For this to be true, a ball that is offline would have to be knocked online at a higher frequency than a ball that is online being knocked offline.
That's not how that works.
Imagine a basketball player who shoots at 80% and another who shoots at 60%. Something is installed in the basket that rejects 50% of the shots, randomly. What was a 20% gap in separation becomes a 10% gap: the 80% shooter makes 40%, the 60% shooter makes 30%.
Let's say that this thing also randomly directs 10% of the misses back into the basket. The good shooter now makes 42%. The bad shooter now makes 34%. That narrows the gap to an 8% difference, when they started at 20%.
Play with the numbers all you want: the effects of both, even if applied "equitably" as you said earlier, narrows the gap any way you cut it.
If both are done at 50% (which is silly, because putts are far more likely to be diverted out of the hole than misses are to be diverted into the hole), then both become 50% shooters. It's entirely random. If it's only 10% on makes an 1% on misses changing their outcomes, the 80% shooter becomes a 72.2% shooter and the 60% shooter becomes a 54.4% shooter - what was 20% becomes a 17.8% difference.
"Just as easily knock it back on line."
It doesn't work that way. More bumps = more offline on average (a wider distribution).
A ball that is traveling towards the middle of the hole could be misdirected both left & right and still be holed.
I think you're grossly under-estimating how large the distribution pattern is for even a good putter. Are you only thinking about like 4' putts or something? I'm talking about ALL putts.
A ball that is going to go in and which is "deflected offline" is going to miss most of the time, while a ball that is going to miss can only go in if it's mis-directed the proper direction — a putt missing only barely left can only go in if it's mis-directed to the right, not if it's mis-directed to the left (or not mis-directed at all).
A "made" putt has a nearly 100% chance of missing if it's "misdirected," while a missed putt (assuming it's mis-directed the proper amount) has a 50% chance of going in if it is mis-directed in the proper direction.
The end result is the hole would effectively play smaller, benefiting the player who makes more putts in the middle of the hole.
A 0.6° deviation is enough to divert a putt that is going to roll about 18" (capture size is about 2.3" at that speed) away from the hole (outside 1.15") from as little as just inside 10' from the hole.
Look, I can take a Perfect Putter and roll balls from the same height to a hole 20' away. I did this the other day, and 2 out of 7 went in. Three missed low and finished about 13-15" past the hole. Two missed high and finished the same distance past the hole. That's due to randomness. If the green was a billiards table (but a bit slower, of course), I could up that make %. If the green was bumpier, I'd miss more.
When you point out (correctly, I might add) that an offline putt can only be knocked online in one direction, while an online putt can be knocked off line in two directions, you are actually arguing that a better putter will be impacted more, and there's no way around that.
Thank you! Yes! Mark Broadie talked about the effects of a larger hole in his book, and many (like Ben) thought a bigger hole would favor good putters. People (like Ben, apparently) thought that good putters
just missed or
nearly made a lot more putts, so with a larger hole, those that just missed would go in, while bad putters missed badly enough that they'd just keep missing them.
This "larger hole" effectively creates the same situation as increased randomness resulting in a larger finish position distribution of putts. Broadie's conclusion?
Luke Donald and Gene Sarazen were right: Poor putters would benefit from a larger hole more than good putters. Simulation results with an eight-inch-diameter hole show that a typical pro putter would gain five strokes from a larger hole; a 90-golfer would gain 6.5 strokes. The gap between good and poor putters narrows with a larger hole. Here’s the intuition: Poor putters have more room for improvement, so the larger hole will benefit them more. Pro putters rarely three-putt and they average about seven one-putts and 11 two-putts in 18 holes. The only room for improvement is turning some two-putts into one-putts. With a larger hole, a 90-golfer will eliminate most three-putts and will have a bigger increase in one-putt holes. A larger hole narrows the difference between good and poor putters, making putting less important.
If you want to question Mark Broadie's grasp of probability and statistics, go ahead. Since it aligns with all that I've been saying
and the guy probably knows his stuff… I'm going to go with it.
Better putters start the ball online more often than lesser putters, don't they? So the better putter doesn't need the "help" in having the ball knocked online you are talking about, even if it's only in one direction, as often as the lesser putter. Meanwhile, the better putter's online putts, which are more frequent to begin with, will also therefore more often be knocked offline, and in two different directions.
That's almost exactly the same wording as Broadie used above.
That's randomness, for sure, and there is NO way that doesn't impact the better putter more. The lesser putter is going to miss more often anyway; the better putter is going to miss more than they would have otherwise. Again, there is just no way around that.
Yep.
Randomness in sports, ALL sports, reduces the gap between better players and teams vs lesser players and teams. I have NO chance of beating Lebron in basketball, but I might be able to take him in a coin flip contest.
Indeed.
The same logic was once thought to apply to making the hole larger. A larger hole would hurt the better putters because others near misses would go in more frequently. What was found was a better putter's advantage actually grew. A good putter makes more putts than an average putter AND a good putter has more near-misses than an average putter.
OMG! I'd written all of what I wrote above before I read this response of yours.
Also, you seem to contradict yourself: you said a larger hole would "hurt" the better putters, then you talk about how the better putter's advantage grew. Also, I don't think the second statement is true. Broadie found the opposite to be true, as I quoted above.
For a misdirection to matter, the magnitude of the misdirection must be in proportion to the line of the putt. A ball that has a perfect line would need to be misdirected more than 2 inches left or right to miss the hole.
Only golf balls that barely reach the middle of the hole will go in "more than 2" left or right" of the hole. You're not factoring in capture size on putts hit past the hole, and again, 1.15" is enough to misdirect a ball from under 10' out after less than a 0.6° misdirection.
So you are correct, the better putter will be impacted more, but in a positive way for them.
Nope. Good putters aren't missing the hole by only a teeny amount. Their distribution pattern — like those of bad putters — only grows with more "randomness."
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Imagine this: players are given a ball that they have to slide or throw into a basket or bucket or hole. There's nothing in the way, there's no wind, the hole doesn't randomly move, etc. This is a game where skill is almost entirely determines the outcome (I'm saying "almost" because I'm reluctant to say always/never). It's like shooting free throws in basketball in an empty arena, except that there's really only one fairly narrow path that really works (like in putting, where the highest and lowest lines aren't all that far apart).
Again, it's a game that's nearly entirely skill-based.
Now imagine instead of just having a free throw or a free line to drop the ball into the bucket, a single "object" is put somewhere in the way. Maybe it'll be along the chosen path, maybe it won't be. This favors the bad player, but not much: when it's on the correct line, the good player is more likely to hit this object and "miss" what would have been a made shot than the bad player. When it's not on the correct line, it doesn't "help" either player on a good shot, but it helps the bad player more often than it helps the good player only because the bad player has more chances for it to help them.
That's just one object in the way.
Now imagine a Plinko field full of objects in the way: the good and bad player would have almost no separation between them at this point. It's almost entirely luck. Sure, the good player's distribution will still be a little bit narrower, but it'll be much wider than it used to be, and the bad player will STILL have more chances for the ball to be diverted into the hole than the good player, and the good player will have more chances for the ball to be diverted OUT of the hole when it was going to go in than the bad player.
Or, as I said a few days ago:
More luck, more randomness, decreases the separation between higher skilled and lower skilled players.
And
A lighter ball would be more affected by little imperfections and would bounce around more. Randomness levels the playing field and favors "bad" putters over good putters. The more "luck" plays a role, the less important "skill" becomes.
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Edit to add this:
Now, since that should put that to bed (and if not, seriously, take it up with Mark Broadie or something), could we get back to talking about the "rollback" since the comment I made which got this started was that a lighter ball would not be enjoyed by good putters as they'd lose some of their advantage over worse putters? It's a tiny little side topic to this point:
IF the ruling bodies do eventually do something in this area, I hope they consider and understand
ALL of the ramifications.