One way to try to model and analyze this problem is to say that playing only involves two skills: shot making and position play.
Shot making can be characterized by the player's "spread" or the distribution of errors in where they send the object ball. Better shot makers have a smaller/tighter spread. Usually this is assumed to be a bell-shaped curve (gaussian) where most shots are pretty close to the target and large errors are rare.
Position play can be characterized by the length/difficulty of the shots a player leaves for himself. You can assign a difficulty number to each shot by noting the two distances of the shot -- CB to OB and OB to pocket in diamonds -- and multiplying them together. If you make either length twice as long, the shot allows only half the spread. Cut angle adds to the difficulty in a fairly simple way.
In this analysis I'm going to ignore strategy and just look at those two factors. I don't know how to put a number on strategy and various other factors.
Suppose you have two players who are equal with 5-inch pockets but one -- call him SaM -- is a shot maker and one -- PoP -- is a position player. Let's say that they are each 95% to make their shots and Pop has, on average, shots that are only half as hard as Sam's. Sam must have half the spread (twice the accuracy) on where he sends the object ball measured as an angle.
In the end, the spread for each of them measured at the pocket has to be the same. Each of them misses 5% of their shots which are out on the "tails" of the bell curve.
Now, make the pockets tighter. How do the misses change for the two players? The change will be exactly the same because the spread measured at the pocket is the same. If Sam is missing 10% of the time, Pop will also be missing 10% of the time.
Ignoring strategy might bother some, but I don't see how to include it. Note that Sam, the shot maker, may have figured out a good set of strategies for his abilities, like leaving tough shots when he pushes out. Pop may have a set of strategies that is only equal in usefulness -- we don't know. And maybe Sam jumps well.
As far as the shot difficulty measurement, I did the stats on some top players in the 1970s (14.1) in tournaments. Among the ones I clocked, Irving Crane consistently had the easiest shots at somewhere around 3. The other players were like 4 or more on average. Crane was a pretty good shotmaker as well.