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It's Dexterity based since to hit something, you need fair accuracy. Strength would affect damage, not necessarily how good you are at hitting the thing you're trying to damage in the first place. Plus it made little since to make it Strength-based since it's silly to make an attack with a Crossbow - That doesn't normally utilize your Strength score at all - Using Strength.
This Attack skill also brings back to life an old variant rule from 2nd Edition - Weapon Speed. In this case Weapon Speed is the number divided into your Attack bonus to determine how many attacks per round you can make with the weapon, and at what bonus.
Average weapon speeds are as follows. Non-repeating crossbows have their own special attack rate, so these are not listed.
This system evens out the issue with weapon damage versus number of attacks. I know I, for one, cannot swing a Greatsword at the same rate at which I can swing a Dagger.
With this system, you simply locate the weapon's Speed number and divide that into your total Attack bonus with that weapon (Accounting for enhancement bonuses and so on). If you have extra points left over, those are extra attacks, but with a penalty equal to the difference between the remaining bonus and the weapon's Weapon Speed. If your weapon's Weapon Speed is higher than your total Attack bonus, then you take the difference as a penalty on attack rolls.
*A small example would be a 20th-level Fighter with somewhat average Dexterity (14, a +2 bonus); We'll call this fighter Bob. Bob has maxed his ranks in Attack (Which gives him 23 ranks in attack, plus his +2 Dexterity bonus). If Bob makes a full attack with a Dagger (Weapon speed 4), his attack sequence would look like this: +25/+21/+17/+13/+9/+5/+1. An astonishing flurry of 7 attacks, but for only 1d4 damage each. Th average of 4 is 2, so that's an average of 14 damage assuming all attacks hit.
