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What's more valuable?

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A workhorse pitcher or a feared hitter?

Going by Leverage Index (LI), which measures the contextual impact of every single plate appearance (where PAs in close games count more), starters come out on top (because their LI multiplied by PAs is the highest overall), while position players trail and relievers lapse into third. Common sense tells us this is right. We know that six innings of scoreless pitching is a lot more important than one. Just as a home run in the 9th doesn't count any more than a home run in the 1st.

The most PA a hitter ever gets in a season is in the high 700s. But a pitcher can impact more than 1000 PA. That could be the answer, if all we care about is a position player's offense, and not his defense.

In that case, we can undoubtedly say a DH pales in comparison to a pitcher (or even other hitters for that matter). To find out how many plays in the field are impacted by an individual defender, we take the total at-bats in the league (because the defense has no affect on walks), subtract home runs and strikeouts (for the same reason), then divide by the number of teams (30), and then divide by the number of defenders on a team (9). That gives us about 478 plays per year per player. That's a rough average, which doesn't account for the differences in position (a first baseman affects a lot more plays than a right-fielder), but it's fine because we're talking about an average position player.

Adding that to the number of plate appearances a hitter has will roughly will make him more valuable than a pitcher, but the pitcher plays defense too, though only 35 games at most in a season.

Where does that leave us? Perhaps with the question: is it worth more to affect many games a little, or a few games a lot? I don't know how stats could give us that answer.

Does the fact that a position player (Arod) is the highest paid in the game mean anything relative to this study? (This could perhaps be attributed more to the 'draw factor' of an everyday player (and home runs) and the injury risk pitchers carry. I admittedly haven't accounted for the injury risk with pitchers, but on the other hand, does that make a healthy 'workhorse' pitcher even more valuable?)

I'll leave it up to you, and this poll, despite using a current situation, should reflect the general consensus (they're both great players, both the same age, both free agents, both will require a lot of money, and neither has had a serious injury):

If you could only add one player, would it be Sabathia or Teixeira?