Personally I have seen it make a difference to teams in our loop. Sample size is a very important thing to consider, it does requires a little knowledge to make it work for your team.Changing teams midseason for anything other than abuse is bad, I agree. In that case you just have to suck it up (by the time you figured you were getting screwed the season would probably be half over anyway).
However the point of this thread was whether statistics should be used and while I say sure you can do that (if you trust the statistics) I am not how much of a difference it will make in the team performance if the coach was on the up and up and has a clue as to what they are doing. The other question, which is an important one, is if you do use statistics to set your lineup, what sample size do you use? Too small and you could end up chasing your tail, too big and you miss opportunities.