General Protection

Thursday, February 16 2012 @ 07:00 AM EST

Th is for Thursday and for theoretical and for thought experiment...

Okay. Think of Nick Swisher. To give yourself a frame of reference, think of what BA/OBP/SLG he is going to put up this year. No need to write it down or anything.

Now then. Consider the following two teams. They have identical pitching staffs and fielders, and they play in identical parks, against identical schedules, with identical uniforms, identical bench units, the same manager and the same mascot (it's an aardvark). The only difference is their lineups:

Team A	Team B
1. Jeff Mathis 2. Jeff Mathis 3. Jeff Mathis 4. Jeff Mathis 5. Jeff Mathis 6. Jeff Mathis 7. Nick Swisher 8. Jeff Mathis 9. [pitcher]	1. Jacoby Ellsbury 2. Jose Bautista 3. Albert Pujols 4. Miguel Cabrera 5. Jeff Mathis 6. Jeff Mathis 7. Nick Swisher 8. Jeff Mathis 9. [pitcher]

(... and a tip of the hat to Anders for suggesting Mathis, who's way funnier than Lou Marson.)

From the perspective of the traditional "protection theory," Swisher shouldn't really gain much from having four all-stars at the top of his order instead of four Jeff Mathises, since he has the same two guys in front of him and the same two guys behind him.

Nonetheless, I submit to you that Nick Swisher will put up better production stats on the second team. He will have a considerably better BA, OBP, SLG, possibly a better K/BB ratio (Swisher A will get pitched around or IBB'd in tie games, but rarely when his team is losing by 2+). I'd wager Swisher B would hit at least 20 points higher in a 50,000-PA sample. Maybe 40 points.

Why? The physical pitches he sees will be worse. Swisher B will face pitchers who are, on average, ...
- on higher pitch counts
- more likely to be long relievers
- less confident (whereas Swisher A will consistently face pitchers who are working on no-hitters and feeling ultra-locked-in as a result; I actually think this may be the most important point, particularly in its effect on Swisher's BABIP, but that's just hack theorizing)
- less likely to be late-inning shutdown relievers

And so on. As a result, he is going to have an easier time on the second team than on the first one, and that should be reflected in his production.

How do you test this empirically? I suspect it would involve pitch-fx and be extremely difficult. In the absence of such research, I think the logic here is unassailable and would be shocked if this effect didn't exist in real life. Jayson Werth's lousy 2011, after he moved from the stacked Phillies to the mediocre Nats, may be one example. Or perhaps he just got old and left a hitters' park. Or maybe he was good and the hits just didn't fall. Or... at any rate, it's clear that the effect would be really, really hard to isolate using the blunt stats.

I've never seen this idea stated explicitly anywhere, though I'm sure billions have come up with it before. At any rate, it's just a curiosity, most useful for fantasy baseball, awards voting, and assessing what effect switching teams will have on a player.

At the end of the day, as I see it, this little thought experiment leads to the stunning and profound conclusion that the better your team hits, the better your team will hit.

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