The updated World Amateur Rankings came out this morning. Will has now moved to #3 in the world! He was outside the top 3,100 when the summer started.

Holy shart.

http://www.wagr.com/

I've got some stuff I've been working hard on for the last two months that I'll be bringing to the forum next week most likely. I think it will blow most of your minds....I'm sure the suspense will eat you alive this weekend.

That is awesome.

Can't wait for the post next week!

#3 in the world. So sick.

holy ****!

this is one of my favorite threads ever

This is awesome! Also looking forward to your posts next week. I want an autographed copy of Ship's Super System when it comes out

sorry...couldn't help fixing your post.

Well this sucks, zero chance to get any value on betting him to win a major in the future.
In all seriousness though pretty big this is ****ing awesome is due for him. Makes me curious how many shots you could take off a 10-20 handicap players game in a summer just from course management and the mental side of golf.

****, I just tried to start Camtasia for a screen recording session to put this together for you guys and my 30 day trial expired. I bought it but the key hasn't come through my email yet so I guess it's stuck somewhere in cyberspace. I'll get the video together asap and post.

Oops.

Never mind, the code came in so I made a quick video. I’ve got a business I’m working on to teach correct strategy and mindset to the masses. I’m going to shoot some videos similar to this (except not hurried and ****ty) to explain some concepts to you guys.

I’m hoping for feedback on if the ideas translate well via video and whether or not they seem valuable.

I’ve got a series of about 8 videos I’m planning on shooting that will be very informative I think.

Enjoy, sorry it’s slightly hurried but it’s been a hectic week with other crap.

https://www.youtube.com/watch?v=fFL40fWTJxc

valuable? are you kidding? i'd honestly be more shocked if tools of this nature weren't already being used..

Just an FYI

You can't really calculate the true EV with just the median leave %. It's really not as easy as just having the median leave % all be on the green. You need the standard deviation for the players distance and directional control to create a normally distributed shot dispersion pattern. Then you have to calculate the strokes to hole out from all of the different locations where his ball can finish up(this is incredibly difficult to do because you have to calculate how far each shot finished from the hole and the surface it finished on be it green, fairway, sand or rough)

The video is OK but the calculation for an ideal target is in no way shape or from a "simple" equation. It's a decent baseline for most amateurs to use but if you are a professional looking to shave a quarter to half a shot off your game(or more) using better course management then you have to dig deeper.

Here is an example. We have a player who is facing a 150 yard shot. I set it up so that his std deviation for distance is 4 yards and his std deviation for direction was 10 yards. With those numbers when I modeled it he had an ~5.5% median leave which is pretty decent.

Here is what this players normal shot dispersion would look like at 150 yards. It's normally distributed especially directionally but should be skewed distance wise towards the short side as you are more likely to hit it 20 yards short than 20 yards long but this will suffice. It's certainly not random within the median leave % circle. The most likely single outcome is that you hit it 150 yards and dead on line, even though it will happen a very small % of the time. As you move away from the target the chance of that shot occurring decreases by minimal amounts until you get to the edges of your dispersion.



Since it is so incredibly hard to calculate all of the different outcomes when you are talking about a real green/pitching areas/bunkers layout of a hole, I kept it simple and said any shot 6 yards left of the hole would be in the sand regardless of how far he hit it. If he didn't hit it 6 yards left of the hole, then as long as if he was within 100 feet of the hole I considered him on the green, otherwise he was in the rough.

Let's look at 3 different targets and what his Strokes Gained outlook is for each.

1. Player takes dead aim at the flag.

He ends up with an average strokes gained of -.009 per shot.

2. Player selects a target so that his median leave % circle bumps up against the edge of the bunker, this would mean his target is 8 yards right of the flag.

He ends up with an average strokes gained of -.01, actually slightly worse than taking dead aim at the target. Essentially to conservative of a target for the players skill set.

3. Player selects a target 5 yards right of the flag(tried to use excel to solve for the perfect target but its a bit too complicated of an answer for excel so I just used trial and error)

He ends up with an average strokes gained of .017. That is roughly .026 shot better than the other 2 targets and if you found this edge on each of your 18 approach shots for the day it would be worth almost .5 shots at this skill level(PGA Tour skill level based on std deviations and median leave %).


The shots saved can be even more drastic for worse players. I tweaked our player now to have a standard deviation of 7 yards(rather than 4 yards) in the distance department and 12 yards(rather than 10 yards) in the directional department. This takes them to a median leave % of roughly 7.3%. I also accounted for the poor sand play of most amateurs and had his strokes gained out of the sand 25% more than the PGA Tour baseline(essentially making hitting it in the bunker more costly)

Here is this players shot dispersion pattern from 150 yards, notice he has a wider dispersion than the previous player.



Here are his 3 scenarios

1. Player takes dead aim at the hole

Player will lose on average -.30 shots.

2. Player aims 5 yards right of the hole

Player will lose on average -.21 shots.

3. Player aims 9 yards right of the hole

Player will only lose -.17 shots per hole.

Versus scenario 1, scenario 2 will save you .09 shots per swing and roughly 1.7 shots on the round if you replicate the good decision on all 18 holes. Scenario 3 will save you .13 shots per swing and will be good for 2.4 shots over the course of an 18 hole round. Again it's worth noting that if you wanted to make the target so just edge of the median leave circle bumps it the player would have to aim 11 yards right of the target and would be costing himself a little bit in EV.

Different hazards(sand vs water vs out of bounds) effect things in very different ways as does a players skill level on certain shots. Water and out of bounds have to be avoided much more carefully than sand so our targets when those hazards are lurking need to be much more conservative.

I fully understand that. That's why I said I simply want that video to illustrate the basic idea to have you guys start thinking of shot in a dispersion pattern as a shotgun and not a rifle. It's also why I said you need TrackMan data on a player to really hone their targeting in perfectly.

I truly want your input on this as I do find you both intelligent and a good player. Let's not turn this into a flame war, ok?

Shot distribution actually is not normally distributed so your example is not quite correct. The distribution for a right handed player is skewed long left and short right. Obviously a result of pulls being typically hammered and blocks being fanned. The innermost portion of the distribution is not normally distributed either. Yes it is centered on the target, but as it moves outward the distribution is not completely normal.

Not even the median leave numbers from the PGA Tour are relevant because you don’t know what their target was. That is why I showed that I tracked Will’s shots to our ACTUAL target as well as to the hole. I then used that data to approximate what I think his distribution pattern is as well as using it to somewhat back into the PGA Tour players. I also have access to my own TrackMan data as well as about 10 PGA Tour players from my instructors clientele.


So yes we agree that unless you have the ability to get a specific player on TrackMan over many sessions it is impossible to isolate the math perfectly. Not to mention, to get one players distribution over the course of enough shots would take a year and in no way is indicative of that players abilities at any given time.


As a result you must generalize the concept a tad. That is why the boiled down formula I’ll show you later is as close of a proximity as I believe can realistically be created. I certainly do understand that it is not a perfectly accurate equation as that equation simply can’t be created.


However, after spending the summer watching the horrendous course management of the worlds best amateurs I can assure you they all would have scored significantly better had they used what I will illustrate here.

I actually almost sent you a PM to see if you wanted to collaborate on this idea as I do think it is right up your alley. That offer potentially still exists if we can communicate in a reasonable manner on this.

No flame war is good with me, I think we can have a good discussion about this topic.

Don't have a lot of time right now but I'll mention a few things. My thoughts are that direction is almost definitely normally distributed, the most common outcome is you hit it dead straight and as you move away from center on each side it becomes less and less likely.

Distance is tough for a few reasons
1. Distance is a dependent variable
2. Like you said if you hit it left(as a righty) its more likely to go long and right is more likely to be short.
3. There is a lot more room for error on the short side than the long side

Interested on why you don't think direction is normally distributed.

This is advanced. But I like it.

I should clarify that i dont mean literally "dead straight" is the most likely outcome, i mean hitting the center of your distribution is the most likely outcome.

Your normal shot may be a 5 yard fade and that is the most likely outcome. If you start the ball 5 yards left of the hole than the hole will be the center of your distribution, and just about 50% of your shots will finish left and about 50% will finish right.

Now if you start the ball at the hole and fade it 5 yards the overwhelming majority of your shots will finish right of the hole and may lead you to believe that your shots are not normally distributed bc they are so skewed to the right but thats not correct because the hole is no longer the center of your distribution. 5 yards right of the flag is your center and its likely 50% of your shots fall on either side of that.

This in part is why im skeptical of the "eliminate one side of the golf course" line of thinking as i dont think its possible to miss golf shots on one side of center more often than the other. You can miss on one side of a "target" more often than not but you must shift your center to that side of the target.

Imagine you are on a range hitting at a target recording the final resting place of every shot, and then removed the target from the scatter plot. That scatter plot for most professionals is not perfectly normal due to rarely double crossing yourself relative to intended shot shape and target. Since I am not a classically trained statistician, as we all know by now, I’m not sure if I am being nitty with that distinction. Almost all of my “big” misses will be way right since I try to cut everything. I almost never have a big miss left. Even my smaller misses (aka normal shots) are slightly skewed right. I think this would result in the median shot being dead on the target but the average shot would be slightly right for me. Like I say, I’m not sure if I’m being a total nit on that as we are talking about a small distinction, but to get really tight on the expectations I think it is worth noting.

I envision the actual scatter plot for a righty playing a cut being skewed slightly long left to short right and somewhat teardrop shaped in the direction of the shot shape.


To play good golf you must keep the face and path relationship correct to what you are trying to do…i.e. if you are trying to hit a cut, it better cut. This, as you agree, is not to take one side of the course out of play, it is simply to tighten the distribution as much as one can hope to. If you have big misses left and right, good luck.

Mark Broadie in Every Shot Counts defines accuracy as the standard deviation of miss in degrees offline. I think that he is missing this slight variation due to using huge amounts of data as a whole population and not looking at each individuals results. He takes the center of the distribution for every single hole and then computes how far offline each player is relative to that point. I don’t think that is entirely accurate when helping specific players with their games and strategy. We agree that a complete set of TrackMan data for a specific player is the only way to make that happen. However, that data would have to come from a long timeframe to get a true sense of their ability and gain a reasonable sample size. Thus, I do believe that using the data from the entire population and then adjusting based on if the player is either better than or worse than the general population is as good as we can hope to do. What I’ve come up with is a good enough start for getting kids and college kids viewing the problems correctly. Then they can adjust based on their own experiences as time evolves, but at least they have a good starting point. Their current strategy is simply awful.

Amen.

The best drivers on Tour miss the same amount of shots left as they do right. They don’t eliminate half the course as traditionally stated. They create this distribution via optimal target selection, not changing their shot shape accordingly.

The first Tour player I took this strategy to a few months ago was Edward Loar. He’s been a longtime friend and I wanted to have a few quasi off the cuff conversations before taking it mainstream (like here on Two Plus Two right now). The most glaring thing I saw from him was that he misses 19.2% of fairways right and only 12.6% left. That shows poor target selection almost immediately. He is a big lefty that hits a huge hook, but that shouldn’t matter over the course of a few seasons. His distribution, and thus target, is skewed too far right. He misses an appropriate amount of fairways, but simply needs to allocate them better around the fairway. That would turn his far right shots in hazards or recovery situations into balls in the rough, and some of his balls in the left edge of the fairway would now be in the left rough. However the overall EV of that distribution should result in better scores, with his exact same skillset.

That point actually made me think of a good real world example of the distribution not being exactly normal. This summer Will drove it great with a nearly perfect distribution between left and right misses. I think we managed his targets perfectly and the results obviously agree. However, I can’t think of a single big miss right he hit all summer. He did however hit quite a few big hooks left.

This illustrates the same issue why Broadie uses the medians vs the mean. There just isn’t much we can do about the big misses aside from hope they happen at the right time. Will’s shot pattern was correctly focused on the fairways, but his big misses were entirely to the left side. He got lucky and none of those misses bit him too much.

Here's a quick video with what I took to Ed Loar so he could see where he was off....don't forget he's a lefty.

https://www.youtube.com/watch?v=X8Jn1zrxIZ4

I also made a peace offering avatar removal...onward and upward.

I'm a bit confused here. You seem to be saying your go to shot is a cut that lets say you are aiming to finish right at the hole. However most of your shots miss right, and you are more likely to hit one way right than way left. If that is the case I don't understand how either the average or median would be near the flag?

If you hit 1000 shots and the majority of them miss right(let's say 65% right and 35% left) then your median will be further right than you think. And then if the shots you miss right are more likely to be farther from the target than your left misses, your average shot will be even further right.

Here is a scatterplot I had excel calculate based on a player trying to hit it 150 yards at the target(150 distance, 0 direction on the plot). So for distance his mean is 150 yards and his std dev is 7 yards. For direction his mean is 0 and his std deviation is 12 yards. This player isn't really very good but that isn't relevant really.

I also added a multiplier so that if he hit the ball left it would go slightly further and if he hit it right it would go slightly shorter.



What I'm curious to know is how by looking at someone's scatter plot like the above are you able to tell what sort of shot shape they play? Or how that effects one's scatter plot.

These 2 quotes from you seem a bit contradictory in the sense that it would seem possible to me to eliminate one side of the golf course. The key line being this

Here is my issue with this statement. Your face and path each are likely normally distributed. Good players likely have very tight std deviations for their club face and club path(creating very narrow shot distributions) where as amateurs have wild std deviations(creating incredibly wide shot distributions). Just by hitting one shot shape I don't think you magically narrow your club face std deviation or make it more likely your distribution is skewed one way or the other.

If you want to play a 2 yard cut, then generally your club face will be slightly shut to the target line(to start left) and your path would be a little left of that(to cut the ball).

You could in theory eliminate the left side of the course by just hitting a 2 yard cut, since you would very rarely double cross yourself, but I don't think that is possible. It would be nearly impossible for the center of your distribution to be a 2 yard cut, if 90% of your shots are between 2 yards left of the target(the dead straight shot) and 25 yards right of the target(the weak fade right) and only 10% of your shots go left of dead straight.

It's my thinking that shot shape is somewhat irrelevant when you want to determine targets. Your target should be based on your skill level and your standard deviations. If you have a std deviation of 5 yds directionally vs someone who has a std deviation of 10yds, you can be much more aggressive than they can at tucked pins.

It basically boils down to my opinion being you have as good of a chance of hitting it X yards left of your target as X yards right of your target. If you are trying to hit a 5 yard cut that starts at the hole and finishes 5 yards right of the flag. It's my opinion that the chance that you hit it right at the flag( 5 yards left of target) and 10 yards right of the flag( 5 yards right of target) are equally likely. I also don't think the %'s change if you switch the person's shot selection to a draw aimed 5 yards right of the flag.

Its a bit complicated when you are talking about club face and club path at impact because of the different spin you can impart but I would be interested in seeing some evidence that those 2 variables aren't normally distributed leading to non-normally distributed shot dispersion(or maybe they are normally distributed but still lead to non-normal shot dispersion. IDK.


The Will example is interesting but I have a feeling that is either a sample size error or there is some confirmation bias in there. If Will's big misses were exclusively left then he would have to have a much larger % of his shots right of his target to counter the big left misses. To me it seems you are saying he missed left and right an equal amount of time but his left misses were much further left than his right misses were right. This would shift his average shot to the left but the median shot would remain in the center.

Broadie has a few images in his book where he is trying to show optimal target selection for 80s golfers and pro golfers on a specific hole that has out of bounds to the right.

Here's the 80s golfer


And here is the pro golfer


To me those shot dispersion's he's drawn are normally distributed(bc they are symmetrical), and not skewed one way or the other. Yes it is an average but I don't think an individual's shot dispersion will really differ as you are just taking their mean and drawing the edges based on their standard deviation. It's also worth noting he doesn't mention in the book what sort of shot shape they are hitting.

This is what I'm imaging you describing Will's shot dispersion as.


But to me that distribution would shift his "target"/Mean well to the left of where you think it is(the black circle being where you think his average is when in fact it is quite a bit left of that). This would create the illusion that Will misses the majority of his shots to the left even though that is not actually the case. Does this make sense?

Overall thoughts? Do you have any data that shows non normal shot distributions bc I think that would be interesting to look at.

I don’t think it is skewed that much to the right. I think shots are basically normally distributed aside from approximately a 5% big miss that is always to the same direction. I believe this drawing is representative of my distribution is full shots with seven iron and longer. As we know the less loft there is the easier it is to tilt the spin axis and you get more lateral dispersion vs. distance error. The scatter plot is more oblong with distance error being the issue with wedges.

I agree I said that even my standard shot is slightly teardrop shaped to the right and I think that is true. I’m not sure how it relates to the target or hole though. It gets a little abstract when trying to visualize a scatter plot both with and without a target. The drawing with the median barely shifted off dead center of the innermost distribution is what I think is likely correct though. It’s not much.

As the drawing shows however, I agree the average will be well right of the pin for me. We can’t wash away our worst 5% shots with proper strategy so I believe we need to effectively act like they don’t even exist when choosing our shots. They simply occur randomly and we need to get lucky they don’t kill us, we can’t live in fear of that shot. We want to optimize where we leave the vast majority of our shots.



I don’t think I could tell what kind of shot they play based on a scatter plot.
I don’t think so. Again, I believe (and this is controversial and I not the standard opinion, but I know for me it results in my best golf and I believe it is the optimal way to play) the best way to play golf is to solely hit one shot shape. The only time I try to hook a shot is when there is a tree in the way. Period.

I think the paradox of choice is prevalent in trying to hit the 9 box Tiger Woods shot. You become a master of nothing and very average at everything. I know for me, and believe for everyone, that you will have superior distance control, directional distribution, and pace of play if you aren’t constantly trying to make the ball do a ton of things. I walk up to every shot knowing what shape I’m going to hit and then simply need to choose my club. I then simply need to think of an overhead view of the target and decide how my distribution will best lay over it.

I will say that I doubt you can become the best player in the world with that strategy, but I do think you can play VERY successfully on Tour with only one shot shape. Zach Johnson, Kenny Perry, as a perfect examples. It’s interesting because the obvious examples are hookers because they tend to really move it hard, but there are countless guys on Tour that hit fades exclusively but they don’t stick out like sore thumbs.

I do think that by having one shot shape you narrow your clubface std deviation. Changing the face and path relationship is hard. Having the ability to do both at will and consistently is simply very difficult. If you never try to make that huge change I do believe you wind up with a tighter face/path/shot standard deviation.

For simplicity, if the Broadie diagrams you posted had no trouble at all on them aside from rough your target would be the dead center of the fairway. You would then miss half your shots left and half right. Then in the Broadie example we have OB right so the target shifts left. I still hit my cut and have x% go OB and more balls miss left than right due to the left FW target. Flip it to OB left and I shift my target right. I still hit my cut and have x% go OB and more balls miss right than left now.

The sum of these 3 scenarios should result in half my missed being left rough and half being right rough. Over the course of a year on Tour there will be just as many trouble spots left as right and thus without changing shot shape at all you will have equal distribution of shots left and right. This is why I say you eliminate the correct half of the course based on the location of trouble with target selection and not shot shape. The best drivers of the ball miss as many left as right. They do not eliminate half the course. I think you agree with that.

Completely agree.
I agree it doesn’t change if you change the player hitting the draw and fade.. Will will hit his draw better than his fade every time. I will hit my cut better than my draw every time. His shot pattern and my shot pattern (when I’m playing well) are probably identical. It’s not the shape that makes it hard, it’s the player trying to hit both shapes.



He probably missed more left than right, but not by much. I do think that as he gets better the big miss left will be smaller. As it does he could potentially favor the right side a tad more to help out those now smaller misses maybe keeping some in play. As it stands now they are simply so big they just need to be abandoned as they can’t be helped.

To my Ed Loar example he misses 50% more right than left, that is not ideal. Kenny Perry hooks it exclusively too and he does miss more left than right, but not as drastic as Ed. Will is probably similar to Kenny in distribution.

Broadie is using averages and not individual golfers. That is one thing I told him on the phone when we talked that I thought he had wrong in the book. I don’t think that for discussion on strategy you can take the general population average and lay it out as a normal distribution. The entire population likely is normally distributed in degrees when viewed for accuracy. This is also why he uses the middle of the distribution on every hole instead of the middle of the fairway when computing accuracy in degrees.

It’s hard because without some serious programming ability and a TON of TrackMan data on a specific player this can’t really be proven. I am talking from my experience (going on 20 years as a +5 or higher) and of what I watched while caddying and observing a great ball striker as well as the top amateurs in the world. I understand that could have bias and be wrong, but I truly don’t think it is. I’m a pretty objective person who is trying hard to challenge the assumptions and old school dogma. I also don’t think this could really ever be proven one way or the other so I’m simply trying my best to illustrate the ideas I believe.

That’s it exactly. But you have to remember the yellow circle is basically a three sigma miss. It will skew the average, but hardly dent the median.

I feel like I'm watching a documentary on particle physics. Interesting as hell but I don't understand much of it

The problem I'm having here that is depending on which side of the hole out of bounds is on, your EV is going to change significantly.

I have taken your distribution and overlayed it to a make shift hole.


The green lines represent the edges of the fairway and the blue boxes represent out of bounds in the lower 2.

The first distribution is set so that around 70% of your shots hit the fairway, the 50% oval and most of the next 25% oval fall within the fairway. However notice how depending on which side of the fairway the trouble is on, your target has to shift tremendously.

When the trouble is on the right side, you have to shift a good bit to the left. So much so that only 30% of your inner 50% hits the fairway, and roughly 12.5% and 10% of your next two ovals fit into the fairway. Fairway % drops to about 40% and we still will even hit a couple of balls out of bounds for every 100 shots.

When the trouble is on the left though, you don't have too much trouble since in my mind you have eliminated the left side miss(we both agree this isn't possible but to me this seems to be what you have drawn). We are not worried about missing it left out of bounds hardly at all and only have to shift a little bit to the right. Most of our 50% circle still remains in the fairway, lets call it 45% and then entire halfs and then some of the 2nd two ovals fit into the fairway for 12.5% and 10%. So now we still hit the fairway 67.5% of the time and never hit a ball out of bounds.

These tee shots would have different EV's and different targets which seems off to me. It's my opinion that no matter what side of the hole trouble is on, you should have to shift your target X yards away from it but that is not the strategy given your shot dispersion. That seems off.

Does this make sense? Am I misunderstanding something?

First of all, I don’t think it will change it *that* much. In your diagram it shows that we can expect to hit about 3-5% of balls OB. 6 penalty shots over 100 attempts is probably about right. If we aren’t hitting any balls OB our targets are too conservative.


Second, and most important, I would think these two holes SHOULD play with different EV’s. Meaning if those two holes appeared back to back on a course and were exactly the same aside from the OB being on different sides I would expect them to play with different EV’s for different players. I don’t think that makes the target right or wrong in and of itself.
The main thing I would change with your diagram is that I think the only portion of the distribution we can care about is the 2 sigma 95% miss. The worst 5% are simply throw away shots that we just have to get lucky don’t kill us on a week to week basis. Trying to optimize strategy to get those shots safe will simply result in missing the fairway to the opposite side too often to be optimal.

Rather than looking at how much white space is in that outer 5% miss bucket, remember how few shots are in that portion of the distribution.

So your drawing with the OB right does have the target too far left IMO. Redraw that target and then for me I simply accept that the hole with OB right is a harder hole as a cutter. But playing it that way is better than trying to change my shot shape based on which side of the hole the trouble is on…especially since I don’t think you can hit it both ways better than one consistently.

Obviously the only other option is drawing the ball off the OB so my miss is left and ok. No chance I don’t leave fewer than 5% double crossed right and OB.

A follow up courtesy of the USGA http://www.usga.org/news/2014/Decemb...Terrific-2014/

I'll be caddying for Will at the Northern Trust Collegiate Showcase on Monday. Pretty stoked to check out Riveira and hopefully get Will in the event.

Really fun because I've now given seminars at several of the schools sending players....Oklahoma State, Wake Forest, Texas A&M, and have been working with Kramer Hickok from UT. I've got 4 of the 14 players in the field....one time!

http://golfweek.com/news/2015/feb/10...lege-showcase/