Ship,

I've been working with an instructor for about a year now. The approach is to teach my body the correct, bio-mechanically optimal movement patterns by getting in thousands of reps doing the movements themselves, then introducing complexity and finally stacking everything with the club in hand.

As a result, my path is what we call "zeroed out," meaning my natural path is right down the target line with a neutral face. It's been mentioned as well that ideally (from the top) the angle of the face is not accelerating, so it's roughly rotating at a constant rate to impact even though the speed at which the club itself is travelling is increasing. This is not something I think about or feel over the golf ball, FWIW.

I'm very happy with the results so far but am curious if having a stock straight shot is ideal from a strategy standpoint.

Taking your tee shot as an example: if you compared your shot dispersion to that of a straight ball hitter, is there an inherent skill difference that must be overcome by the straight ball hitter?

Haven't logged in here in a long time, but thought I'd see what's up tonight.

There is no chance hitting it straight is optimum. With a zero path you have to be PERFECT to hit a good shot. Path for good players is VERY consistent. Face, less so. So, if you are trying to hit a straight ball your misses wind up being block cuts or pull hooks. Shot patterns get HUGE compared to working the ball. This is a very consistent theme I see from mediocre players all the way to major champions, especially with the driver.

Thanks, Ship. I'd like to follow up on face if I could.

With you as an example, your miss with the stock cut shot is right of target, and you site an exaggerated path as the likely cause. Chicken/egg question here, did you build your swing with the cut in mind because that pattern naturally eliminates the left side, or is your miss right (for whatever reason) and you decided that playing a stock cut improved your distribution pattern?


Bonus questions:

Is face variance higher for a neutral path as compared to others? What factors would you think about when deciding how to work the ball as a standard shot?

Misses for elite players are rarely a path issue. They are amazing at repeating their swing and hitting the center of the face. The misses normally come from the face being more opened or closed then they want.


If you want to feel bad about your game here is either 5 or 10 swings of Justin Rose and his driver.

I have to assume the low marks are just from the tee and not that he bottom-rung-skulled a couple? lol

Yeah they are from the tees. Good chance they might have been from artificial grass ones.

This sort of theory and the above Ship reply about no way straight can be optimum has always been an intriguing to me. It never has really made much sense to me but I have never really been able to find any research or data pertaining to the subject.

Today in my free time I decided to model the different scenarios and see what the results were.

Theories to be addressed
1. Straight can never be an optimal ball flight
2. Shaping the ball in a certain way can "eliminate one side of the course"/give you a "one way" miss which you hear analysts talk about all of the time

My (certainly not perfect but hopefully decent) findings:

It is my assertion that no matter your ball flight, you will miss 50% of your shots "left" of your "TARGET" and 50% of your shots "right" of your "TARGET". I have never seen anything to suggest that golf direction isn't somewhat normally distributed. The tails can get wider/further away with different shot shapes but I don't think its possible for one shot shape to shift your distribution such that 50%+ of your shots would lie on one side or the other of your target.

Here is a simple drawing of the golfer on the left trying to hit a straight shot, and the golfer on the right trying to hit a little fade and their respective ball flights given a consistent path.



Does one the player hitting the cut "ELIMINATE" a left miss? I would say no, he hit's just as many shots left of his target as he does right of his target.

These were my rough estimates of the different ball flights produced by each golfer assuming that their path was always as described at the top and their club face angle varied to similar degrees from their "intended" club face angle.

For example, on shot 1 each golfer's club is 4.5* shut compared to where they wanted to be at impact. The "straight" golfer starts the ball 4.5* left and hooks it because his path is inside/out. The "cut" golfer starts the ball 6.5* left(wants 2* left but face is 4.5* more closed than he wants) and draws it because his path is also inside/out relative to the face but not as severe as the "straight" golfer.

As you can see the distribution of shots is relatively similar assuming that each sequential shot experiences a club face that is an extra 1.5* open. (shot 2's club face is only 3* shut, shot 3's club face is only 1.5* shut, shot 4's club face is 1.5* open etc. etc.)

That is just a rough estimate however so I decided to try and model the ball flights in excel. This was not an easy task as there is no real info anywhere on the web regarding modeling ball flights(especially when you are interested in direction rather than distance).

I did find some TrackMan info that I used.

According to this TrackMan newsletter

http://trackmangolf.com/media/9ac950...ewsletter5.pdf

Spin axis for a 6 iron is tilted 2x the difference between face angle and club path. Spin axis for a driver is tilted 4x the difference. This is how I calculated spin axis.

Then TrackMan lists these numbers for a driver
6* Spin axis would be 10 yards offline
20* Spin axis would be 35 yards offline
I used input those values into excel and had them calculate what other hypothetical spin axis would produce.

This led me to the following driving calculations
(Again negative numbers are left/closed and positive numbers are right/open)


Hopefully it is easy to follow what is going on there. At the top you have the club face angle variance that each golfer has on that particular shot. Negative numbers indicate left/closed and all positive number indicate right/open.

So for the shot on the left the golfer swings the club face 4.5* closed compared to where they wanted it. (Straight guy wants his face at 0 so the result is just closed 4.5*. Cut guy wants his face -2 closed so 4.5* more close gets you to 6.5* close at impact)

Where the shot starts is just some trigonometry assuming that we are hitting a 300 yard drive. For the straight guy, 4.5* left(bc he's closed) at 300 yards would mean he hits it 24 yards left. However then you must factor in the fact that he is going to hit a pull hook with his 0* path(which will curve it another 30 yards left) and now he is 53 yards left of his target.

If you can follow that than you will be all good to understand the charts.

The assumed path and club face for the "CUT" guy was created by wanting to hit a fade. The parameters for his perfect shot is a 10 yard cut at 300 yards.

Interpreting Driving Results
These results were rather interesting. According to the above, you cannot conclude that the "CUT" golfer eliminated the left side of the golf course like announcers tell you. He did cut off 2 yards on the left side but he opened himself up to a 10 yard larger miss to the right. It's not all bad for Mr. Cut though because his dispersion between his -.5 and .5 std deviations(I assumed 3* is a standard deviation, or +/- 1.5*) is actually tighter than Mr. Straight. Whether or not this is enough to outweigh his much bigger misses to the right would be a much more complicated calculation, however it seems pretty certainly hard to conclude that a "cut" shot is incredibly superior to a "straight" shot off the tee.

While looking at the narrower dispersion in the -.5 to .5 std deviation miss I thought it would then be interesting to look at approach shots of 175 yards. If a "CUT" shot on approach shots could narrow the dispersion in the very center of your distribution like it does with the driver that would be very very beneficial.

Again according to the TrackMan article posted above I was able to garner some actual spin axis results to calculate hypotheticals off of.

For a 6 iron the spin axis are as follows.
2* spin axis results in 2.5 yards off line
7* spin axis results in 8 yards off line.

I also lowered the standard deviation of the face angle down to 1* or +/-.5* either direction. This is because a golfer is generally able to control a shorter club better than longer ones.

Here are approach shot calculations
(Again negative numbers are left/closed and positive numbers are right/open)


Interpreting approach shot results
Now as you can see the more concentrated center of distribution experienced in the driver by the "CUT" shot carries over a little but nowhere near to the degree it did in the driver. That concentration is nice but as you can see the benefits of the cut shot fade away very quickly and actually become a very big problem especially on right misses IMO.

The problem here is that since spin axis grows exponentially, when the "cut" guy is delivering his most open club faces to the golf ball his spin axis grows to a point where he is hitting monster cuts. His misses to the right are huge and yet he still has not "eliminated" the left side of the golf course.

Conclusion
Overall the above is a very rough calculation of 2 different shot shapes with a driver and approach shot. In both cases the very center of the distribution(center 1 std deviation) is more concentrated for the "cut" golfer however it is likely that the benefits received from that are wiped out by the wider overall dispersion they experience outside of that first 1st std deviation. To calculate that would be a large undertaking that is outside of my abilities, however unless the above is seriously flawed(and maybe it is?) then I'm not sure you could reach a conclusion that a straight ball flight is nowhere near optimal. One important factor is that it would seem that the "Straight" ball would experience less dispersion in distance as they are dealing with a smaller range of spin axis but maybe that is not correct.

The other thing that is to be taken into consideration is skill level and that is what would make this difficult to solve empirically IMO. Certain golfers are just better/more comfortable with a certain shot shape. If you try to take someone who has hit a cut for the last 5 years and go out and have them try to hit it straight they likely will not be nearly as good at it. Trying to compare the results of their 2 different shot shapes would be a waste.

My viewpoint is from a purely mathematical stand point(and possibly a flawed one at that), however if you are just as comfortable/good at hitting a straight shot vs a shot that curves I wouldn't be so quick to say that the shot that curves is going to present you the highest EV. That doesn't seem 100% clear to me.

If anyone has any insight into data/research contrary to the above I'd love to take a look at it.

Going to have to read that one a few times before I can try and make intelligent comment

If I had to guess the thing in the above calculations that had the highest chance of being flawed it would be the spin axis calculations and those could certainly affect the outcome.

And check out what Moe Norman would have had to say about it!

For clarity

"Shot starts" is the direction the ball is launched at

"Curvature" is the curve amount (negative number curves left, positive number curves right).

If you had those 2 together that is how I got "Final Distance" from target. Ie a ball launched 18 yards left of the target that cuts 5 yards back would end up 13 yards from the target.

It's also worth noting that each shot on either side of "Perfect shot" is .5 std deviations.

To make a reasonable conclusion it would help to understand how the body randomizes movements, and if those movements are distributed in a symmetrical way. Very small variances from the mean may be Gaussian, but larger variances are probably not. And it is the larger variances that concerns players like Ship-this.

The bolded is what I was going to offer the discussion.

Do you have any info on the above with regard to body movements?

I find it a bit hard to believe that given the 2 examples I outlined, a golfer would be able to control the club face at a much better frequency(and thus lower their standard deviation) just because of the direction of their path or their club face angle at address. Or maybe you are implying that they have fairly normal distributions around the mean but for some reason the straight swing produces more high variance club face angle readings at impact compared to the cut swing. To me again that seems like quite a stretch, these swings are not very different fundamentally speaking.

The next question I guess I would have with regards to the implication of body movements is a certain curvature ideal? Are draws and fade body movements fundamentally different in their ability to control the club face compared to a straight swing? And then how much curvature are we talking about?

Do you go from having really great club face control when trying to his a draw of X yards, to slowly losing control of the club face as you move towards trying to hit a straight ball, and then slowly gaining amazing control of the club face as you move towards hitting a cut of X yards? I'm not sure this is what Ship was getting at above.

Draw of X yards > > > > > > Straight shot < < < < < < Fade of X yards

What I implied from Ship's reasoning(and maybe this is wrong) was that when you are trying to hit it straight your misses curve in both directions(pull hooks and push cuts) which leads to wider distributions. Unless my spin axis calculations above are woefully wrong that is not really the case. Yes straight ball misses curve in both directions but so do some cut shot misses with the driver(double cross). The curved shot also experiences a higher degree of spin axis tilt which affects their distribution because spin is not linear. This causes wider overall distributions because these high spin axis numbers lead to some big misses.

This is observable in the Approach shots image quite clearly. Each shot shape has the same range of spin axis(12). Straight shot goes from -6 to +6(12) and cut shot goes from 0 to +12(12)**. Now even though the straight shot has balls curving in different directions, because the curve is relatively benign there is not a lot of curvature. The total curvature range for the straight ball is only 12 yards however the total curvature range for the cut shot is over 20 yards. Again despite similar total ranges of spin axis when you start dealing with very high spin axis(12 for the curve guy and a max of 6 for the straight guy) that can skew results.

**(I see some of the "curvature" numbers in the cut shot are off, on the far left spin axis of 0 should be 0 curvature and spin axis of 2 should curve ~+2 but those don't really affect much as they are just switched).

Again what is interesting is that when you look at misses within .5 std deviations in either direction(which will occur ~38% of the time) the curved shot is beneficial. The problem is outside of that(especially in approach shots) the straight shot begins to have better results and then at the edges of the distribution the straight shot is far superior. You would have to weigh the results versus how frequently they occur and the strokes you gain from each of those occurrences but I'm a bit skeptical that it is so easy to dismiss a straight shot as a very viable option.

Another factor that I did not even begin to account for is distance control with each shot shape. That is an entirely whole other animal but to me it would seem easier to control distance on shots where spin doesn't vary quite as much(straight shots) compared to (cut shots).

I think this is an interesting discussion and I hope more people have some stuff do add.

Nxt, don't we also need to consider potential roll after landing in the draw vs cut vs straight debate? Also, figure out if draw and cut spin continue offline at the same rate/angle post landing?

If an offline cut shot has 50% the roll out of the offline draw/straight, for example (I don't know if there is published data on this and obviously conditions are vital in this scenario), then you'd need a smaller shot distribution with the draw shots to keep all else equal, right?

Also, now that Broadie has shown the importance of distance, we shouldn't we also keep in mind the strokes gained cost of sticking with a cut vs draw/straight? Even if you definitively proved a smaller shot distribution with a cut shape, you'd have to prove the cost in distance is worth that % gain in accuracy.

Also, on a broader topic, I think the reason it's commonly believed that it's ideal to "take one side out of play" is simple.

Professionals generally prefer 1 shot shape, whether scientifically justified by the type of data discussion above, so it becomes sort of an appeal to authority, where we (and announcers/analysts who tell us, the public) assume they must be doing it the most optimal way.

On top of that, when the professional does have the occasional double cross, you never hear them go back to that line of thinking and point out the issues of "taking one side out of play" (maybe the majority of your misses are smaller, but the bad ones are worse than they would be if set up down the middle trying to hit a straight shot). They, and viewers, will inevitably just chalk it up to being an outlier rather than actually considering it in regards to the take a side out of play argument.

This is all of course reliant on the assumption player x can, in theory, execute each shot/shape with the same frequency/efficiency.

Overall, yes you would want to include the answer to all of these questions in any in-depth calculation of EV for different shot shapes. If a typical draw goes farther than a typical cut then the draw could make up some potential loss of accuracy in the distance department with regards to strokes gained.

The main purpose of my calculations is to show that it doesn't appear to be as cut and dry as saying straight can never be optimal and working the ball is always better. To someone very insistent on that belief, my first two questions would be

1. Is trying to curve a shot always superior to a straight shot? Even a 20 yard chip shot?

2. At what distance does curving the ball become superior to hitting it straight?

Most golfers/analysts/instructors in my opinion are incredibly results oriented. The bolded is what makes this a tricky discussion.

While doing a bit more research on spin axis I found another TrackMan source(their blog) describing spin axis as being constant at a given yardage.



This would seem to be contradictory to what they had previously published in their newsletter.

Going off of this sort of spin axis and resulting curvature calculations you get the following at 150 yards out and 200 yards our respectively.





This changes things quite a bit. Now total dispersion is basically the same(minus some rounding going on) and overall distribution is nearly identical. A constant spin axis calculation at specific yardages would make playing a curved shot vs a straight shot basically identical.

This is much more interesting than a totally flat 100 foot putt

Right, downhill is easier ldo.

I believe top pros look at variance in their body movement as somewhat controllable, i.e. the error residuals would not be random. But if this were true then they are playing sub-optimally by default, because their mean square deviation from the "perfect shot" is biased toward one direction (short/long, left/right).

I don't buy the idea of a preferred shot shape being optimal, but I do buy into the notion of a repeatable motion being easier for one shot shape over another.

Downhill with a lot of break is even easier.....

...than uphill with a lot of break.

I don't have time to respond to all of this, but the "take one side out of play" cliche is completely incorrect. If you ever hear anyone say those words it is a sign they don't know what they are taking about...unless they say "take the side with the hazard out of play". The best drivers during the ShotLink era miss effectively the exact same amount left and right. That means they are adjusting their targets based on where the trouble is and hitting the same shape.

Jordan missed 40% more shots right than left in 2014. He spread his tee shots perfectly in 2015 and that was one of the main reasons he excelled last year. To steal a line from Hogan I believe "if you can't putt you can't score, if you can't drive it you can't play".

Jordan's strategy changed early in the year with regards to shot shape and target selection. He was pretty solid after the adjustment.

As for straight not being optimum, what I believe NXT is missing (and I didn't read all of it for comprehension) is that a straight ball in reality is a much wider normal distribution around the center of the pattern. Meaning you hit the middle of the pattern materially less with a straight ball than you do a slightly curving one. I'm not sure if he actual math will agree with that or not, I'm just telling oh in reality that's the way it works. I've seen it many times in the last two years with the BEST players in the world in a controlled setting. If they can't do it under perfect conditions I can assure you they can't under any pressure.

I'll go deeper later if I have time.