THE BOOK--Playing The Percentages In Baseball

Tango,

I suppose this falls under WAR (feel free to ignore it if it doesn’t), but how stable do you think the positional adjustments are over time and do you have historical values?

Put another way, any comments on this? http://www.fangraphs.com/blogs/index.php/historical-position-adjustments

Is Sean on the right track here?

Thanks as always.

Jeff Sullivan actually wrote the attributed line over at LL, but since he and I share a brain, I’ll take credit for it.  Gassko said he knows more about the M’s than anyone else alive in his HBT Preview column, so I’m fine stealing his line since he’s stealing my title. 

Also, good luck with this thread, Tom.  I have a feeling those guys would be much more agreeable on these issues if I wasn’t such a big proponent of WAR - they’re part of of a group of M’s fans who think I’m Satan on earth.

Matt: I wouldn’t go past the last 15 years for historical purposes. 

I’d guess that in the 1970s and 80s that the 2B was ahead of the 3B.  Just a matter of applying the numbers historically, which I haven’t done yet.  I tend to focus these days on 1993-present with my database.

***

Ok, now that I read your link, I see that Rally is doing what I’d be doing.  Let’s see what he says…

{clap clap clap}

Very good.  All Rally has to do now is create a smooth function, so that he doesn’t have the jumps from the arbitrary cutoff periods, and we’ll have something great.

While I love the system, I’m having trouble accepting that 3B=2B in terms of defensive value. Why are they weighted equally?

Look on the bright side, Dave. The rest of the M’s fans think you’re Santa.

Jl:

The guys who play 2B do as well at 3B as the 3B who play at 2B.  And they both do equally worse at SS.  In a nutshell. 

You can also read these:

http://www.insidethebook.com/ee/index.php/site/comments/2b_v_3b/

http://www.insidethebook.com/ee/index.php/site/comments/2b_v_3b_v_cf/

***

Dave: I’ve never been to that Mariners site before, and they seem receptive at the moment.

How soon do you think it will be before some team tries to play someone like Rolen or Beltre at second?

Dave, Tom:

I’ve been at MC since the beginning, but also visit USSM and LL regularly.  You are always welcome at our place.

Cheers,

ess

Jl: the issue is that established players don’t move.

Scott Rolen, Adrien Beltre, Eric Chavez, Ryan Zimmerman are such fantastic fielders that one can easily create a scenario where those players would be playing SS on their HS and college teams, and that the quickest path to the MLB was playing SS (ala ARod, Ripken).  As it stands, if you are a great player and you are 3B, you don’t move.  The chances for equilibrium isn’t that great when it comes to 3B.

Tom, 

Thanks for stopping by MC.  Please do so ANYTIME.  I really appreciated the thread today.

Not sure if this falls in the WAR category, but I’ve read in various places online that a team of nothing but replacement-level players would expected to win between 43 and 48 games in a season. Is this accurate?

Also, as I’m relatively new (over the last six months or so) to the concept of “replacement-level,” I was wondering if you could link some basic literature regarding how “replacement-level” was decided upon? I guess another way of saying it would be, I understand WAR intuitively…it makes sense to me…but I’m not exactly sure how you came upon the replacement-level value itself.

Thanks,

Andrew

Okay, here’s the thing I don’t understand (to the extent I’m keeping up with this stuff at all).  I do understand the position adjustments as a way of reconciling how hard it is to play that position (and, hence, to estimate how many players can even reach a decent threshold to play it at all).

But do your position adjustments also account for how much more *important* specific positions are?  For instance, shortstop is more important than third base just because a shortstop handles more chances than the third baseman (regardless of whether it’s easier or harder to field there). I know Win Shares captures this, but I don’t believe this is captured in WAR, since the position adjustments are based on variances from average at each position.

As the owner of MarinerCentral.com I would like to express my joy in your participation in the WAR thread at my site! 

At MarinerCentral we have a VERY diverse reader/poster community.  We cover a pretty broad spectrum of fandom of baseball in general, and the Mariners in particular.  We range from casual fans to students of the game.  We are also blessed to have a few real professors of the game. 

Anyway, thank you again for dropping in and educating some of us!

Lonnie

studes, I think it’s included. See this comment by MGL.

Basically, the value of a fielder (in defensive adjustment) is partially determined by the amount of balls in play for a position as I understand it. Therefore, the amount of runs for SS is higher because the position is more important and more challenging.

That is then multiplied by playing time, so it runs through the whole calculation.

Tango, MGL, et al. feel free to correct me if I’m wrong.

I think Sal’s got it down.

***

No problem, Lonnie.  Always fun…

http://www.hardballtimes.com/main/article/replacement-level-article/

Good explanation of replacement level, and talks about positional adjustments as well. I’m with you sabermetric noobs as I’m just trying to catch up with a lot of this stuff.

Also, don’t know if this is relevant, but in a recent FanGraphs post dealing with player win dollar values, is an extra 20 runs added for being above replacement after the offense/defense numbers have put in? Does that have to do with PA?

I kinda butchered the question…I don’t need an answer based on the FanGraphs post, just meant to mention that’s where I saw the calculations.

Uhhh…maybe something weird is going on, here’s what the post should have said.

http://www.hardballtimes.com/main/article/replacement-level-article/

Theres a nice explanation of replacement level. Deals with positional adjustments as well. Good for us sabermetric noobs who are trying to catch up.

Also, do players get +20 wins merely by being above replacement level? I thought I saw that on a FanGraphs post dealing with win values for players; maybe I misread it.

I think Studes is right.

The problem he seems to be identifying is that these positional adjustments are usually applied per PA, which simply isn’t all that meaningful when it comes to fielding - looking at BIP (as measured by ZR chances or what have you) would look very different, and I think it would be a more accurate model.

A SS and a 3B with an equal number of PAs will typically have a very different number of BIP chances. If we scale the positional adjustments based upon BIP chances instead of PAs, I think the gap between the typical shortstop and third baseman will widen. (I also think the gap between the typical 3B and 2B will widen, and that might go a long ways toward explaining the equivelence between 3B and 2B as per WAR.)

While I’m on the topic, I have an idea I want to float. I have three data points in mind:

1) Tango’s study on positional adjustments:

http://www.insidethebook.com/ee/index.php/site/comments/uzr_positional_adjustments_revised_with_2008_uzr/

Note where 1B appears before he adjusts.

2) Teams seem to pay a premium for 1B above and beyond what we would expect:

http://www.insidethebook.com/ee/index.php/site/comments/average_payroll_per_position/

3) When I looked at average performance of free agents making the league minimum over the past decade or so (trying to create an example of rep-level for Bradbury), one thing stuck out at me - 1B making the league minimum were worse hitters than corner outfielders.

Is it perhaps time to reconsider where we put 1B on the positional spectrum?

Re Tango/#3 - remember, I did do those smoothing calculations last month
http://statspeak.net/2008/12/batting-runs-above-position-1.html

What is a “smoothing function”? In #3 Tango says that you need to use a smoothing function when dealing with cut-off points. Brian also mentions this in #19. Is it a moving average? I like to group Linear Weights and offensive positional adjustments by Eras. What bothers me about doing this is the jumps you get when you move on to a new Era. How would I incorporate this smoothing function you guys are talking about. If it is just a moving average, then it would be fairly easy to implement.

studes, I think it’s included. See this comment by MGL.

But I thought the positional adjustments were based on how the Willie Bloomquists of the world did between different positions.  That doesn’t capture the opportunity difference between the positions, unless I’m missing something. So, what did you do to add that?

Colin:  I’m not sure I buy the notion that 1Bmen are overpaid.  We should expect them to be the highest paid position, because it’s the end of the defensive spectrum.  Assuming that defensive and offensive skill are largely independent, there will be some very great hitters whose fielding is so weak they must play 1B (or DH).  These great hitters will “stack up” at the end of the defensive spectrum.  And since the variation in offensive skill is greater, it makes sense that 1B will have the highest average value.  (That is, there are few if any SS who can save as many runs as Ryan Howard produces, and thus can play despite a .550 OPS).

Guy, you must have missed the recent thread where I showed that 1B were way overpaid.

You must have missed my post where I questioned that conclusion…  :>)

I think Colin’s pts 2 and 3 in #18 are more hostile to one another than complementary.  If teams pay a premium on 1B over what we expect, then shouldn’t we also expect 1B who make the minimum to be worse than those that make the minimum at other positions?

If we believe that teams overvalue offense relative to fielding, then it would seem to follow that there are a number of guys who “should” be in the reserve first baseman pool (in the mold of an Ibanez, but less productive), but are put in an outfield corner because there is a premium placed on offense.  I believe Tango wrote that he found that replacement LF were slightly better fielders than average, and that LF was unique in this respect.

I think Colin’s pts 2 and 3 in #18 are more hostile to one another than complementary.

Can’t our points all just get along??!!

Studes:  nice.

Tango:  Even if your 1B results are not the result of few Esasky type outliers, that still leaves the possibility that some other valuation problem is disproportionately impacting 1B. Maybe big, slow players are more likely to underperform than the market understands (or understood in the past).  Or maybe, as Moneyball and Sauer argued,  SLG has been overvalued vis-a-vis on-base skill, and 1Bmen have a higher than average SLG/wOBA ratio.  I’m sure the Sauer paper hugely overestimated the extent of this, but some overvaluation is certainly possible.

I thought that’s what I said was happening, Patriot. These scrub-level 1B were worse hitters than corner outfielders.

What I’m suggesting simply is that 1B are better fielders than we thought they were. Look at Tango’s study of positional adjustments. The study says that very thing - 1B are better fielders than corner outfielders. He adjusted the numbers so that they’re worse. I’m not so sure about that adjustment anymore.

I’ll probably never live that one down.  I was having a hard time thinking of an antonym for “complementary” in the morning.

My point was that if 1B as a group are being overpaid, then 1B making the minimum should be worse than those making the minimum at other positions.

Of course, it could well be true that we are wrong, and that the 1B are being compensated fairly because they are indeed better fielders.  But both are valid explanations for the phenomenon (repl 1B

“The study says that very thing - 1B are better fielders than corner outfielders. “

Where did the study say that? 

Indeed, every time I do the dual-positional comparisons, the 1B is always worse than each position.  The only issue is that the 1B is equally below from each OF as he is from the rest of the IF.

Colin:
Nate Silver, in his FAT analysis
(http://www.baseballprospectus.com/article.php?articleid=4891) found that freely available 1Bmen were about 5 runs better than corner OFs.  That seems more plausible to me than your result (but of course doesn’t make it right).  Perhaps looking only at FA making the league minimum restricts your sample too much?  Also, he decided to weight every player equally (roughly), rather than by PA.  If you weight by PA, that might explain the difference.  It’s probably more common for a lg-minimum FA to put up a surprisingly good performance and grab playing time at a corner OF position than at 1B, because there are two slots in the OF and 1B is more often blocked by an older veteran incapable of playing anywhere else.  At least, that’s a possible factor….

BTW, I’m not sure why you say your numbers in the average payroll per position thread supports the idea that 1Bmen are overpaid.  Your data seems to show they are paid about the same as LF and RF. Right?  Or am I misreading your data?

Guy, I think there has to be a happy medium between doing it by PA and doing it by player. I don’t know what that would be just yet, though. I’ll muse on it.

Tango, I was looking at the chart after the handedness adjustment.

The result that the 1B were equally far away from the three IF and the three OF position seems to be an unusual one, and difficult to reconcile.

I keep coming around to the same issue - maybe I’m reading things wrong, but (to get back to studes’ point) what’s the unit of playing time for these adjustments? Is it games?

I agree that the unit of playing time is important.

After all, if the 1B gets say 0.1 plays, while the SS gets 10.0 plays per game, then it would be impossible for Ozzie Smith to have an impact at 1B.

So, there are two steps to do the conversion: one is to first focus on the “rate” (per play) conversion, and then the other is to do it as opps per game.

This was discussed five years ago here:
http://tangotiger.net/UZR9903TT.html

And it comes with a handy-dandy excel workbook.

Colin:  I oversimplified Nate’s approach a bit:  he maxed out all players at 130 PAs.  I do think you need to do something like this, because a couple of breakout players at a position will have so many more PAs than the average replacement player that it would really skew your position mean.  Ryan Ludwick this year (salary: $411K) is a good example.  A lot of these guys could probably play LF, RF, or 1B, but if they hit their way into the lineup it’s more likely a team can find space in the OF.  I’d also guess the OFs are younger, and thus there’s more chance of a surprise upside performance.

Guy-

If, as you claim, there is a glut of good hitters who are forced to the end of the spectrum due to poor fielding, wouldn’t that drive their value down rather than up? The number of spots (demand) on a roster for starting 1B/DH type players is basically fixed, so having a larger supply of players who can only fill that role would seem have the effect of lowering the price for these types of players.

This might be looking at it the wrong way—I’m no statistician or economist—so correct me if I’m wrong.

My favorite “what?” quotes:

“There’s a big difference between how much you should pay a guy and how much he helps you win baseball games.”

and

“I also have a major problem with equating uniqueness with real value. One could make the same kind of argument for base-stealers…they are very rare and hard to find these days…but you don’t see sabermetricians arguing that base-stealing has twice the value it appears to have because it is unique.”

You HAVE to play a catcher every innings of every game.  You don’t have to steal a certain number of bases.

And how about that whole Endy Chavez versus Raul Ibanez thing?  Given the same playing time, the baseline is irrelevant.  If Endy has a 25 run advantage on defense and Raul has a 25 run advantage on offense, I don’t see how it’s possible for them not to help their teams win the same number of games…

Matt:  The idea is that the less defensive skill you demand at a position, the larger the pool of players you can then select from (searching for the best possible hitters).  The pool is largest at 1B (or DH in the AL), and thus we expect to find the highest average level of hitting there.  My point is that because there is more variation in hitting ability—overall, players are paid more for their hitting than their defense—I would expect to find the highest total value (offense and defense combined) at 1B. 

Sky:  ?

Sky was quoting some passages from MarinerCentral.com

This was discussed five years ago here:
http://tangotiger.net/UZR9903TT.html

Nice, Tango.  Thank you.  So all of these position adjustments you use include both a difference in “ability vs. average” and “impact?”  If you know what I mean?

Well, “on average” they do.  But, for specific cases, you have to go through the whole step-by-step of it.

Tango/Sky:  Ah, now I get it —I hadn’t read the thread. 

I think SABR Matt’s confusion about value and scarcity—he says “I think you’re completely off base to attempt to equate scarcity with value unless you’re talking only about monetary value”—is a common one.  But there is literally no such thing as value in baseball without scarcity.  The only reason Ibanez’s .837 OPS has value is because it is scarce.  If everyone could do it, then Ibanez’s hitting would have no value.  Baseball is a zero sum game—the whole point is to score more than other teams.  Only scarce skills can do that, by definition.

Now, scarcity does not ensure value.  A skill can be scarce but still not valuable.  But a skill cannot possibly be valuable unless it is scarce. 

And why you would pay someone to do things that don’t help you win—or refuse to pay for things that do help you win—is a true mystery.

Sky was quoting some passages from MarinerCentral.com

From one specific, adamant, and often rude poster who does not reflect the thoughts of others on the forum.

“And why you would pay someone to do things that don’t help you win—or refuse to pay for things that do help you win—is a true mystery.”

Well, winning itself for an owner may be a means to an end (say, maximizing net revenue) rather than an end in itself.  Winning is certainly a powerful way to help maximize revenue but it may not be the only (or in some cases perhaps not even the most efficient) way to do so.  If a slugging first basemen generates higher ticket sales or TV ratings than a slick-fielding center fielder, even if the latter might generate a couple of more wins, then the former may be worth more to the owner (especially an owner who does not believe a couple of wins will make the difference between making or not making the post-season) despite the latter’s higher contribution to win totals.

On the “And why you would pay someone to do things that don’t help you win—or refuse to pay for things that do help you win—is a true mystery.â€? front.

Wining helps, but for an owner, having All-Stars on his team also matters, even if there is a better player available to replace them.

Here is a link to a good study on what brings fans to a stadium:

http://armchairgm.wikia.com/Predicting_MLB_Attendance:_Multiple_Regression_Analysis_of_MLB_Attendance_and_Ticket_Prices

Looking at his numbers it looks like the “better” player needs to be ~6 wins (39777/6184) better than the previous All-Star for the team to replace him.

Studes, sorry if I didn’t explain it properly. I think you get it now, but for anyone who is confused, let me give it another shot.

Each position has two different components to decide its value: difficulty and opportunity. In order to properly value the difficulty, you have to use the opportunities at that difficulty as a multiplier.

So when SS has a +7.5 win adjustment, that’s actually X wins for difficulty * Y for opportunities = +7.5 wins.

If someone’s range drops they lose defensive value because opportunities decrease, not because the position got more difficult.

Maybe I am missing something, but shouldn’t the higher number of BIP for SS or 2B over 3B simply translate into a higher variance in defensive performance, and not require any sort of further adjustment?

Ok, thinking about it a little more, I can see some relationship in equilibrium.  Let’s suppose, as is true today, that 3B and 2B are equally difficult positions, but that 2B has twice as many chances as 3B (this is obviously false, but I’ll assume it for the sake of argument).  Then an average fielding 3B would be an average fielding 2B, while a +5 3B would be a +10 2b, a -5 3B a -10 2B, and so on.  In that case, teams can improve their performance by shifting their above average third basemen to second, and shifting their below average second basemen to third.  This is akin to simply moving your better hitters up the batting order.  Thus if 2B and 3B have the same objective difficulty but 2B has more fieldable balls, in equilibrium second basemen should be better fielders.

While this argument is valid, the problem is that the distribution of talent is not even close to optimal in current major league baseball, and was even further from it historically.  Thus, when it comes to actually computing the relative value of different positions, the fact that in equilibrium the average 2B is better than the average 3B is irrelevant.

That’s assuming you use 3B or 2B defensive difficulty as the baseline.

If you look at DH as baseline, then even if 3B and 2B are equally difficult (the X portion), 2B would be doubly valuable because they get twice the opportunities. Therefore X would be the adjustment for 3B, and 2*X would be the adjustment for 2B (because of twice as many opportunities).

And the -5 v. -10 comment as well depends on what you’re measuring. A player who misses 5 balls at 3B that the average player would have gotten would miss 10 balls at 2B (theoretically). But as a percentage of their overall opportunities, they would miss the same amount. And yes, you’re right, if the owners/managers were smart, in that case they’d move their better fielders to the position where more plays go, because the overall value of defense at that position would be higher.

Gee whiz, you all are well-thought out and smart and such. I’m just glad that I’m able to follow what you’re all saying

Why is the league average wOBA used to calculate batting runs above average (wRAA)? I would choose the average wOBA for that player’s lineup spot.

For example, Ryan Howard had a .366 wOBA last year, and the league average was around .330 (a guess). But the average hitter in the #4 slot according to baseball-reference had a .360 wOBA, showing that he was just above the average player at his lineup spot.

Zach, what’s the point? Teams tend to put their better hitters in the lineup spots that maximize their abilities, and their worse hitters in a spot where they come to bat less often. Why should we pretend that the average #4 hitter and the average #8 hitter were equally valuable to their team? After all, they weren’t.

“But the average hitter in the #4 slot according to baseball-reference had a .360 wOBA, showing that he was just above the average player at his lineup spot. “

Fine.

But, the #4 hitter gets paid alot more than the #8 hitter.  How much more?  Exactly the difference between what the average #4 hitter produces and the #8 produces.

That is, your two-step process can be turned into a one-step process by giving them all the same baseline to compare against.

I posted at Mariner Central:

If we are going to compare Endy to Ibanez specifically, then we really don’t need to know about replacement level, or positional adjustments, since they are both LF. Indeed, you don’t even have to compare against the league average. You only need to compare them to each other.

If Endy’s bat+baserunning is say 40 runs worse than Ibanez’ bat+baserunning, and if Endy saves 40 more runs with his glove+arm than Ibanez’s glove+arm, then that’s that. It’s really as simple as that.

The “40” is used for illustration, and I’m not taking a position either way. You guys tell me how much worse Endy’s offense is expected to be compared to Ibanez in 2009, you guys tell me how much better Endy’s defense is expected to be compared to Ibanez in 2009, and you will have your answer. Using runs as your denomination.

There is no need for all the mumbo-jumbo discussion I have with WAR, positional adjustments, and replacement level (in this particular case). So, go ahead, do it, post your numbers, comparing the two directly, and then accept your answer. It’s as simple as it sounds.