I decided to play around with a hypothetical, extreme one-dimensional player as a thought experiment.
This player is an extremely durable first baseman, who is so terrible defensively that he will misplay one out of every ten defensive chances he gets, and his team knows that. However, to compensate, he is guaranteed to hit a home run every time he comes to the plate (even if the other team tries to walk or plunk him). He's also slower than molasses, but because he always homers it doesn't matter. How many runs will this player create offensively, compared to how many he will give up defensively?
I put him in the 1979 NL, where the average first baseman who played every inning of every game saw 1609 defensive chances. I'll assume 1600 for now, with 160 errors (the average team saw 13 errors at 1B). An error is worth about 0.51 runs, on average (some more, some less). That's 75 runs worse than an average first baseman - perhaps worse than that, since this guy has no range and a terrible glove and arm, so he gets to fewer balls than average. Let's give him another 25 runs lost defensively, compared to an average first baseman.
He's also going to bat about 700 times - 4.3 times per game, which is about typical for a player playing every inning of every game. In reality, you'd probably sit this guy in the last inning of close games where you're ahead in favor of a defensive whiz who can't hit, but let's ignore that for now since it'll hardly affect his plate appearances. A home run is worth about 1.4 runs, on average. That's 980 runs created.
Very few teams in major league history have scored 1000 runs in a single season. This guy is giving you 700, minimum, and in reality closer to 1000. That ignores what the rest of the team contributes offensively. If the rest of the team is average, you're probably going to give up (in a 1979 NL environment) something like 750-800 runs. You're also going to score some stupid number of runs - 1200? 1300? I don't even know. Your team ERA is going to be north of 4.00, maybe close to 5.00 (assuming average pitching). But you're going to score 7-8 runs per game, and a guaranteed 3 at minimum. You're going to slug your way to a championship, odds are.
...
Now, this is an admittedly absurd example, but my point here is that it doesn't matter how you generate your value. If you generate all of your value through power, and give the team no excess value in the field or on the bases, you're still just as valuable as a player who generates the same number of runs through plus defense and speed but who uses a banjo at the plate instead of a bat. I don't care how many "dimensions" a player had when they're being evaluated for the Hall of Fame - I care how many runs, and thus how many wins, that player's "dimensions" created.
