% (4.92% 31+).

I used the difficulty of achieving the points as a scale. Using the 5.9 hcp or less, to shoot a birdie goes from 5-10. Eagle, 5-23. Albatross, 5-57. So rounded, 2x, 4x, 10x.

So using 5 as a base, a birdie is worth 10 pts, an eagle is worth 20, and an Albatross is worth 50.

Now odds of achieving by handicap: I averaged all the percentages from handicaps 13.0 to 31 (Birdie 12.26, Eagle 7.48, Alba 4.45) and then figured a percentage difference between that percentage and the 5.9 or less percentage (10, 4.35, 1.75). So the “penalty,” or adjusted handicap allowance on junk, would look like this rounded up:

Birdie 80% Eagle 60% Albatross 40%

So scoring: Birdie 10 for “natural” / 8 with handicap Eagle 20 “natural” / 12 with handicap Albatross 50 “natural” /20 with handicap

Is my math defensible? Sound? Or is there another method to extrapolate the information from the chart or am I just nuts…

Hope someone can provide guidance. 

[cnosil]

My initial thought is that you are trying to redo the handicap system because you don’t think it works.  It doesn’t work when people take their handicaps.    Statistics show that handicap differences aren’t related to getting more birdies and eagles but more about avoiding bogies and worse.   You method seems to look at the birdies, eagles, and better that the higher handicap player is getting.  Are they really getting that many more birdies in you events?   How about look at bogey and double averages and add strokes to the higher handicapper score  If they don’t do bad enough.   I’ll beat your system as a high handicapper by just getting more pars.   

[TomeeGee]

12 minutes ago, cnosil said:

My initial thought is that you are trying to redo the handicap system because you don’t think it works.  It doesn’t work when people take their handicaps.    Statistics show that handicap differences aren’t related to getting more birdies and eagles but more about avoiding bogies and worse.   You method seems to look at the birdies, eagles, and better that the higher handicap player is getting.  Are they really getting that many more birdies in you events?   How about look at bogey and double averages and add strokes to the higher handicapper score  If they don’t do bad enough.   I’ll beat your system as a high handicapper by just getting more pars.   

Thanks for the reply. This is partially inherited from a 25+ year tournament in which the organizer asserts "the data shows the lower handicaps get more junk!" and made the adjustments. I have unsuccessfully argued the point that the handicap system is the great equalizer and no adjustments need be made. This year, however, the argument came back is the USGA's "handicap allowances" (https://www.usga.org/content/usga/home-page/handicapping/roh/2020-rules-of-handicapping.html#!rule-14387). The lower handicappers insisting the junk point system favors the high. So I started my digging and came across the probabilities chart and wondered if there could be a correlation. 

Last spring, however, I ran my spring tournament last year straight up. When a 25 handicap won there was no end to the griping (which gets pretty insulting) from the single digit golfers. 

 

[cnosil]

12 minutes ago, TomeeGee said:

Thanks for the reply. This is partially inherited from a 25+ year tournament in which the organizer asserts "the data shows the lower handicaps get more junk!" and made the adjustments. I have unsuccessfully argued the point that the handicap system is the great equalizer and no adjustments need be made. This year, however, the argument came back is the USGA's "handicap allowances" (https://www.usga.org/content/usga/home-page/handicapping/roh/2020-rules-of-handicapping.html#!rule-14387). The lower handicappers insisting the junk point system favors the high. So I started my digging and came across the probabilities chart and wondered if there could be a correlation. 

Last spring, however, I ran my spring tournament last year straight up. When a 25 handicap won there was no end to the griping (which gets pretty insulting) from the single digit golfers. 

 

I totally understand as it is always the complaint…are people cheating or do they somehow manage to score their career rounds in these tournaments.  In most cases I’d lean towards people are cheating and agree with the lower handicaps.   Since you ran the tournament,  how many of each score type did the winner have?  

[BMart519]

Another option is make some prizes flighted. Having 20+ index playing against low single digits is not ideal. You could still have something for low net for the entire player pool. Also important to realize it is impossible to make everyone happy, there will always be a complainer. Some courses play harder than their ratings and some easier, some also favour longer hitters, right to left ball flights, etc. 

I have a friend who sets up an annual match play tournament with singles and doubles matches and makes a mess of trying to apply handicaps in that format by basically taking the differential between teams and cutting them in half. He is usually on the losing team because he posts scores with lots of gimmes and assigns indexes to people based on his opinion if they don't maintain one.

Sometimes, simpler is better.

[THEZIPR23]

I am confused. Are you playing "Net" junk? I have never played or seen this done before, always gross. Isn't that the point of the handicap system? 

[TomeeGee]

30 minutes ago, cnosil said:

how many of each score type did the winner have?

 

Here's a synopsis. Of course, you don't see the match results broken out. The Birdies (natural and bastards) along with B Eagles are  here. The column is Average over/under against index. I think it shows the higher hcps played better to their index and therefore secured more junk. 

[cnosil]

29 minutes ago, TomeeGee said:

 

Here's a synopsis. Of course, you don't see the match results broken out. The Birdies (natural and bastards) along with B Eagles are  here. The column is Average over/under against index. I think it shows the higher hcps played better to their index and therefore secured more junk. 

Looks like they played pretty close to their indexes which is what you want and the birdies/eagles don’t seem unreasonable.  As I keep  saying,  you can’t just look at birdies and eagles to judge scores.  If you really want to understand why they are those handicaps you need to look at scores above par too.  

[TomeeGee]

1 hour ago, cnosil said:

Looks like they played pretty close to their indexes which is what you want and the birdies/eagles don’t seem unreasonable.  As I keep  saying,  you can’t just look at birdies and eagles to judge scores.  If you really want to understand why they are those handicaps you need to look at scores above par too.  

We don't make any handicap allowances on rounds. Everyone plays their full handicap against their opponent. We have match play and skins, and a couple of scrambles thrown in for the last nine of 36 hole days. For match play, each nine holes are worth potentially 20 (if swept), and skins 18.

I haven't analyzed what percentage of winning numbers came from rounds versus junk. But I will. 

BTW, I really appreciate all the input here!

[Stuka44]

On 11/22/2021 at 10:38 AM, TomeeGee said:

I have been trying to establish guidelines for handicap scoring "junk points" (birdies, eagles, and albatrosses) in our golf tournament. For years we have discounted the scores for points earned with handicap (b*stard birdies, etc). Natural vs Handicap were 5/3 Birdie, 10/7 Eagle and 15/12 Albatross. I've tried to find guidance and justification for these amounts and percentages on the USGA site and others with no results. 

I realize this is a little old but here is my input.  Seems like your group may be suffering from the same gripes as a group I have gone with several times.  Last year a very high handicap won the weeklong tourney. But other years the lowest handicap won it.  This is what the handicap system is supposed to do.  Give a high handicap a chance to win against lower handicaps.  If the low handicaps don't understand this, you can not help them.  I'm not a handicap expert in any way shape or form, but you have to just trust it.  Establish a handicap based on the courses you are playing, and that historical data if you can, and go with it.

As for cheating or "sandbagging" You can't do anything to compensate for cheating, so the only way to correct for the sandbagger, who wants to win that badly, if there is someone like this  is to not invite those people to participate.

Lastly the USGA handicap system has a provision on what to do about "exceptional scores", or how they affect handicap . Don't know if this will help.