Golf stats and correlation to average score vs. handicap

[RandallT]

@natureboy - all I can say is my head hurts . Good stuff- solid analysis. It's just way over my head! Looks like your analysis is solid though.

Regarding recovery shots, my only rule has been simply this: charge the previous shot.  If you hit a ball into a bad position, count the subsequent shots against the drive (until you are back in position).  For example, 400T to 135C to 130C to 125F (two recovery shots to get to the fairway again).  I use the strokes gained from 400T (3.99) to 125F (2.865), but you compare with 3 shots you actually took, not just one (3.99-2.865-3= LOST 1.875 strokes from the drive).  The drive was the culprit for any lost strokes, so until you get back into position where you are shooting at the green (a non-recovery shot), it all counts against the drive.

That flies in the face of Broadie's stuff, I know. But frankly, I think he's wrong in choosing to analyze recovery shots much. The other guys that I've seen doing strokes gained do it Broadie's way (and your way),  so maybe I'm off-base or just lazy.  I'd just prefer to focus on what skills you can improve to avoid recovery shots , not the statistical analysis of the recovery shots themselves. I just don't see a lot of point looking at recovery shot data personally. If I'd hit a better drive, I could've saved 2 shots almost in my example, because I wouldn't have been hacking around at all.

But again, very interesting stuff. Keep cranking out the interesting data relationships.

[Lihu]

Quote:

Originally Posted by Lihu

To me, experience factors into putting more so than handicap? I know a lot of senior golfers who only drive about as far as my 6i or less, but some of them make 20 foot putts with great regularity (more than 3 per round).

I think HCP is a reflection of both physical skill and game savvy which experience (including course / green knowledge) contributes to.

It seems that with most skills that correlate well to average score there is a general tightening of the variability in variability / ranges of averages (with scoring too) as you move toward lower average scores, while there is a decrease in power, precision, and touch as you move to the high end. Seems obvious. What's not obvious is how the decrease in distance for higher HCPs (which should make recovery shots less costly) along with the decrease in precision and special shot savvy (which should make recovery shots more costly) will balance out? Add the fact that generally higher handicappers play shorter courses than low HCPs and it makes for a bit of a moving target.

Here's my rough idea of what I would expect to happen for baselines for higher HCPs. Basically for decreasing skill a recovery shot would become less costly vs. fairway and the low point would shift toward the target due to the decreasing avg driving distance.

I have mostly eliminated 4-putts but am still above my HCP in putting performance, so to have an 11 HCP you must have a great iron and/or short game or play really tough courses.

You are mostly correct about experience and handicap as well, but there are exceptions. I do know a couple people who started 3 years ago who are in the single digits. They drive far and have decent approach shots.

Unfortunately, I have good putting days and really bad ones. My irons play is so so and gets me nGIR conditions on more than 14/18 holes, and I hit them reasonably far enough. GIR is only about half of that and some days is really good. Plus the course I usually play is rated 72.9/131 but only for its 6800 yard distance. The greens are relatively easy to hit and I can still make nGIR from other fairways or rough.

[natureboy]

@natureboy  - all I can say is my head hurts . Good stuff- solid analysis. It's just way over my head! Looks like your analysis is solid though.

Regarding recovery shots, my only rule has been simply this: charge the previous shot.  If you hit a ball into a bad position, count the subsequent shots against the drive (until you are back in position).  For example, 400T to 135C to 130C to 125F (two recovery shots to get to the fairway again).  I use the strokes gained from 400T (3.99) to 125F (2.865), but you compare with 3 shots you actually took, not just one (3.99-2.865-3= LOST 1.875 strokes from the drive).  The drive was the culprit for any lost strokes, so until you get back into position where you are shooting at the green (a non-recovery shot), it all counts against the drive.

That flies in the face of Broadie's stuff, I know. But frankly, I think he's wrong in choosing to analyze recovery shots much. The other guys that I've seen doing strokes gained do it Broadie's way (and your way),  so maybe I'm off-base or just lazy.  I'd just prefer to focus on what skills you can improve to avoid recovery shots, not the statistical analysis of the recovery shots themselves. I just don't see a lot of point looking at recovery shot data personally. If I'd hit a better drive, I could've saved 2 shots almost in my example, because I wouldn't have been hacking around at all.

But again, very interesting stuff. Keep cranking out the interesting data relationships.

Your approach is interesting. I'm not sure that it flies in the face of Broadie's method.

Remember he is using well mapped courses where the expected shots from most specific (or at least similar) locations is known statistically for certain HCP groupings. You are using a strictly distance-based SG table that doesn't take into account the gnarly position in the trees. So the expected strokes remaining from that lie vs. the tee might give you a negative SG drive if it is was mapped for expected strokes to go. Your approach for hellish lies might get you closer to the right number.

I think you have to try to be accurate in assessing whether a subsequent stroke after the recovery attempt was due to the initial lie (I expect to hit trees and branches in deep woods) or an 'awful' recovery shot (I don't expect to badly mishit the ball if it's a relatively clean lie).

You are mostly correct about experience and handicap as well, but there are exceptions. I do know a couple people who started 3 years ago who are in the single digits. They drive far and have decent approach shots.

Unfortunately, I have good putting days and really bad ones. My irons play is so so and gets me nGIR conditions on more than 14/18 holes, and I hit them reasonably far enough. GIR is only about half of that and some days is really good. Plus the course I usually play is rated 72.9/131 but only for its 6800 yard distance. The greens are relatively easy to hit and I can still make nGIR from other fairways or rough.

I said physical skill and game savvy / experience mattered. Obviously there are many high handicaps who are distance limited, but have stellar short games so there will be a fair number of outliers...I'd say that's why the variance in the stat averages tends to widen at high handicaps.

[Lihu]

Quote:

Originally Posted by Lihu

You are mostly correct about experience and handicap as well, but there are exceptions. I do know a couple people who started 3 years ago who are in the single digits. They drive far and have decent approach shots.

Unfortunately, I have good putting days and really bad ones. My irons play is so so and gets me nGIR conditions on more than 14/18 holes, and I hit them reasonably far enough. GIR is only about half of that and some days is really good. Plus the course I usually play is rated 72.9/131 but only for its 6800 yard distance. The greens are relatively easy to hit and I can still make nGIR from other fairways or rough.

I said physical skill and game savvy / experience mattered. Obviously there are many high handicaps who are distance limited, but have stellar short games so there will be a fair number of outliers...I'd say that's why the variance in the stat averages tends to widen at high handicaps.

Yes, I agree.

[natureboy]

@Lihu & @RandallT - I think I've got a workable estimate for recovery shots. I made a very rough guess estimate of different SG cost for a recovery lie vs. Fwy baselines for higher handicaps along the lines of what I skectched. Then I estimated their average 2nd shot distance on driving holes for a 'Typical Course' of 6500 yards and plugged in the shot fraction at that distance for their baseline. Then I plotted the result. Obviously it's a bit raw since the higher HCP baseline curves are pure guess, but I think that it's a reasonable estimate since it's based on the pro baseline shape and what is a reasonable expectation for higher HCPs - that being partially blocked out is not as big a factor in their expected score because they aren't as long or accurate as pros.

Here is the resulting plot of 'recovery cost' by HCP for a 'Typical Course' of 6500 yards. When you plot the numbers for expected approach from USGA recommended tees, the shape still fits a power law curve, but it is flatter.

Here is the revised chart with the calculated 'baselines' for 'Effective Driving Distance' by HCP. Another caveat is that for shots hit to penalty, each was counted as two extra possible fairways, but if you play on courses with water, there will be situations where the ball has travelled a significant distance before crossing the boundary so it would be less than the full cost of '2' for stroke and distance with L/OB. Since I don't have an estimate of what fraction of drives hit to penalty carry for pros or ams, it was simpler to just count them all as L/OB. All the values for each HCP / Avg Score was calculated the same, though so still valid for comparison. If that info becomes available the chart can be tweaked.

Avg Score	65	70	75	80	85	90	95	100	105	110	115
~ HCP (Course Rating 75)	-11.1	-6.5	-1.9	2.7	7.3	11.9	16.5	21.1	25.7	30.3	34.9
~ HCP (Course Rating 72)	-8.6	-4.0	0.6	5.2	9.8	14.4	19.0	23.6	28.2	32.8	37.4
~ HCP (Course Rating 68)	-4.0	0.6	5.2	9.8	14.4	19.0	23.6	28.2	32.8	37.4	42.0
~ USGA Reccd Tees (Yards) Per Avg Drive Dist	7,542	7,016	6,573	6,232	5,986	5,814	5,687	5,568	5,419	5,200	4,861
Broadie-Ko 'Typical Course' (6500 Yds) Simulation
Std Dev Degrees Offline From Tee	2.7	3.8	4.7	5.5	6.2	6.9	7.4	7.9	8.4	9.0	9.5
# Fairways	10.8	9.1	8.0	7.2	6.7	6.4	6.3	6.3	6.3	6.2	6.0
% Fairway	77.0	65.3	56.9	51.2	47.6	45.7	45.0	44.9	44.9	44.5	43.2
75% Driving Distance (Good Drives )	314.1	283.1	260.3	244.3	233.3	225.9	220.6	215.7	209.7	201.1	188.3
Avg Driving Distance	298.8	266.7	242.5	224.6	211.6	202.0	194.5	187.6	179.7	169.5	155.5
Effective Drive Dist - Rgh Adj	286.0	254.3	232.2	216.7	205.7	197.7	191.3	185.2	178.0	168.2	154.5
Effective Drive Dist - Rgh & Penalty Adj	281.9	248.0	224.2	207.0	194.5	184.8	176.5	168.3	158.9	147.2	132.0
Effctve Drive - Rgh, Pnlty, & Recvy Adj (@ USGA Tees)	277.6	238.6	213.4	196.4	184.6	175.9	168.6	161.4	153.0	142.1	127.9
Effctve Drive - Rgh, Pnlty, & Recvy Adj (@ 6500 Yrd Tees)	276.6	237.5	213.3	197.2	186.0	177.7	170.7	163.6	155.1	144.2	129.7
# Long Tee Shot To Recovery	0.29	0.91	1.41	1.80	2.11	2.34	2.52	2.66	2.79	2.91	3.05
% Long Tee Shot To Recovery	2.09	6.53	10.09	12.89	15.06	16.72	18.00	19.02	19.91	20.79	21.78
# Long Tee Shot To Penalty	0.10	0.18	0.25	0.33	0.40	0.49	0.59	0.70	0.84	1.00	1.19
% Long Tee Shot To Penalty	0.73	1.28	1.80	2.33	2.88	3.49	4.20	5.02	5.99	7.14	8.50
Effective Yardage Loss On Pxy From Rough	55.7	35.8	23.7	16.1	11.2	8.0	5.8	4.3	3.2	2.4	1.9
~ Avg Stroke Lost To Recvy Lie v Fwy (@ 6500 Yrd Tees)	0.93	0.69	0.52	0.41	0.32	0.25	0.20	0.17	0.14	0.11	0.10
~ Avg Stroke Lost To Recvy Lie v Fwy (@ USGA Tees)	0.75	0.62	0.52	0.44	0.38	0.33	0.28	0.25	0.22	0.20	0.17

[Lihu]

Regarding the plot, I presume those distances are in yards from the Tee? Your typical 6500 yard course is going to want to see numbers like 60 to 250 yards, and would take something like a 250 yard drive to approach "0" recovery strokes?

For instance, if I hit the rough from 200 yards out versus 250 yards on a 400 yard hole, the chances I need a recovery shot are pretty high on the 200 yard recovery versus the 150 yard shot. There's 4 clubs difference between the two. Is this what your are stating?

[natureboy]

Regarding the plot, I presume those distances are in yards from the Tee? Your typical 6500 yard course is going to want to see numbers like 60 to 250 yards, and would take something like a 250 yard drive to approach "0" recovery strokes?

For instance, if I hit the rough from 200 yards out versus 250 yards on a 400 yard hole, the chances I need a recovery shot are pretty high on the 200 yard recovery versus the 150 yard shot. There's 4 clubs difference between the two. Is this what your are stating?

If it's the plot just above your post, then the y-axis is expected average cost (in strokes) of a recovery lie vs. Fwy lie and the x-axis is average score on a 'typical' course of 6500 yards. It's the next step of extrapolating the cost of recovery lie plot to an average driving distance (inverse of fractional remaining length on driving holes) and the correlated average score for that driving distance.

Those expected average stroke costs are related to average distances remaining to the hole after tee shots. Lower HCP players - on average - are closer to the hole on a 'typical' course of 6500 yards (which is more costly to expected score) and more accurate at a distance so generally find interference of any kind more damaging to their expected score.

[Lihu]

Quote:

Originally Posted by Lihu

Regarding the plot, I presume those distances are in yards from the Tee? Your typical 6500 yard course is going to want to see numbers like 60 to 250 yards, and would take something like a 250 yard drive to approach "0" recovery strokes?

For instance, if I hit the rough from 200 yards out versus 250 yards on a 400 yard hole, the chances I need a recovery shot are pretty high on the 200 yard recovery versus the 150 yard shot. There's 4 clubs difference between the two. Is this what your are stating?

If it's the plot just above your post, then the y-axis is expected average cost (in strokes) of a recovery lie vs. Fwy lie and the x-axis is average score on a 'typical' course of 6500 yards. It's the next step of extrapolating the cost of recovery lie plot to an average driving distance (inverse of fractional remaining length on driving holes) and the correlated average score for that driving distance.

Those expected average stroke costs are related to average distances remaining to the hole after tee shots. Lower HCP players - on average - are closer to the hole on a 'typical' course of 6500 yards (which is more costly to expected score) and more accurate at a distance so generally find interference of any kind more damaging to their expected score.

I think handicap would be clearer, but the other thing I noticed is that the expected average cost in strokes for a lower scorer is higher than that of a higher scoring individual? Am I reading this correctly or is there something wrong with my logic?

[natureboy]

I think handicap would be clearer, but the other thing I noticed is that the expected average cost in strokes for a lower scorer is higher than that of a higher scoring individual? Am I reading this correctly or is there something wrong with my logic?

Yes.

Assuming the baselines for higher HCP players progress roughly as depicted in post 72 then on the same course length the pros will always have a higher cost of being in a recovery situation vs. a Fwy lie because they are more accurate and longer and therefore have a higher expectation of a scoring opportunity on the Fwy than higher HCPs so being in recovery lie is more costly to them.

You will note when the 'effective distance' averages accounting for tee shots hit to 'recovery lie' are projected for USGA recommended course lengths the pros improve in average 'effective distance' this is because their expected recovery lie distance to the pin is shifted further away from the hole at USGA recommended course lengths, so the lie becomes less costly to them from a scoring perpective while for higher HCP's they are moving closer to the hole which raises their expected cost from hitting to recovery lie.

In reality on a 6500 yard 'typical' course Pros would likely have an easier time of it with less relative 'trouble' so their % tee shots to recovery lie would likely be lower just due to the easier setup thus mitigating the expected penalty to their effective distance from being closer to the green on those 'expected' recovery lies.

[Lihu]

Quote:

Originally Posted by Lihu

I think handicap would be clearer, but the other thing I noticed is that the expected average cost in strokes for a lower scorer is higher than that of a higher scoring individual? Am I reading this correctly or is there something wrong with my logic?

Yes.

Assuming the baselines for higher HCP players progress roughly as depicted in post 72 then on the same course length the pros will always have a higher cost of being in a recovery situation vs. a Fwy lie because they are more accurate and longer and therefore have a higher expectation of a scoring opportunity on the Fwy than higher HCPs so being in recovery lie is more costly to them.

You will note when the 'effective distance' averages accounting for tee shots hit to 'recovery lie' are projected for USGA recommended course lengths the pros improve in average 'effective distance' this is because their expected recovery lie distance to the pin is shifted further away from the hole at USGA recommended course lengths, so the lie becomes less costly to them from a scoring perpective while for higher HCP's they are moving closer to the hole which raises their expected cost from hitting to recovery lie.

In reality on a 6500 yard 'typical' course Pros would likely have an easier time of it with less relative 'trouble' so their % tee shots to recovery lie would likely be lower just due to the easier setup thus mitigating the expected penalty to their effective distance from being closer to the green on those 'expected' recovery lies.

Aha, makes sense.

[natureboy]

Aha, makes sense.

And HCP is correlated with Avg score (depending on course rating) in the table.

[Nosevi]

Sorry Natureboy, got your PM so will reply. The snag with this from my perspective, and why I dropped out of the thread so to speak, is that the way our handicaps are worked out over here are different to over there. I far prefer the way they are worked out over there but here if you are either improving or going the other way your handicap often very little correlation to your ability. Here's an example:

I'm a 5.1 handicap officially yet shoot scores that would put me at about scratch. Those scores invariably don't count as only competition scores count to handicap here but even if they did it would take me shooting to scratch 26 times in a row in competition to get to a handicap of 0.0 and any score over handicap that was shot would automatically put my handicap up. I won't bore you with the maths or a full explanation of how our system works (or doesn't IMO) but what is does mean is that any correlation between stats and handicap that you can show doesn't really apply to us as our system works so differently.

One thing I would say, and it's a counter argument in a way and is merely thrown out there to prompt discussion, feel free to ignore the point, is there's an old golfing saying over here - "It's not how, it's how many." In a nutshell it doesn't matter how you get the ball in the hole it only matters how many shots it takes you. I track my stats so I can use them to focus my training and I also use Randy's Strokes Gained spreadsheet (which is fantastic IMO) to give an idea of how I compare on the course to the pros. This is all looking at ways to assess where I am ability wise but there will always be things I am better at than a generic golfer of a given handicap and things I'm not as good at. In the end the only stat that really matters is the little box in the scorecard where you write down how many shots you took to get the ball in the hole and we all do that in slightly different ways.

[natureboy]

Sorry Natureboy, got your PM so will reply. The snag with this from my perspective, and why I dropped out of the thread so to speak, is that the way our handicaps are worked out over here are different to over there. I far prefer the way they are worked out over there but here if you are either improving or going the other way your handicap often very little correlation to your ability. Here's an example:

I'm a 5.1 handicap officially yet shoot scores that would put me at about scratch. Those scores invariably don't count as only competition scores count to handicap here but even if they did it would take me shooting to scratch 26 times in a row in competition to get to a handicap of 0.0 and any score over handicap that was shot would automatically put my handicap up. I won't bore you with the maths or a full explanation of how our system works (or doesn't IMO) but what is does mean is that any correlation between stats and handicap that you can show doesn't really apply to us as our system works so differently.

One thing I would say, and it's a counter argument in a way and is merely thrown out there to prompt discussion, feel free to ignore the point, is there's an old golfing saying over here - "It's not how, it's how many." In a nutshell it doesn't matter how you get the ball in the hole it only matters how many shots it takes you. I track my stats so I can use them to focus my training and I also use Randy's Strokes Gained spreadsheet (which is fantastic IMO) to give an idea of how I compare on the course to the pros. This is all looking at ways to assess where I am ability wise but there will always be things I am better at than a generic golfer of a given handicap and things I'm not as good at. In the end the only stat that really matters is the little box in the scorecard where you write down how many shots you took to get the ball in the hole and we all do that in slightly different ways.

If you wanted, you could adjust the table by replacing the handicaps as they correlate to score with the CONGU step function you use over there. I would imagine the basic skills progression trends are about the same though the scores vs. HCP will differ. You could even estimate the course rating for 'The Hotchkin' based on average scores posted there by handicap (second chart relates to USGA HCP).

Obviously the score is what ultimately matters, and as they say over here, there are many ways to 'make the sausage'. But there are definitely trends of skill development as handicaps get lower so making this effort has made it easier for me to clarify relative weaknesses and strengths in my game at the comparatively low skill level where I am. I get that you are only interested in comparing your game to pro level benchmarks. Best of luck with your efforts.

[danL]

I reworked my swing a bit to try and fix the outside to inside slice swing. I got that corrected for the most part and at the same time picked up an extra 20yds with each club. My 160yd club is now my 8i and I've found that if I have a 7i or less into the green, I usually stick it. GIR is definitely the biggest factor in my scoring.

[Jeremie Boop]

Maybe I'm missing something, but no way is that thing accurate. 47% GIR for a > 30 handicap? 55% for a 10-15?

This one I can believe:

So… they labeled the axis wrong. It's not GIR%, it's "FIR%". Which is one of the more meaningless statistics out there…

Things like this always remind me that I don't fit in well to the groups for what my HI is. My stats for GIR show that I should fall into the 10-15 HI range, my swing speed/average distances would also put me into an even lower HI range. Now, if there was a stat that tracked number of OB per round I'd be expected to have a much higher HI. I guess if I averaged out the expected HI it would probably give me a decently accurate number.

[Nosevi]

Things like this always remind me that I don't fit in well to the groups for what my HI is. My stats for GIR show that I should fall into the 10-15 HI range, my swing speed/average distances would also put me into an even lower HI range. Now, if there was a stat that tracked number of OB per round I'd be expected to have a much higher HI. I guess if I averaged out the expected HI it would probably give me a decently accurate number.

This is kind of what I was saying about people having strengths in different areas. You can say an average 10 handicapper hits x greens in regulation but some hit less but have an above average short game, some hit more but can't putt to save their life. It's useful as a guide to see where you can perhaps target your practice but very few people are going to fit perfectly into the mould.

I actually practice with 2 tour pros maybe 1/4 of my practice time. One is a lass who was playing off plus 3 before turning pro and she's fantastic around the greens, doesn't matter where the ball is she's getting up and down. The other is a guy who was off plus 5 at one point and played for the Ireland national team, his forte is the long game and he'll regularly carry a drive (ie in the air) over the 300 yard mark. That's not 'internet yards' that's measured on a launch monitor. I walked with him during a tournament a couple of weeks ago and he had 50 yards on the other pro (an ex-England international player) in the group, in still air he was a 7 iron into 2 of the par 5s. Anyway, sometimes we all practice together but generally I practice long game with him, short game with her as those are the areas of the game each excel in and therefore the areas I want to learn from them in. But both are amazingly good golfers and both will get the ball around the course in very few shots. They just do that in a totally different way.

[natureboy]

Things like this always remind me that I don't fit in well to the groups for what my HI is. My stats for GIR show that I should fall into the 10-15 HI range, my swing speed/average distances would also put me into an even lower HI range. Now, if there was a stat that tracked number of OB per round I'd be expected to have a much higher HI. I guess if I averaged out the expected HI it would probably give me a decently accurate number.

Take a look at post #77

@Nosevi That's kind of the point of the chart. It tracks stat averages vs. the average for each handicap. Since there is a general skill progression in all facets of the game as HCP lowers you can ID strengths & weaknesses relative to your HCP peer group. Two players with same HCP but different strengths will have that higher scoring skill offset by a relative weakness in another facet of their game.