Nail said:
In the games I play, it's far more likely that the party is attacked by a group of mooks, sergeants, and 1 - 3 main critters. Given that, the impact of each individual mook is minor, and rolling the init for each mook is a waste of good gaming time.
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The word "slighty" is a bit of a stretch, methinks. We can show that a +4 init is significant, even against groups of opponents.
That is where the first assumption comes in. The math does show that it really is not signficant most of the time. If you generally go against a bunch of mooks and sergeants, then it does not really matter if you beat them in init or they beat you. The party can easily handle mooks and sergeants. They are not the serious threats.
It is the 1-3 main critters (and mostly if these critters have spells or special abilities) where it might really matter that an arcane caster has +4 to init.
Against one such foe, if the arcane caster has the same Dex, he goes from:
First 50%, Last 50% to
First 70%, Last 30%
So, 1 combat in 5, the caster goes first compared to the main opponent where he would not go first anyway. This means that Improved Initiative only really seriously affects one combat in five when there are mooks, sergeants, and one main opponent. 4 combats in 5 (the majority of combats), nothing significant has happened here.
Against two such main foes, if the arcane caster has the same Dex, he goes from:
First 33%, Second 33%, Third 33% to
First 55.5%, Second 29%, Third 15.5%
This means that in 2 combats in 5, he improves his init compared to at least one (or both) of his two main foes. 33% of the time, he is still in first, 15.5% he is still in third, and some significant portion (about 2/3rds) of 29%, he is still in second. 3 combats in 5, nothing has really changed.
And remember, PC Arcane Casters still tend to be fairly well protected before combat starts. They tend to be behind other PCs, they tend to have protection (and even contingency type) spells up before entering dangerous areas, they might be invisible or otherwise hard to detect, etc.
You cannot have it both ways. Either mooks are minor to the overall scheme of combat and not worth even rolling individual inits for, or they are major enough that Improved Initiative actually matters with regard to them.