Here's another cool website:
www.walkoffbalk.com
They have a win expectancy calculator, which can be used to see how valuable anything you do in a situation is.
So, for instance, if you start with "Visiting Team, 1st Inning, 0 outs, Bases Empty, Score differential = 0 ", which is basically the situationwhen the leadoff hitter steps to the plate, you see that between 1979 and 2004, teams in this situation won 46% of the time.
Now, put in "Score Differential = 1" (a leadofff home run), and the percentage goes up to 56%. So, that's a 10% difference.
But, let's say you look at the same two situations, but in the bottom of the ninth, 2 outs. With the score tied, the visiting team has a 38.6% chance of winning. But, if the next batter hits a home run, their chance of winning goes all the way up to 82.7%, a 44% difference. Which shows how much more valuable a ninth inning home run is compared to a leadoff homerun in the first inning.
I think an interesting thing to do would be to take Ortiz and A-Rod's game-by-game results from last year, and figure out who was the most valuable by adding up how much they contributed to their teams chances of winning, using this calculator. It would take FOREVER, but maybe if I have nothing to do on a Saturday afternoon, I'll work it all out