THE BOOK--Playing The Percentages In Baseball

Subscribing to thread for future explanations…

Another “pick the replacement level” poll...but I have a question:

Do you want us to do the math? Because I see the point, I understand what I need to do, but I’d rather not put pencil to paper to decide my answer. Am I supposed to vote on gut? With the first two polls I was able to do it in my head (close enough to know which answer to choose), and while this one is just the same principle, I can’t come up with an answer without writing it down.

Are you trying to get our gut, or are you trying to get us to calculate it out? In which case, why not just ask us what we think the replacement level should be, and skip the math?

It doesn’t have to be replacement level. 

It’s about people understanding the implications of their choices, that all the players in the team they are selecting are going to get 20MM$.  That all these players are equivalent.

It’s about people deciding for themselves what kind of baseline they prefer.

Unfortunately I already knew what you were doing, so I put a little thought into replacement players, which I assigned about .3 runs/game talent to, and so I went with E.

I really think this is the only way to do it, the 80 game player on team E produced 52 runs above average in half a season, while the 160 game player took a whole season to produce 12 runs less than him. Paying them the same seems fair.

I’ll explain what each team is after I get about 100 votes.

But isn’t the implication that, since these players are not playing full seasons, that you need to supplement their performance with additional player-innings, presumably by players who are “replacement” since they are not good enough to be playing full seasons? I am not sure I see the distinction between baseline and replacement, if one approaches the problem logically.

I think that you are setting up this entire series to as a way to reinforce the idea of replacement level without directly talking about it, but it just feels awkward to me, since the questions always seem to ask, very indirectly: what level of player is available to your team at a negligible cost. I can jump through these hoops and pick from this hypothetical, sure, but isn’t it more constructive to talk directly about the concept of replacement level itself?

Am I missing something? I think I might be. Sorry if I am. I’m trying to take different angles at this series and keep following the same logical progression.

I have at least a dozen threads that talks about replacement level directly.  This one is more indirect, but it also doesn’t presuppose its existence.

Furthermore, each of the teams has their five players with the exact same amount of playing time.  So, it’s not clear that you necessarily need to have that worry about “replacement player”.  They are all going to pay the same amount for the missing games.

This thread is about trying to find an equivalency, so that if someone says “120 RC in 160 games”, then I can say “45% of my readers said that that’s the same thing as 92 RC in 80 games.

So that next time, when someone is presented with two players of different playing time, we can say how we can make them equivalent.

But, there’s also a healthy minority that believe in comparing above-average (or better), or even just only paying for actual production, regardless of the number of games played.

It’s about giving a voice to everyone out there, that WAR or its equivalents only has the support of say 30-50% of the saber followers.

I’m surprised at the huge numbers for Team A, agreeing to pay the 120 run guy in 160 games the same 20MM$ as the 60 run guy in 80 games.

I can see the argument on the Team G side, that they pay for runs, and they don’t care how many games it takes.  I don’t see the argument for Team A.

For those who answered that: can you explain your reasoning?

Re Tango#8 I can explain my vote.  I completely missed the sentence “all players are paid at the end of the season”.  I read the question as “this is how these guys have performed previously, what would you pay them going forward”.  Since their production/game was equivalent, I imagined they’d get paid equivalently (even then I probably should have accounted for the probability of future missed games).  So you can account for at least one poor vote.

I voted A.

Same reason as #9.

I’ll read more carefully next time.

Thanks guys, I appreciate the response.

This is the problem I have when I make the intro so long, that it has the danger of being scanned.

I’m not familiar with replacement value (at least no more than in theory) so my answer is probably representative of a type of naive response.

If you’re paying $20MM to each player, then my presumption is that each player is of “equal value,” whatever that means. Team G has equal output, but G080 appears to be twice as productive as G160. It’s difficult for me to see these players as having equal value. Team A pays each player based on rate/output. Certainly there are other considerations, but what are these? Did A080 play only 80 games because of injury? Did the manager simply choose not to play A080 as much as A120 or the others? Based on rate of production I’m presuming that A080 would have produced 120 runs in 160 games. This is somewhat foolish (since I may expect the rate to regress as sample size increases...) but if I’m equating “equal value” with “equal output” then it’s not hard for me to buy this metric; I would expect that if A160 played 80 games then he produces 60 runs, and likewise if A080 plays 160 games he produces 120 runs.

For me, the crux is being paid at the end of the season.  It doesn’t matter if G080 was “twice as productive” during active playing time - he was precisely as productive for the season.  I guess that’s a simple view, but assuming RC omniscience, isn’t it the most reasonable one? Does it make sense to pay a player for his replacement? It would seem to defeat the purpose of above replacement metrics.

Here’s my thinking (I voted for Team D).  At the end of the season, AFTER the games have been played, there’s no replacement value.  All the other players in the league not listed here, by construction, average 0.5 runs/game.  This is equivalent to all of them producing exactly 0.5 runs per game for the purposes of the discussion.  This means either the teams listed here are very large, or there are a lot of other teams.  I basically assumed the latter, though I don’t think it matters.  In any case, what value has each player provided?  The contribution each player has made to your run differential.  That value is Runs - Runs scored against IN THE GAMES THEY PLAY.  So the baseline here is going to be the COMPETITION, which is 0.5 runs/game.  Using that baseline, the guys on Team D all provide 40 runs of value during the season.  So, that’s my thinking.

Building off #14… If you talk about getting average production for the “missing” games, don’t you also need to talk about how much you have to pay this average player? So you’ll get .5 more runs per game, but you’ll also need to pay X more dollars per game for that production. What is X?

15:

Good point.  I assumed 0 since I had no information to assume otherwise.  There’s no league budget here so how would you know?  I couldn’t assume these players make up the whole league since they are all above average.  I suppose this means there are some other assumptions I ought to think through.

Obviously the average player is going to be paid more than 0 dollars.  You should assume reasonableness whenever you need to make a decision.

And yes, I said this is a pure pay-for-performance, after the season.

If you go to work, and are injured on Jan 2, and don’t come back until Dec 31, you are only going to get paid for 2 days of production under a pay-for-performance.

I thought about this a little more, and it doesn’t actually matter what you pay all the average guys, my answer to the question posed would be the same.  The players on Team D all provided equal value, so they’ll all get paid the same, it doesn’t really matter what the conversion function for runs to dollars is, it will be $20 million for 40 runs above average, since that’s the one thing Tango defined.

The only thing I defined is that the 20MM$ guy generated 120 runs in 160 games.  That’s it.

#19/Larry—I think the key here is that Tango defined $20M for 40 runs above average *over 120 games*.

Your model says 40 runs above average is the same for any number of games, whether it’s 41 runs in 2 games, 80 runs in 80 games, or 120 runs in 160 games. The implication there is that getting average production over the remaining 160, 82, or 2 games is equally easy/valuable. Is it. Would you pay a league average player the same amount for 2 games as 160 games?

As James Cameron wrote to Bill James, “Ice berg, straight ahead!”

Tango, you give several explicit constraints and numerous implicit constraints. The first is that the value of x160 = 120 runs = $20MM. The second is that we must choose one team to pay each of the identified five players $20MM. The third is that this is a “pay for performance” setup, whatever that means.

Implicit constraints are: $20MM is a maximum value (if not the max, then near the max). Also, the team selected is presumably the highest-paid team in the league (see implicit #1). Also, performance is equivalent (or close enough) between players 160 and 080. I’m sure there are other implicit constraints, but these stick out; also, these constraints are conflicting (which is ok.)

This is interesting but problematic for me, and I’ll change my preference by the time I’m finished. If my metric is rate of production relative to average/replacement then I choose Team A (0.75 runs/g vs 0.50 runs/g). If my metric is total production relative to the average/replacement then I choose Team D (each scores 40 runs/season more than average/replacement. If my metric is total production, then I choose Team G because no team scores more runs.

I voted Team A, but my preference has changed to Team G. Presuming that this is the highest payroll/the team with the most pay-worthy performance, that’s got to be Team G. Afterall, G080 is the most productive player in the league and he, above all others, is the most valuable player. G080 + his average replacement score 160 runs in the course of the season.

These are the constraints I laid out:

1. “And, all players are paid only at the end of the season.  A pure pay-for-performance setup.”

2. “For which Team would you have the league pay exactly 20MM$ for each of the five players?  That is, for which Team do you find that the five players listed are equivalent to each other, in terms of their past performance?”

From TT#18:

“If you go to work, and are injured on Jan 2, and don’t come back until Dec 31, you are only going to get paid for 2 days of production under a pay-for-performance.”

Just following this analogy: you’re an attorney, and in those two days you win a case for your client that saves or makes them $20MM.  You provided them $20MM of value, regardless of whether or not you provide them ANY value for the remainder of the year.  So on a pure, looking back, pay-for-performance system, you should be paid your cut of that value, whether you managed to generate it in 2 days or 365.

Sky/21:

I admit that you point out a serious flaw in my logic with respect to an average player.  It doesn’t make a lot of sense to pay an average player the same for 2 games as for 80 games, but that’s what my logic does.  I will have to consider the consequences of that. 

However, while I have said nothing thus far to dispute 2G/41R = $20M, I do argue against it.  The real currency is wins.  As long as there is a linear relationship between runs and wins, then runs as a measure is ok.  But, once the runs get put in very few games, then the runs/wins relationship becomes non-linear, and I’m going to have to convert to wins before doing the analysis.  Since 1W=10R, roughly, given a 4.5 R/Team/G environment, 40 runs is 4 wins.  A player playing in 2 games can produce no more than 2 wins in the standings.  But, Tango was very careful (I argue) not to put this discussion in that regime.  So, I chose not to worry about consequences in this regime.

Nate/24: correct.

The difference is that in baseball, you need to have someone on the field for all the days you are not working.

@ Tango/26,

If there’s a league minimum salary, I see your point. But if we’re paying for performance, ownership only has to pay the replacement player for what he actually produces. And one assumes they would have had to pay our disabled (or whatever) player even more than his replacement for those games had he not been out. So why are we dinging the primary player?