I didn't show the 2 inch miss because I'm working on the assumption that on the worst day of the shooter's life, he can't miss the ball by that much.
Obviously you don't know me. Can you say 1/2 diamond? lol
If the worst day of his life is a 2 inch miss, then it's the exact same situation: He can overcut really badly by 2 inches or he can undercut really badly by 2 inches. Only one of those 2 options leads to sinking the ball. It'd be cheating to say "let's add the possibility that he can undercut by 2 inches, but we won't ever overcut it by more than 1 inch"
I'm not saying that he can only miss by two inches one way and not the other. All I'm saying is the outcome where he favors the pro-side and undercuts by two inches and sinks it is pertinent and needs to be included in your list of outcomes. Of course he can overcut it by two inches as well but that outcome is not pertinent because it's a miss in either scenario-whether aiming to the middle or the pro-side.
Also don't forget that while a cut miss of 2" is probably infrequent what I am actually talking about is anything over 1". An overcut by 1.001" is a miss while an undercut of 1.999" is a pot.
BTW, in situations where I am "cheating" the pocket I will not over and under cut with the same frequency. I will undercut the ball (from where I'm aiming) far more than overcut it and miss the facing (and the shot) altogether. So I may still hit it center pocket or hit the rail and sink the shot.
The reason is that if I'm favoring one side of the pocket (rather than the center) I'm more aware of not exceeding the limit to that side. I guess another way to put it is I am giving myself more leeway to one side but am conscious not to exceed it. Perhaps even a better way to put it is that because I'm allowing more margin of error to one side my misses will tend to more frequently be towards where I've allowed for error. Of course this doesn't mean I never do over-cut the ball, but it does not happen with near the same frequency. With shot aimed to the center of the pocket I am closer to 50/50 missing on either side, which makes sense to me since I've allowed for the same margin of error on either side.
But that's just me. Naturally, YMMV. :wink:
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