Lets compare a longsword to a battle axe again, this time with improved critical. Lets assume that all threats are confirmed.
A longsword will crit(add 100% damage) 20% of the time(17-20). 1x.2=.2 That equals a 20% bonus to overall damage.
A battleaxe will crit(add 200% damage) 10% of the time(19-20). 2x.1=.2 That equals a 20% bonus to overall damage.
We could also compare a falcion to a scythe w/improved crit. Falcion = 100% x 30% = 30% bonus damage.
Scythe = 300% x 10% = 30% bonus damage.
Basically the damage bonus for crit range a is equal to crit multipler b when a = b-1