The players' demands are based on his playing time from the prior season in relation to his overall rating, so his stats won't play into it. The salary guide on the arb negotiations page (minimum-average-max) uses just his years of experience in relation to his rating. I look at the playing time and try to get a feel for which of the three he is closest to. If he is definitely a regular and his demands are are in between average-and-max, I'll offer just slightly less than his demands. If he is a platoon type, I'll offer slightly more (about 10%) than the "average." If he is strictly a bench player with very little playing time, I'll offer slightly more than what he made the prior season. The player usually still wins, but I'd say since I got a feel for this system, I win between 30 and 40% of the cases.
I have not found evidence that a player gets bent over a low ball offer. I think the help pages that suggest this are referring to the fact that if you arb a player all three times, he will not sign with you long term without testing free agency.