» those thousand words ♥
OH GOD NO NOT EVASIVENESS(no offense) that is the worst stat to ever have been included ever. Reasoning follows bellow:
I know you've stated that hey, it's not necessary to have a Pokemon evade every single attack. But the problem with that is...well, weavile would be able to evade slower Pokemon like Slowbro, but taking in your previous stat into consideration(endurance), then that would make the likes of Slowbro/Slowking literally untouchable. Think about it, unless Weavile uses Night Slash, it cant make a damn dent in those two Pokemon, and they wouldn't even have to use speed to crush Weavile, they could just use a move like I dunno, Surf to KO it really. I'd say it's pretty damn hard to dodge a tital wave coming for you, but that's just me. XD
But really, i think that the stats that we have now are balanced enough as it is. you'd have sturdy Pokemon being literally untouchable by your standard neutral moves, since they have ridiculous endurance, and then you would have the Pokemon would high evasiveness being untouched by moves that require physical contact, so I do think that it'll be quite a bit unfair, and it'll definitely make competitive battling more of a struggle than it is. For example, you have a Pokemon like....Staraptor, right? Alright, we'll take Staraptor as an example. It's a pretty fast Pokemon, let's give it a good level of evasiveness.
And then let's try it's opponent. Luxray for good measure. Of course, taken into account that Luxray is a slower Pokemon than Staraptor, it's a bit of a problem. Not only this, but if you're applying that logic, then Luxray can't really touch Staraptor much, because Staraptor is a bird, and it can outspeed pretty much just about every single move that Luxray could do it, bar thunder/thunderbolt, and Lux is more of a physical attacker anyway, so it already has a disadvantage from the start.
Ultimately, I feel that I wouldn't be very comfortable with these changes because it would give certian Pokemon a -huge- boost while it would just bump down so many other Pokemon, making them have some sort of unfair disadvantage against those who have higher speed, and those who have higher speed having an unfair disadvantage against those who have extremely high endurance. It'll just really make things a lot more complicated than it should be, which is how things shouldn't be, especially when you consider that kids play these games, and the last thing that we need is for them to be throwing their 3DS' at the wall because (insert 6th gen pokemon here) has higher speed and, by mere luck, keeps dodging the opposing Pokemon's attacks. Even if it's 1 in 4, you have to admit that 25% is still quite a big number in terms of battling, and can make a -huge- difference in the long run.