The Issue of Positional Inequality

As we rolled out the Positional Power Rankings over the last week, several people noted that there were some pretty large variances in the WAR totals between positions. Indeed, if you look at the totals by position, you see two distinct groups:

Catcher: +107 WAR
Center Field: +104 WAR
Third Base: +101 WAR
Left Field: +81 WAR
Shortstop: +80 WAR
Second Base: +80 WAR
First Base: +78 WAR
Right Field: +74 WAR

Side note: The projected WAR totals here are higher than observed WAR totals because projections essentially put a lower bound on bad performances, with very few players projected for negative WAR. Because of injuries and the non-normal distribution of variance around a player’s true mean, it’s easier to underperform than overperform projections, and inevitably, there will be below replacement level performances in MLB next year. Because of this lower bound, the replacement level in this system is more like 39 wins, so adjust accordingly. Now, back to the subject at hand.

C/CF/3B are all expected to perform at a similar level, and that production is quite a bit higher than the LF/SS/2B/RF/1B group. Instinctually, this feels incorrect, but I think it’s probably worth talking about the reasons for why positions might not be projected to provide the same value.

As far as I can see — and I very well might be missing something, so don’t take this as the authoritative last word on the subject — positions could be forecast for unequal production for three reasons:

1. The distribution of playing time could be more heavily skewed towards starters at those positions.

2. The positional adjustment aspect of the WAR formula could be overstating the gap in defensive value between positions.

3. The natural cycle of talent could have pushed better players towards those top three spots at this point in time.

The first one is pretty easy to test, as we can just look at the projected PA totals for each of the 30 projected starters. Here are those totals, by position.

C: 421 PA, 66% of allocated PAs
1B: 560 PA, 80% of allocated PAs
2B: 532 PA, 76% of allocated PAs
SS: 554 PA, 79% of allocated PAs
3B: 551 PA, 79% of allocated PAs
LF: 530 PA, 76% of allocated PAs
CF: 546 PA, 78% of allocated PAs
RF: 544 PA, 78% of allocated PAs

We can basically eliminate this as a primary reason for the differences. The gap between the highest and lowest playing time allocation is just over 800 PAs, and both of those spots actually come from the lower performance grouping. Starting CFs are not getting significantly more playing time than starting RFs or LFs. Starting 3Bs are expected to play less than starting 1Bs. Starting catchers are correctly expected to play the least of any position, and yet they still come out on top in terms of total projected WAR.

That leaves us with points #2 and #3, with the former representing a potential flaw in the WAR calculation and the latter simply being a reflection of the shifts in talent over time. These aren’t as easy to test as point #1 was, and the reality might be that it’s some combination of the two. But, let’s talk through both of those points real quick.

For those who aren’t aware, the positional adjustments are a necessary component because defensive metrics calculate a player’s performance relative to his peers at that position, but an average defensive shortstop is almost certainly a superior defender to an average defensive second baseman. Same for center fielders versus corner guys, and third baseman versus first baseman. The positional adjustment is in the calculation in order to reward players for their ability to defend the more important spots on the field. The scale of the position adjustments, per 162 games played:

Catcher: +12.5 runs
First Base: -12.5 runs
Second Base: +2.5 runs
Third Base: +2.5 runs
Shortstop: +7.5 runs
Left Field: -7.5 runs
Center Field: +2.5 runs
Right Field: -7.5 runs
Designated Hitter: -17.5 runs

In other words, catchers get the most defensive credit of any position, then SS, then CF/2B/3B, then LF/RF, then 1B, then DH. This mostly follows the traditional defensive spectrum first popularized by Bill James, though it slightly eschews the idea of “up the middle” defenders by equating third baseman and second baseman as equally challenging defensive positions. If you’re interested in where these numbers came from, I’d highly encourage you to read the conversations on positional adjustments at The Book blog over the last few years.

Because we can assume that Major League teams are not stupid and that they understand the distribution of balls in play, it’s a pretty safe assumption that center fielders — as a whole — are always going to be better defenders than corner outfielders, and shortstops are always going to be better defenders than third baseman or second baseman. However, offensive performance doesn’t always follow this same scale.

Last year, for instance, the average center fielder hit .265/.330/.418, while the average left fielder hit .261/.326/.431. Meanwhile, catchers (.248/.318/.400) outhit both shortstops (.257/.310/.388) and second baseman (.257/.318/.383), while third baseman (.266/.327/.427) hit nearly as well as both corner outfield spots. For the three positions that are projected significantly better than the others, we essentially find evidence that their most recent offensive performance is significantly better than it has been historically, relative to their peers at least.

However, this doesn’t necessarily answer the question. Does this mean that catchers, third baseman, and center fielders are just better hitters now than they used to be while also maintaining the same gap in defensive performance that has been seen in prior years — meaning that this is just a cyclical talent boom at those three spots — or are Major League teams redistributing their talent around the field in a way that is narrowing the gaps between positions both offensively and defensively?

Mark Smith wrote about the evolution of the catching position two weeks ago, noting that the recent trend has catcher offensive performance spiking while caught stealing rates are steadily falling, which might suggest that teams have been more wiling to trade defense for offense behind the plate in the last few years. Just from an anecdotal perspective, you could find support for that idea in the crop of starting catchers being handed jobs this year — Jesus Montero, Wilin Rosario, John Jaso, and Tyler Flowers are all bat-first catchers that have poor-to-awful defensive reputations, but they’re all penciled in as big league regulars for 2013. Of course, there are also some pretty terrific defensive catchers at the beginning of their careers as well, and there have always been bat-first catchers in Major League Baseball. Just pointing at those four doesn’t prove that teams are definitely shifting towards offense behind the plate.

The same is true in the outfield. We could point to Shin-Soo Choo going to CF and Mike Trout going to LF as examples of how the defensive gap between the positions could be shrinking, but then that might be somewhat offset by increasing CF playing time for elite defenders like Peter Bourjos and Ben Revere. Anecdotal evidence just isn’t going to answer the question definitively, as you can find an example or two to support any conclusion you want to come to. I’ve seen people write that Choo’s move to center is a sign that teams are moving away from overrating defense, while ignoring the fact that the Angels chose Bourjos over Kendrys Morales, the Nationals chose Denard Span over Michael Morse, and that the Rangers are replacing Josh Hamilton with Leonys Martin.

It certainly seems possible that the positional adjustments for outfielders were based on the traditional model of a speed-and-defense guy in center flanked by a couple of lumbering sluggers in the corners, and that teams are beginning to adjust their rosters to include more speed-and-defense guys in the corners, which would narrow the gap between CFs and corner guys in both offensive and defensive performance. Mark Smith wrote about this too, and noted that it seems to be that left fielders are seeing an uptick in stolen bases and a downturn in power, which would go along with that theory.

But, again, that’s not conclusive evidence that the positional adjustments are outdated. If you believe in the offensive-dampening effects of PED usage, it could be that more corner outfielders were negatively affected by the limitations of chemical enhancement than center fielders, and has disproportionately deflated their offensive performance. It could also just be a normal fluctuation with a handful of great players all coming into their primes at the same time. This has happened before, as center fielders hit better than right fielders for a stretch of time when guys like Willie Mays and Mickey Mantle were running around the outfield. We can seek to explain these kinds of variances as much as we want, but sometimes, it really is just randomness.

I’m at least content that we were able to eliminate an error in playing time projections as a major influence of the differences in projected WAR between positions. The question of whether the positional adjustments need, well, adjusting, is one we’ll continue to explore. It’s possible that corner outfielders are both worse hitters and better fielders than they used to be, which would lead to the fixed positional adjustments overrating center fielders and underrating corner OFs. It’s possible that teams are now trading defense behind the plate to get more thump in the line-up, and that the positional adjustment for catchers is too high.

At third base, though, I think we might just have a pretty exceptional crew of talent right now, at least relative to the weak crop of second baseman and first baseman. Guys like Miguel Cabrera, Evan Longoria, Adrian Beltre, David Wright, Ryan Zimmerman, and Pablo Sandoval are excellent players, and the position is deeper than I remember it being in some time. We can’t look at the fact that 3B are projected for 25 more WAR than 1B as clearly wrong. There are natural cycles of talent, and in looking at the groups of players at each position, the idea that first baseman are currently as good as third baseman does not ring true.

Positional inequality is a real thing, and it does vary based on the population of players in the sport at any given time. That said, it’s worth investigating whether or not the fixed positional adjustments in WAR are overrating some positions and underrating others, and you can bet we’ll be writing more about that subject in the coming weeks.



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Dave is the Managing Editor of FanGraphs.


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ALEastbound
Guest
3 years 2 months ago

Second base is way harder to play in 3…2…1

O's Fan
Guest
O's Fan
3 years 2 months ago

Obvious next step: compare the distribution of actual WAR between positions over the last 10-15 years and look for patterns.

O's Fan
Guest
O's Fan
3 years 2 months ago

OK, I just graphed the total WAR for each position 2000-2012. The three outfield spots almost always have the most WAR. Catcher usually had the least. Shortstop was usually near the bottom of the pack. Any way I can post my graph as an image?

Anon21
Guest
Anon21
3 years 2 months ago

Does anyone know if the catcher positional adjustment takes into account reduced playing time? If not, that would probably explain why catcher has the least WAR. If it does take into account reduced playing time, maybe injuries are the answer.

Nat
Guest
Nat
3 years 2 months ago

upload to imgur and post a link?

O's Fan
Guest
O's Fan
3 years 2 months ago

Thanks.

Here it is: http://imgur.com/OqKGOpe

jim
Guest
jim
3 years 2 months ago

nobody click that, it’s squid porn

Jaker
Guest
Jaker
3 years 2 months ago

This is what I would have figured which makes these projections really seem out of whack.

Rusty
Guest
Rusty
3 years 2 months ago

It’s amazing how much Bonds skews the early portions of that graph, O’s fan.

O's Fan
Guest
O's Fan
3 years 2 months ago

That’s true.

Also, CF have been on top by quite a bit for three years, thanks to a whole variety of different players: Trout last year, Ellsbury in 2011, Kemp, McCutchen…

DCN
Guest
DCN
3 years 2 months ago

We really are in a boom era for third base, like the late 90s/early 2000s for shortstop. When has the position ever been that deep?

DD
Guest
DD
3 years 2 months ago

In 5 years, 1B will become deep as those guys get moved down the spectrum but keep hitting.

DCN
Guest
DCN
3 years 2 months ago

You might be right. Cabrera is already a natural 1B, Zimmerman’s shoulder problems might move him pretty soon, and Sandoval can’t stay at first too long. Wright is slowing down too. Then there are some promising young players already at the position like Rizzo and Goldschmidt, and people like Votto who will be past their prime but still slugging.

TKDC
Guest
TKDC
3 years 2 months ago

I don’t see Wright or Longo moving off 3rd base. Sandoval is 5’11”, which is pretty short for a 1B (he’s more likely destined for DH).

DCN
Guest
DCN
3 years 2 months ago

Longo, no. But David Wright had three straight years of worse than -10 UZR defense before a great +15 last year. It was a monster year for him overall, and I’m not sure if he’ll regress or not.

Sandoval might want to stay in the NL, or play every day (mentally a lot of players hate the DH spot). He’s short, but not uniquely short. Prince Fielder is 5’11”. Jeff Bagwell was listed at 6 feet and probably wasn’t.

You might be right, but I wouldn’t rule it out.

johnorpheus
Guest
johnorpheus
3 years 2 months ago

It seems like at least one team, the Cardinals, agrees that second base isn’t any harder to play than third or some other positions. They keep trying to convert guys there.

guesswork
Guest
guesswork
3 years 2 months ago

“Side note: The projected WAR totals here are a higher than observed WAR totals…”

Except at SS, 3B, LF, CF, and RF. In fact, all three outfield positions last year were 20+ WAR more than these projections. I understand what the note was trying to emphasize though, and agree that it is an important point.

Daniel
Guest
Daniel
3 years 2 months ago

Observed means 2013 not 2012.

guesswork
Guest
guesswork
3 years 2 months ago

Point still stands, I doubt the production of the outfield in the entire league will suddenly fall by 17% in 2013

yaboynate
Member
yaboynate
3 years 2 months ago

Second base is way harder to play.

Ron Washington
Guest
Ron Washington
3 years 2 months ago

Firse Base, however, is incredibly hard to play.

Vladimir Guerrero
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Vladimir Guerrero
3 years 2 months ago

DH is tough because then you have to think about your at bats the whole game

Dave S
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Dave S
3 years 2 months ago

Your post is good but it incorrectly attributes Vlad with the ability to speak English.

LTG
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LTG
3 years 2 months ago

Only 15th century Romanian then?

DCN
Guest
DCN
3 years 2 months ago

That’s what a lot of people say. Some players can handle it and others can’t. Adam Dunn’s crazy drop-off was at least partly due to that, and Dunn always talked about how he liked to be in the field (even though he didn’t do very well).

RaoulDuke37
Guest
RaoulDuke37
3 years 2 months ago

Free Base!

Billy Beane
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Billy Beane
3 years 2 months ago

Good one Wash.

MrKnowNothing
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MrKnowNothing
3 years 2 months ago

Better athletes. The sport is no longer as dominated by purely skills as it may have once been. The days of guys who can only hit but can’t field so they’re stuck at 1B are lessening. As the crop of athletes gets better, you will find more players who can “play anywhere” so to speak. They will gravitate towards the more demanding positions, because those positions pay more. As they are now able to handle the defensive demands of the position, their offensive positives now become greater. Think A-Rod playing SS. His bat was obviously good enough to play anywhere. He would’ve been an elite 1B with his offensive numbers. But he was a good enough athlete that he could play SS (at a darn high level too).

As society has become grooming kids to become professionals from younger and youngers ages (and perhaps more importantly) as the game has expanded internationally, there is a greater pool of super athletes to choose from.

CSJ
Member
3 years 2 months ago

I noticed this earlier this month while I was working on some fantasy research. The fantasy replacement value is all over the place by position and is currently particularly high for catchers and outfielders (catchers are at their highest point since 1990). It put doubt in my mind as far using a constant value of replacement level. I suggest basing it off of a three or five-year average.

CSJ
Member
3 years 2 months ago

Obviously fantasy and real baseball have a different focus and purpose, but the larger point still stands.

jfree
Member
jfree
3 years 2 months ago

“Because we can assume that Major League teams are not stupid”

Not so sure this is a safe assumption. And it has little to do with saber.

Science
Guest
Science
3 years 2 months ago

I agree, I would like to see the math on ML teams non-stupidity.

Westside guy
Member
Member
Westside guy
3 years 2 months ago

“Because we can assume that Major League teams are not stupid and that they understand the distribution of balls in play, it’s a pretty safe assumption that center fielders — as a whole — are always going to be better defenders than corner outfielders”

And here I figured you’d notice the outfield Eric Wedge ran out there Thursday night… guess I was mistaken.

Clippers
Guest
Clippers
3 years 2 months ago

Yeah, Dave is not a front office scout so you can completely ignore his observation

Eric
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Eric
3 years 2 months ago

Not sure if this adds anything, but the gap in WAR between C/CF/3B and other positions is extremely consistent whether you’re looking at the AL or NL.

Tim
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Tim
3 years 2 months ago

Having more offensively-minded catchers and center fielders might matter for an average-based metric, but you’d need a ton of them to change replacement. The vast majority of replacement-level guys at those positions are still glove-only.

Bookbook
Guest
Bookbook
3 years 2 months ago

One thing to note: even the entire major leagues is a pretty small sample size. Put Cabrera back at 1b, and return Beltre and Wright to their previously scheduled declines (circa 2010), and all of a sudden the outperformance of the 3b position all but disappears.

Joe Girardi
Guest
Joe Girardi
3 years 2 months ago

“it’s a pretty safe assumption that center fielders — as a whole — are always going to be better defenders than corner outfielders, and shortstops are always going to be better defenders than third baseman or second baseman.”

What is this blasphemy?!

bohknows
Member
bohknows
3 years 2 months ago

Agreed. Joe, you yourself have a lot of experience dealing with a SS who is a worse fielder than his infield teammates.

brendan
Guest
brendan
3 years 2 months ago

sorry to beat a dead horse, but the BsR numbers for catchers are pretty small (max was < 3 runs). That could be inflating their total WAR significantly, since that are probably all in the -5 to -10 range

Jaker
Guest
Jaker
3 years 2 months ago

This comment deserves some attention. The BsR for catchers appears a bit too high. The average BsR last year was -1.2 among catchers with at least 30 PAs last year (which is about the cutoff of the FG positional power rankings for catcher). Whereas the average here is -0.99.

Kiss my Go Nats
Guest
Kiss my Go Nats
3 years 2 months ago

a very slow player can still get an ok BsR (not great) by making very good decisions on the base-paths while much faster players who run for the extra base all the time, but get caught more, will get punished for getting caught. Not running when most other players run and make it hurts your BsR score, but running and getting caught punishes you far more. BsR is measuring baseball smarts as much or more than raw speed. I would bet, on average Catchers have more baseball smarts than other positions and this is showing in BsR.

jfree
Member
jfree
3 years 2 months ago

My guess is that catchers are slower than molasses and they are thus reaping the benefits of complete baserunning inactivity. BsR being one of those saber stats where inactivity is generally better than activity and where a Brazilian donut salesman who doesn’t even play in MLB and doesn’t even know what baseball is has better BsR stats than most MLB catchers.

rusty
Guest
rusty
3 years 2 months ago

Conceptually, isn’t positional adjustment just a way of neutralizing the defensive component of WAR? So if Josh Rutledge is a -5 UZR/150 at short, but moved to second is +2 — so shortstop is estimated to be 7 runs more difficult to play based on his (hypothetical) experience.

At least that was my interpretation of posts like this http://www.insidethebook.com/ee/index.php/site/comments/uzr_positional_adjustments/ is that at least on the right track?

Newcomer
Member
Newcomer
3 years 2 months ago

This is correct.. to a point. But SS isn’t really 7 runs more difficult to play; the average SS is 7 runs better as a middle infielder than the average 2B.

UZR is a rating based on the average at the position. a -5 UZR/150 at SS means a player will allow five more runs than the average SS. A +2 UZR/150 at 2B means that player will prevent 2 more runs than the average 2B. So if teams were to switch their middle infielders, suddenly 2B would become 7 runs “more difficult” to play. Teams set the bar of how bad a defender they’re willing to play at a given position, and the group of players allowed to play the position sets the “difficulty,” and thus the positional adjustment.

Matt
Guest
Matt
3 years 2 months ago

Right, the idea is that a hypothetical all-around average defender, with no special talent that could be leveraged to a particular spot, would get roughly the same WAR no matter how he played on the field.

If he played SS, he’d be a -7.5 defender but get the +7.5 positional. At first, you’d expect him to be a +12.5 defender, and he’d get the -12.5 positional. So his WAR would be about the same. This guy who doesn’t have any leverageable defensive skills (like especially good wheels that would suggest he’d be better at OF relative to elsewhere) *should* get the same WAR no matter where he plays.

If the overall defensive talent pool at 2B suddenly went up, this hypothetical all-rounder would suddenly be getting less WAR if he played there versus other positions, because his UZR is compared to the average and would be lower than it should be, and that’s when you need to modify the relative positional adjustments.

Bip
Guest
Bip
3 years 2 months ago

You say that positional bonuses come because one position takes more skill to play than another. That is sort of true, but the most direct reason for positional bonuses is that replacement level offense for each of those positions are not the same. The question is, if I lose a player at a certain position, what is the likely amount of offense I’m losing? Shortstops get a positional bonus because replacement level offense is lower at shortstop.

If all the distribution of offensive ability was totally independent of a player’s position, then there should be no positional adjustment. A shortstop with a .330 wOBA has the same value as a first baseman with a .330 wOBA if minor league replacement shortstops and first basemen both average a .300 wOBA in the majors. Either way, losing one would mean subbing a .330 wOBA with a .300. The assumption in reality is that this wouldn’t happen, because some of those .300 wOBA shortstops in the minors could probably then play another position as an elite defender and give them a better chance at the bigs, which would then lower the offensive average for minor league shortstops.

The skill it takes to play a position is a factor that causes difficult positions to have lower offense in general, but it’s not what determines positional adjustment. If we find that the gap between the offense at each position for replacement level players has changed, we should change the positional adjustment to meet it.

Ruki Motomiya
Guest
Ruki Motomiya
3 years 2 months ago

Positional adjustment has seemed a bit extreme to me. It’s almost always better to play a bat-first person at a better defensive position, which seems counterintuitive, as long as they can do it at all.

For example, Miguel Cabrera’s -10 fielding at 3B is better than him playing DH or 1B every day due to positional adjustments. Heck, but a bad DH at SS and they need to be -25 to break even (+7.5 from playing SS, -17.5 from DH = 25 point difference from 0).

Matt
Guest
Matt
3 years 2 months ago

You don’t think Ortiz would be worse than -25 at shortstop?

Ian R.
Guest
Ian R.
3 years 2 months ago

Ortiz is a bad example because he’s left-handed. I imagine Billy Butler (who did play 3B early in his minor league career) could play a “good” enough shortstop to maintain his WAR.

Matt
Guest
Matt
3 years 2 months ago

Braun was -27 in 112 games at third his rookie year, and he’s a hell of a better athlete than Billy Butler. No, I don’t think Billy Butler could maintain a -25 UZR at shortstop. Not even close.

Ruki Motomiya
Member
Ruki Motomiya
3 years 2 months ago

I wouldn’t say most DHs can maintain a -25 at SS.

They probably can maintain a -20 at 3B, though, which is the breakeven point for that. And I wouldn’t be surprised if some more athletic 1Bs could play -20 SS (Which is the breakeven for 1B to SS).

Paul
Guest
Paul
3 years 2 months ago

I’ll concur on Butler. He was ludicrously played at both 3B and LF in the minors because he could throw 90 mph off the mound in high school, and Allard Baird was running replacement level players out there at 7 positions for several years in a row. Everybody knew Butler was a DH only since he was 14. This comp kind of reminds me of the Robert California era at Dunder Mifflin.

He would hit -25 within the first week of the season at SS. I am not exaggerating.

DCN
Guest
DCN
3 years 2 months ago

I think most DHs could easily do worse at shortstop than -25. They’d never make it through the season, though, because bad shortstop play gets exposed so quickly. Jeter’s been -14 or worse six times, and he’s much better than a lot of non-shortstops would be. Yuniesky Betancourt is -16.7, and he’s athletic and fast but just bad at positioning and reading the ball off the bat (and, generally, baseball). Someone like Adam Dunn, who’s able to cost teams over 25 runs in left field, could single-handedly torpedo a team if you put him in a prime defensive spot like that.

Ruki Motomiya
Member
Ruki Motomiya
3 years 2 months ago

What about at 3rd?

Newcomer
Member
Newcomer
3 years 2 months ago

I’ll just note that Tyler Flowers has been consistently viewed as a good defensive catcher for several years now. It’s true that he was viewed as an offense-first catching prospect when he first came over in the Vazquez trade, but he improved enough to shed that label after impressing scouts with his defense.

jim
Guest
jim
3 years 2 months ago

“Because we can assume that Major League teams are not stupid”

we can assume some teams aren’t, like the rays… but to say that, oh i don’t know, colorado and kansas city, aren’t stupid? i’m not so sure about that…

Keith
Guest
3 years 2 months ago

Sorry if this is a stupid q, but is there any bonus for being the third best shortstop vs. the third best second baseman or firstbaseman given that shortstops are harder to find?

Matt
Guest
Matt
3 years 2 months ago

Anecdotally it appears that more teams are placing value on keeping their most talented offensive players at premium defensive positions which may add to their perceived value.

So the 3B/C who are poor fielders aren’t moving to 1B, the SSs aren’t moving to 2B and the CFs aren’t moving to LF/RF.

I think this is not being caused as much at the major league level, but instead at minor league level where players who are clearly over-matched early-on defensive are remaining at their original position rather than moving to easier positions (I wonder if minor league statistic would back this up?). This may be to artificially inflate the trade value of the player OR it could be a result of players remaining in the minor leagues to develop for longer periods of time because smart teams are trying to maximize the number of years that they retain a young(ish) player at their peak. The extra time in the minors may enable these normally poor fielders to become passable by the time they reach the majors.

That Guy
Guest
That Guy
3 years 2 months ago

If there’s a SABR reason for that, then it’s lost on the A’s. They move prospects off of SS and C to get their bats to play at all at the major league level.

That’s just one team though.

Breadbaker
Guest
Breadbaker
3 years 2 months ago

Of course, if you throw with your left arm, you could be the most talented fielder of ground balls ever, but you’re not going to play the infield no matter what.

1st base
Guest
1st base
3 years 2 months ago

Except for 1st base, that is.

Baltar
Guest
Baltar
3 years 2 months ago

Much ado about nothing. I see no reason whatsoever to suppose that the aggregate WAR should be the same for each position, and I have not seen anybody who is concerned about it give a reason, other than Dave’s comment above, “Instinctually, this feels incorrect…” While that may or may not be true, it is certainly not a good reason to suppose they should be equal.
If they had all been equal in the past, but are suddenly not, that could perhaps be a reason for concern. However, O’s Fan’s excellent work above proves that this is false.

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