I stumbled onto something called Elo Rater. It is a way of rating former or current baseball players if they were to face off in a head to head match up. It was developed by Arpad Elo. He was born in what was at that time Austria-Hungary in 1903 and passed away in 1992. Arpad was a physics professor at Marquette University and was an avid chess player. He developed his rating system originally to rank chess players.
Frankly, I don't completely understand every bit of this. There are original point values for the players. I'm not sure how those are determined. And I don't know who decides how it is determined that one player goes against another. It looks like maybe people can go to the website and pick a couple players and they play each other. Since he was a college professor, I'm going to assume he knew what he was doing. Also his ratings seem pretty accurate. His top five hitters of all time are:
1. Babe Ruth
2. Stan Musial
3. Ty Cobb
4. Lou Gehrig
5. Mike Schmidt
You can check out his full lists at http://www.baseball-reference.com/friv/elo.cgi
Here is an example used on the site.
RA is the rating for Player A and RB is the rating for Player B. Working out the probability that Player B wins where RA = 2450 and RB = 2500:
P(B wins) = 1 / (1 + 10^((RA - RB) / 400))
= 1 / (1 + 10^((-50) / 400))
= 1 / (1 + 10^(-0.125)) =
= 0.571
To analyse how these come out means looking at fraction exponents and negative exponents. You can find the details of the process at http://www.baseball-reference.com/about/elo.shtml
