batchvt

Thank you for saying that what I've written sound right. I probably sounds right to other people too. You did a very thorough job of saying I was wrong and had bad assumptions, but dude, you left out the reasons why. If I had to guess, this belief is the key reason many have argued that randomness decreases the gap between good putters and bad. I understand this seem like it would be correct, but this is just a feeling and there is no settled fact or law of games that states this. On the contrary, there are lots of debates on this topic when it comes to game design and how randomness effects outcome in terms of skill. Just google “how does randomness affect skill” to see that this not a new topic, or a shallow one. And most of those discussion end up at “it depends”. You can’t say that anytime you increase randomness you decrease the role skill plays. Sometimes this is true, and sometimes it’s not. As an example, wind adds an element of randomness to golf. Does wind decrease the role skill plays? I feel like many people would say that wind helps to identify skill in golf. My putt from 3 feet on bumpy greens is another example. The reason the better player is not affected much in that model is most of their putts go into the hole in the middle of the cup. So a bump sill leads to a made putt nearly all the time. But the poorer player has more putts go in on the edge of the hole, so the randomness changes the outcome of more of their putts. Importantly the number of putts they barely make to those they barely miss isn’t equal. The randomness therefore effects the skilled putter less, while affecting the poor putter more. Now even if you don't like my assumptions for putting, many events in life model to a normal distribution, and it's not hard to see why this same logic applies to other games like archery, or darts, etc. Once again, you can't just assume randomness reduces the effect of skill for every skill. Now, yes, these are just two examples. But the key to understanding why the bad putter doesn’t benefit from the bumps is to realize “anytime” is not a correct statement. Sometimes randomness reduces the impact of skill, sometimes it enhances it. You have to study the consequences of the randomness to understand when each case is applies.

Why mention a lighter ball? I thought this question was about bumpy greens.

Let's address this assumption as well. Mark Broadie wrote a paper that simulated the possible effect of hole size on scoring. To do it, he modeled putting variables as normal distributions and then ran thousands of simulations so see how make rates changed. So let’s do that with these short putts instead of just assuming the stats are the same. At 3 ft pros make a 3 ft put 99.5% of the time and amateurs make those puts 76% of the time. So the model is a normal distribution with a standard deviation of .75 inch so that the pro’s puts fall inside the 2.125 radius hole 99.5% of the time, and the amateur has a standard deviation where their puts fall within the hole’s radius 76% of the time. Now let’s assume every put gets bumped by a half inch either left or right with equal likelihood. Run that model through 10,000 simulations and you get this. Simulation of 3 ft putt made out of 10000 with 1/2" bump. Smooth Bumpy Change % Change Good Putter 9955 9865 90 0.9% Bad Putter 7660 7458 202 2.0% Now this is just simulated data, but it follows a thought process Mark Broadie used for a similar challenge. The smooth make amounts are right where we would expect them to be. So the model fit’s the base case. For the bumpy greens, the model the good putter makes 0.9% putts less per round, and the bad putter makes 2% less puts per round. The bad putter is negatively effected more by the bumps on the green than the good putter is. So using Mark Broadie’s modeling method the idea that bumps always mean the better player is hurt more than the bad putter in terms of make percentage is wrong. On short putts, the bad putter’s make percentage will be affected more by the bumps. Back to the three putt example I gave earlier. Not only will the bad putter have more three putts because they get bumped to further way for their second putt, even when they have that second cleanup put, the bumps will effect them more. So this the effect of the bumps is going to be meaningful. @Wanzo is correct on this. This is a good table. And it highlights the key point. With bumpy greens, both the bad putter and the good putter will three putt more. But the bad putter will three put relatively more. To explain what I’m saying, the good putter may now 3 putt 12% of the time, and the bad putter may now 3 putt 23% of the time. This is because the bad putter will end up further from the hole after the first put at times due to the bumps, and on bumpy greens they will miss relatively more of their second short putts than the good player too as shown above. The gap between the bad putter 3 putt % and the good putter 3 putt % grew from 9% to 11% in my made up example. What I’m saying is this gap will grow and it seems like you agree with this directionally. The question then is, does the gap in 1 putt percentage shrink between the bad player and the good player on one putts? Two things to consider here: 1-I’ve shown it doesn’t shrink for short putts, it grows. So an assumption that it will shrink much, if at all for longer putts, may not be well founded 2-Even if it does shrink, the relative benefit here is limited. It can only shrink to zero, meaning the gains to the bad player are capped. The relative difference is not capped when it comes to the relative benefits for the good player in 3 putts. To summarize. It’s been stated that a good putter will be hurt relatively to a bad putter on bumpy greens in terms of make percentage, but I hope people see now, this isn’t true on short putts. Bad putters are impacted more on short putts on bumpy greens. I’ve also shown that a bad putter is affected more by a random alternation between 1 ft second putts and 3 ft second putts, and shown that this is because the make rates at these distance are not symmetrical around the middle 2 ft putt. Therefore, bad putter’s make rates for the second putt are going to fall relatively because the are putting from further away, and because they don’t make as many putts on bumpy greens when close to the hole relatively to a good putter. Now I haven’t seen anyone say how the make rates are going to change between the good putter and the bad putter a distance, and this seems to be a the key point of your position. How many fewer putts do you think the good putter will make, and how many fewer putts do you think the bad putter will make?

Mixing logic and statistics, without actually doing any statistics, can be misleading. For years people assumed that the short game was more important than the long game because 60% of the shots for most players came within 100 yards. This is logical. Mark Broadie blew this idea up with actual numbers by thinking about the consequences of the next shot's location on scoring. I believe Wanzo is thinking about the effect of the next shot and he his correct that three putts will increase more for the poor putter than the better putter. The reason Wanzo is correct is the statistics of the second putt are not symmetrical. From Broadie's stats, the make rate for and amateur at 2 ft is 93.2%. The make rate at 3 ft is 76.3%. The make rate at 1 ft is going to be very very close to 100%. Notice the impact of moving from 1 ft to 2 fts is much smaller than moving from 2 ft to 3 ft. It’s not a symmetrical affect. Every golfer intuitively know this. Do you worry when a put rolls out just a bit more than you thought, trickling a foot by the hole? No. What about when the put keeps rolling out to 3 ft or 4 ft. You're probably yelling at it to stop because you know each and every inch here hurts your chances of making the next putt more and more. Since we have clean statistics for short putt make rates, lest just assume for now the second putt doesn't have bumps. Say a putt would end up at 2 ft on pure greens. If the bumps move a long putt that would have been at 2 ft to 3 ft half the time and to 1 ft the other half the time (randomness), the poor putters’s three putt rate goes up from 6.8% to 11.9%. A 5.1% increase in three putt rate. But a professional’s (better putter)’s stats look like this: 100% at 1 ft, 99.8% at 2 ft, 95.4% at 3 ft. So if they get the same bumps- half to 1 ft, half to 3 ft- the better putters 3 putt rate goes from 0.2% to 1.3%, a 1.1% increase. The randomness on where the first putt causes the worse player’s 3 putt rate it increase by 5 times more than the better player. Now maybe you think the plus/minus 1 ft is too wide, and it probably is. But this doesn’t matter directionally because the outperformance by the better putter comes from the non-symmetric consequences of putting from different distances. This effect still exists even if you think the puts only get bounced offline by a couple inches either way. Statistically the better putter doesn’t really care that much if they putt from 1 ft 6” or 2 ft 6”. The bad player does care about that difference. So in closing, Wanzo is correct, and it's Mark Broadie’s strokes gains that shows us why he is correct. The bumpy green makes the poor putter three putt a much higher rate than the better putter.