Think instead about the fundamentals of baseball. What does each position do? Batters get bases and try not to get out. Fielders get outs and try not to get errors. Pitchers get outs and try not to give bases. There are only certain things each player can do, so don't hold each one responsible for the whole team.

So, we should rate in the following way:

Batters: Bases earned per opportunity, call it BEPO.

This would be calculated based on current statistics as:

BEPO = (singles + 2*doubles + 3*triples + 4*home runs + walks + hit-by-pitch bases + stolen bases)/(at-bats + walks + hit-by-pitch bases)

Fielders: Errors per out, call it EPO. (Obviously you want to minimize this.)

Straightforward to calculate:

EPO = (errors)/(outs)

Pitchers: Bases given per out, call it BGPO. (Again, you want to minimize this.)

This would be calculated as:

BGPO = (singles + 2*doubles + 3*triples + 4*home runs + walks + hit-by-pitch bases)/(outs + other-player errors)

[The other-player errors are included so that pitchers aren't held responsible for fielders' mistakes.]

Unfortunately, most statistical resports don't give out separate scores for singles, doubles, and triples (just "hits" and "home runs"), so it's hard for me to give you any specific examples of what this would mean.

I can tell you a few things, though: A batter who has a 0.250 average but usually gets doubles and home runs would have a high BEPO—and would be a good batter. A pitcher who repeatedly loads the bases but manages to escape without a run scored would have a high BGPO—and indeed, most would agree, is not a very good pitcher. Right now, that batter would be rated poorly and that pitcher would be rated well—and this seems wrong to me.