THE BOOK--Playing The Percentages In Baseball

I’m slotting my 150 RC guy at #3 in the lineup, & shall slip this 105 RC player right after him. But, this is assuming a lot, for a lot of data is missing here. Like—what are my other 7 batters? If I’m making it all up, then I’m taking a 150 RC player & batting him 3rd. I don’t want my 105 batter hitting in front of him, since I’d like to imagine I’ll have a 130 or 140 RC to fit there.

Devon:  You’re either joking or missed what the question was asking, I’m not sure which.  If you’re joking, well done.  If not, go back and finish reading the question ("AFTER which player would you slot him in, wrt MVP?")

wrt="with regard to”: meaning with regard to MVP voting, not lineup placement

The mean is “between 130 RC and 120 RC”.  That sets the equivalency to 125 RC.

We therefore solve for this:

125 - 162x = 105 - 105x
20 = 57x
x = 0.35

That is, the replacement level is 0.35 runs per game.  Given that the average is 0.50 runs per game, then the replacement level is at 70% of league average.

Or similarly, the replacement level is .15 runs per game below average.  At 162 games, that sets the replacement level at 24 runs per 162 games.

Great job guys, for nailing the replacement level!

I will say that i “cheated” with my answer because i already believe replacement level to be about 20 runs below average ( 60 per 162).  I rounded this to 1 per 3 games and did the math from there rounding as needed and came in at 125, which means the 130 guy wins.

I think you might get a very different answer if worded differently and presented to a different audience.  Though i suppose that would apply to most survey questions.  We all generally agree that playing time maters and the difference between average and replacement is abiut 20 runs so this is a layup for your readers! Might be a little different at fangraphs.

I’ll say the same basic thing as Steve - I started from assuming replacement is 20 runs below average, or 61 runs per 162, calculated 0.38 runs per game as replacement, multiplied that by the missing 57 games to add 21 runs to the 105 and come up with 126.  I’d also be interested in what non-Book readers would think, but phrasing it in terms of runs might just be confusing for non-Book readers.

Why would phrasing it in terms of runs confuse readers?

Maybe it won’t - people will think about it in terms of “Runs” and RBI rather than runs and should get to the same place.

I’ll admit it took me about 5 reads to actually understand the question. I also didn’t know what wrt meant… framing it in terms of value would’ve made it more obvious to me what was going on. After it clicked it made perfect sense.

Some Fangraphs readers are similarly perplexed:

http://www.fangraphs.com/blogs/index.php/poll-105-runs-in-105-games-and-mvp/

Feel free to suggest alternate wording, given the maximum characters I’m limited to (above is pretty much the limit).

I, too, struggled with the phrasing/units of the question. I just don’t use the runs created scale, although it should probably be isomorphic to team run scoring.

I subtracted the 105 runs/105 games from the options, figured out how many more runs the average player would produce, and came in a bit under that. Seems like my approach more directly addressed replacement level production than the poll was intending. (I was torn between 120 and 130 runs.)

I updated the options to try to make it clearer.

If you break it down logically, you end up approximating something like the calc in 3/Tango, which I assume is the point. It’s a great, clever way to get you to guess at the replacement level.

Not sure this is a huge improvement, but would’ve made more sense to me:

You have a player who produced 105 runs in 105 games during a season. AFTER which player do you slot him, in terms of value added?

(The average player creates 81 runs in 162 games.)

I chose MVP specifically.  This Fangraphs reader said it perfectly:

So the question is how you handle 57 games of production from somebody else.
a. Do you ignore it completely and just judge the guy on his 105?
b. Do you assume replacement level production (about 20 runs)?
c. Average (about 30 runs)?

And of course, you decide what replacement level is.

Btw, Fangraphs readers also gave the exact same overall average as you guys, though the range of their answers was wider.  That is, less consensus.

Answers are nice and symmetric, centered at the middle option (ignoring the 100 runs option which is the only one less than the original 105). Makes me wonder how much people are just saying “who knows, I’ll go for the middle one shown.” I wonder if the poll software allows for A/B presentation (off-center the responses in both directions and randomly show one poll to half the viewers.)

Maybe you could ask this in terms of OPS or wOBA? If a player has a .900 OPS in 100 games, that’s equally impressive as a XXX OPS in 162 games. (Or AVG, but that’s not as proportional to value as OPS, I wouldn’t think.)