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Why does the Weapon Master have a Base Attack Bonus requirement of 5?

Classes with good BAB reach that requirement when they reach their fifth level. By then, human Fighters will be short one of of the six class requirement feats for the Weapon Master (they wouldn't if Spring Attack had a 3 BAB minimum requirement instead of 4 BAB). No additional feats are obtained on the fifth level, which is why they can't multiclass to Weapon Master until they reach level seven. They have a BAB of 7 by then. A tad late?

Non-human Fighters get one less feat at character creation, so they end up lacking two feats when they reach level five. Level six grants two feats for fighters though, so they can still multiclass to Weapon Master at level seven. Again the minimum BAB of 7. Barely.

I tried multiclassing Fighters to get enough free feats to multiclass to Weapon Master at sixth level, but I couldn't find usable feats in other classes. I'm not sure it would be possible to get enough of them anway. How on earth did they came to that BAB 5 conclusion?

What about a Fighter 2Low Attack4 - human or any race ? That would be the worse case scenario. You have 4 feats from fighter levels and 1st level human. dodge, mobil., comb. exp., spring. You also get 2 feats at 3,6 level: WF and one of your choice that doesn't help the Weapon master.

So you have all of the feats but you don't have a BAB of 5.

Also consider a fighter2rogue3(or other mid BAB)3 - human. Gets 3 feats at first, another at second fighter level. And the final at level 3 but he can't be a weapon master until another bab.

Finally consider a

Fighter2rogue2monk2 any race. Since you are triclassing you can't get the same bab progression for your rogue and it is as if you are a mage etc... So need another level before WM

I admit its a technicality but there may be some extreme builds out there...

The closer (IMPORTANT)

If The BAB was lower human fighters could take weapon master and reach weapon master 5 and 7 VERY early

You could be a human fighter 3 and then take Weapon master 5,7 and be critting your enemies to pieces with your greatsword.

For example it is impossible to make a Weapon master7 (extended crit range and multiplier) Assassin8 (HIPS) Rogue 3 Fighter2

with BAB +4 as a requirement you could. HIDE SNEAK WHIRLWIND HIPS REPEAT

Edit: actually you can make that build if you take assassin first rather than WM my mistake