Lou Stagner vs. GHIN/WHS in "Playing off Low Handicap"

[iacas]

 

He took a 6 and a 12 and played off the low handicap (6) so the 12 got a stroke on stroke holes 1-6.

 

 

The outcomes:

I've seen the USGA studies, though, that show the low player wins just over half the time (53%), so… what I'm not sure of is this: a) Did Lou just happen to choose a gap (with the 12 vs. 6) that shook out the other way? In other words, if an 18 plays a 4, does the 4 win more often? b) Does Lou using Arccos data and not accounting for net double bogey lead to a difference in GHIN/WHS handicap and Arccos handicap? If so, how substantial is it? c) Is there something else going on here that I'm not thinking of?

 

Edit to add some links:

• https://golf.com/news/have-you-been-playing-match-play-incorrectly/ - "In 53.1% of simulated matches, the lower handicap player won; the bias in winning percentage was greatest in the handicap difference range 4 to 10 where it exceeded 54% and least in the handicap difference range of 1 to 4 or greater than 20." (They did some other simulations as well). Note that this was with the 0.96 multiplier and the 10/20 rounds counted. Going from 10 and 0.96 to 8 had almost no effect on handicap indexes, though. I saw many USGA/WHS studies on that back in 2019/2020.
• https://www.usga.org/content/usga/home-page/handicapping/world-handicap-system/world-handicap-system-usga-golf-faqs/faqs---lowest-playing-handicap-plays-at-scratch-.html - "A. By stroking off the low ball, the higher handicap player(s) receive their handicap strokes on the holes where they need them most – resulting in more holes tied compared to holes won or lost. If players used full Playing Handicaps in match play, the better player would have the advantage on the more difficult holes (because he or she would also be getting strokes) and the other player(s) would have an advantage on the easier holes."
• https://popeofslope.com/guidelines/handicap103.html - "The scale is tipped in favor of the better player. The way the formula works, for every six strokes difference in handicap, the better player has a one-stroke advantage, because the lower handicapper is more likely to play at or near his handicap than the high handicapper. In a match between an eight handicapper and a 14 handicapper, the better player is giving away six strokes, yet the odds are still 60-40 that he will win the match."

 

 

Edited May 5 by iacas
Added links

[sui generis]

At my club's match play championship final last summer a bogey golfer played a scratch each using their usual tees. At the turn, the bogey golfer was 4 up. The match ended with the scratch shooting 30 on the back and winning 1 up.

 

This is not evidence of anything, just an anecdote. 🙂

[Ty_Webb]

A few thoughts:

 

- Handicaps tend to follow a bell curve. The closer you are to the mean, the flatter the curve is going to be (at least until you get into the tails, which 6 and 12 I would think are not). That would mean that 12 handicap (meaning 11.5-12.4) is going to tend towards being in the middle on average. 6 handicap is more likely to be closer to 6.4 than to 5.5, which would tend to suggest that taking the average player in each bucket will give a little bit of advantage towards the 12. Another way to look at this is if a 6 plays a 12, that could be 5.5 playing 12.4 or it could be 6.4 playing 11.5. The 5.5 is more likely to win his match than the 6.4 and the way averages work, there are more 6.4s than 5.5s, so small advantage (and it is a small advantage) to the 12s.

 

- The 0.96 and 10 going to 8 had "almost no effect on handicap indexes". Given the size of the discrepancy that Lou is talking about here, "almost no effect" could still flip the numbers. If you're a +4, the 0.96 was pulling up your index. Getting rid of that makes your index lower. Going to 8 instead of 10 also makes your index lower. If you're a 20, the 0.96 was pulling down your index. Getting rid of it makes your index higher, while again 8/20 makes it lower. I guess it's possible that the 8/20 has more of an effect on the higher handicap (that is quite plausible), so the impact may be pretty small, but again, he's not talking about large margins here.

 

- I would imagine that the USGA 53.1% or whatever it is was based on playing to a finish. Given where strokes tend to fall, the first playoff hole is likely to be a high index and more likely to not be a stroke, giving an advantage to the lower handicap in the 12% of games that end in a tie in his simulation.

 

- This is just my impression, but I would expect that the 6 handicap is better at handling the pressure and if the game winds up being close, they're more likely to play better down the stretch than the 12. I think that would pan out in reality, but it would not show up in the simulations he's running.

 

- This is a separate point, but stroke indices are intended to do two things I think - firstly the lower index holes would tend to have a larger spread of scores between good and bad players (I guess you could think of the holes themselves as having higher slope), so it makes more sense to differentiate between players on those holes, regardless of where they would get their strokes. By way of example, a 17 plays an 18 in a match and the way he wants it, the 18 gets a stroke on index 18. Both players play not great that day, submit their scores and each of them sees their handicap go up 1 stroke. Now they play a match and now the 19 gets a stroke on index 1. That would be weird to me. The other thing stroke indices are intended to do is avoid strokes being given on the first hole, the last hole, and not being too bunched up anywhere. If you take strokes the way Lou wants, that's going out the window. 

 

- In general, lower handicappers tend to shoot lower scores and have lower variance in their scores. Given that handicaps are based on the best 8, the higher variance player should win when they both play well and should lose when they both don't play well. That's why the USGA's stance that the lower handicap wins a little more held water. It doesn't make a whole lot of sense to me that it would go the other way.

 

- I assume he's using Arccos data for this, which is going to be prone to user input errors. I would expect those input errors to be larger with the higher handicaps. I'm not entirely sure I trust the high end proportions on his list. I've seen plenty of 12s out for a game who totally blow out a hole and "put me down for a 5". Net double or worse has no effect on their handicap, but it will change the outcome of his analysis.

 

I think the first point is most likely what's driving it. I bet the USGA is using a 6.0 and a 12.0, which Lou is using a 6 and a 12. This feels a bit like the reason why second putts are holed more frequently than first putts in a given distance range (it's because between 3.5 and 4.4 feet for example, a second putt is more likely to be closer to 3.5 and a first putt is more likely to be closer to 4.4).

 

[Augster]

I think I’ll keep using the USGA recommendation. They are drawing from a much bigger database of scores and results. 
 

And, logically, it makes more sense to subtract out. If a 17 is playing an 18, where should the 18 get the shot? On the hardest hole or the easiest? If I’m the 17, I don’t want to be giving my one shot on some 110 yard par 3 where my opponent is going to hit the green, even as an 18 cap, at least 60% of the time. And be putting or chipping for birdie around 100% of the time. 
 

At least I have a chance on the 1-cap in that scenario. There is a real chance I win the hole before the stroke comes into play. Or I lose the hole regardless of the stroke.  
 

On the 18-cap hole, the stroke will almost always matter for the match and is way too large an advantage. 

[iacas]

1 hour ago, Ty_Webb said:

- The 0.96 and 10 going to 8 had "almost no effect on handicap indexes". Given the size of the discrepancy that Lou is talking about here, "almost no effect" could still flip the numbers. If you're a +4, the 0.96 was pulling up your index. Getting rid of that makes your index lower.

 

This doesn't really matter in the context of this discussion. People's handicaps didn't change much across the board. When you got into the +s it did a little bit (both two more scores AND the 0.96 work toward a "higher" handicap index on the + side).

 

For those on the regular side (i.e. worse than scratch), 10/0.96 and 8 resulted in almost the same indexes. Before, the 9th and 10th best differentials raised the index over taking only the top 8, but the 0.96 brought it back down a bit.  Again, overall, the handicap indexes of golfers fluctuated very little when moving from 10/0.96 to 8. And since very few golfers are + indexes… I'm treating that as largely irrelevant.

 

1 hour ago, Ty_Webb said:

- I would imagine that the USGA 53.1% or whatever it is was based on playing to a finish.

 

But… 46.9%, 12.0%, and 41.1%. To get to 53.1%, the ties would have to ALL go to the winner, and that's not gonna happen.

 

1 hour ago, Ty_Webb said:

- This is just my impression, but I would expect that the 6 handicap is better at handling the pressure and if the game winds up being close, they're more likely to play better down the stretch than the 12. I think that would pan out in reality, but it would not show up in the simulations he's running.

 

Perhaps. Counterpoint: they might also feel more pressure given that they're the "better player" and are supposed to be winning. The 12 is just happy to still be hanging around.

 

Applying psychology to these kinds of things is IMO often pointless as there are a lot of personality types out there. What if the 12 is just old but used to be a +2? What if the 6 is on a heater lately but is barely holding it together? Etc.

 

1 hour ago, Ty_Webb said:

- In general, lower handicappers tend to shoot lower scores and have lower variance in their scores. Given that handicaps are based on the best 8, the higher variance player should win when they both play well and should lose when they both don't play well. That's why the USGA's stance that the lower handicap wins a little more held water. It doesn't make a whole lot of sense to me that it would go the other way.

 

That doesn't really say much of anything about Lou's simulations other than what you think makes sense.

 

1 hour ago, Ty_Webb said:

- I assume he's using Arccos data for this, which is going to be prone to user input errors. I would expect those input errors to be larger with the higher handicaps. I'm not entirely sure I trust the high end proportions on his list. I've seen plenty of 12s out for a game who totally blow out a hole and "put me down for a 5". Net double or worse has no effect on their handicap, but it will change the outcome of his analysis.

 

I don't think he's pairing up the golfer's GHIN with their Arccos scores. I think he's using what their Arccos handicap would be, so there is no "put me down for a 5" in Arccos, really.

 

1 hour ago, Ty_Webb said:

I think the first point is most likely what's driving it. I bet the USGA is using a 6.0 and a 12.0

 

I don't think that's true at all. I think they're using all handicaps playing against each other, not a 6.0 and a 12.0. I also don't think your rounding errors are going to shift the matches nearly as much as you seem to think.

[DaveLeeNC]

I just don't understand Lou's analysis. What assumptions did he make about hole handicap allocations? He seems to think that where strokes are assigned is the critical factor here, but I don't see that in his data.

 

Can someone enlighten me? Thanks.

 

dave

[Pepperturbo]

Interesting @iacas.  Thanks for posting that. Never seen the stat breakdown quite like that. 

 

My reasoning is how often "X" low cap wins or loses has to do with whether "X" pays attention to alleged belief, the high-handi has the advantage (If someone thinks that, he's half beaten himself) and was his index founded on a difficult or easy course.

 

As a 2-3 index, I played interclub match play at two clubs for about fifteen years.  Both courses were rated comparatively difficult.  Depending on course, and it's rating the team played, I'd get 1-3 strokes; paired against mostly 10-19 index guys, and won over 50% of the time.  Guess I fit the stats.  One of our team members (+2) won +/-70% of the time.  

 

When I got beat, the guy's home course was similarly rated, and his index was dropping due to improved play.  Based on USGA index stats, on average, most guys are not in that combined position.

 

 

Edited May 5 by Pepperturbo

[iacas]

8 hours ago, DaveLeeNC said:

What assumptions did he make about hole handicap allocations?

 

It's the left column. The stroke index stuff.

 

He used the handicap (stroke index) order from 5000 courses and rotated through them in the million simulations.

[DaveLeeNC]

15 minutes ago, iacas said:

 

It's the left column. The stroke index stuff.

 

He used the handicap (stroke index) order from 5000 courses and rotated through them in the million simulations.

Got it - thanks for the clarification. dave