In arbitration, the stats that are the most relevant for the players agent are those that make him look the best, and you had better believe that management will be arguing different stats to lower the player's value. That's how much consensus there is regarding the best stat for proving value. Lol!
Sure stats are important and they are a lot of fun for fans, but there really is not stat to show if a guy plays the game the right way. I still think that #2 hitters should be able to hit the ball behind the speedy runner to get him into scoring position. I like to see a hitter be aggressive and swing at the first good pitch he sees to drive in a crucial run from 3B with less than 2 outs when an Alex Cora type is on deck-- even if he has to go a little out of the zone. With a big run on second base and two outs, I'd rather send to the plate the guy with the .300 BA who doesn't K instead of the guy with a .250 BA but with a higher OPS. Where are the stats to show me if a guy stretches a single to a double at the appropriate time or gets caught in a run down after getting a hit to make sure that a runner scores.
What is Vin Scully's saying about stats? They should be used in much the same way as a drunk uses a lamp post -- for support and not illumination. Stats can definitively seperate the good players from the bad, and you can use any number of stats to make the case. However, in close calls, no stat or group of stats is definitive. It makes for a good argument, but if you think you can prove yourself right, you are just kidding yourself.