CleverNickName
Limit Break Dancing (He/They)
I appreciate the amount of math you put into this post; it looks like you are very comfortable with probability and statistics. The numbers check, as far as I can tell.The most important is opportunity cost. Do you go for the attack that has a 45% chance of succeeding or the attack that has a 65% chance of succeeding? Do you go for the attack that does 7 damage or the one that does 14 damage? A choice between a 45% chance to do 7 damage and a 65% chance to do 14 damage isn't a choice at all. Only a fool would pick the weaker and less accurate attack. A weaker option may as well not exist so long as the player actually has the freedom to make a choice.
The other issue is a matter of game assumptions. Does the game's math assume that the fighter is making attacks with or without the specialization bonus? If it is with, then the non-specialized attacks will be weaker than acceptable and the fighter will only be able to use specialized attacks to stay on par with his allies. If it is without, then the fighter will be more powerful than his allies whenever he uses a specialized weapon. If there is no coherent game math this argument breaks down, but that is in of itself a bad situation, so...
Also, if weapon specialization is the core mechanic for fighters, then the fighters essentially stops being a fighter when he switches to a different weapon. It is the same thing as a wizard getting caught in an anti-magic field: deprivation of central class features. Not exactly ideal.
Basically, if you want a fighter to ever pick up a weapon other than the weapon he is specialized in, you must never give him even a +1 bonus to a specialized weapon.
The thing is, I don't believe that everyone plays the game like this. My players don't do a quick probability analysis when deciding to arm themselves; they listen to my description of the situation and the setting, and choose the weapon/spell that seems like the best fit. The math is an afterthought, if it is considered at all.
When my players are fighting a werewolf, they reach for the silver arrows no matter what their build or optimization. Fighters will draw a dagger when they are grappling, even if they took the Weapon Focus (bastard sword) feat. I can rattle off a dozen situations in the game where a fighter would reach for a non-optimal weapon, but that's beside the point. They go with the weapon they think will be most effective, regardless of their build.
But let's look at it from another angle. Assuming a fighter spent his life learning to master a particular type of weapon, why wouldn't I expect him to use it as much as possible? Why wouldn't I want to reward that? Samurai are known for their skill with swords, not spiked chains. Other weapons remain available should he need them, and the fighter can fight with them as well as he could before ever specializing in the first place...they do not become crappy choices because they are not "optimized for his build" or something. If a Bow Specialist is beset by skeletons, he isn't penalized for picking up a club...but if he sticks to his "optimized" bow, he has to deal with damage reduction.
I remain unconvinced that weapon specialization will break the game, or that it will make the Fighter class less fun to play. The "+1 to hit and damage for weapon X" mechanic has been around for a long time in many flavors, and I haven't noticed any of the problems I've seen described in this thread.