Brandon Inge, Superstar

Brandon Inge, Superstar.

How many wins is chemistry worth? Do nice guys really finish last?

As a Pirates fan since birth, I’ve grown used to my baseball fandom engendering a sense of sympathy in others. Born in 1989, I came of baseball-loving age in the mid-nineties, immediately following the halcyon Bonds/Bonilla/Van Slyke & co. days and immediately preceding the less-halcyon days of the Aramis Ramirez-for-Bobby Hill trade, “Operation Shutdown,” the expansion-drafting of Joe Randa, Pat Meares’ general existence, the Moskos pick, the Matt Morris trade . . . (list of soul-crushingly depressing baseball stories truncated for reader’s mental health).

And yet I remained faithful, despite having no conscious memory of a Pirates team being anything other than heartbreakingly awful. I’ve since likened this experience, in conversations with friends, to Linus sitting in the pumpkin patch each year, waiting for the Great Pumpkin to appear. It sometimes seemed that the Great Pumpkin would never come.

It’s ironic, then, that in the year that finally saw the Great Pumpkin arrive in Pittsburgh (2013), the same city also witnessed the end of the career of one Charles Brandon Inge.

Inge, nicknamed ‘Cringe’ by some of the crueler Pittsburgh faithful for his anemic .181/.204/.238 batting line during the 2013 campaign, was at that point in his thirteenth season as one of baseball’s premiere utility men, playing every position on the diamond during his career. During his peak, he was a slick-fielding third baseman who also clubbed 27 HRs en route to a 4.1 fWAR season in 2006. But by 2013, Inge was 36 and on his way out of the league. Signed before the season to provide depth behind Pedro Alvarez and Neil Walker, Inge’s poor performance eventually led to his unceremonious release by the Pirates at the end of July.

And yet, this article has less to do with Inge’s on-field merits (which, as the previous paragraph suggests, were both significant and significantly variable), and more to do with Inge’s impact off the field. Inge won the 2010 Marvin Miller Man of the Year Award, given to the player whose “performance and contributions to his community inspire others to higher levels of achievement,” for his work with C.S. Mott Children’s Hospital. A frequent visitor to C.S. Mott, Inge also donated $100,000 for a new infusion center to treat pediatric cancer and twice hit home runs for young cancer patients. Dude’s a nice guy.

Perhaps more relevant, though, is pitcher and noted stathead Brandon McCarthy’s statement that Inge and fellow veteran Jonny Gomes had been worth twenty-four wins to the 2012 Athletics through chemistry alone. Normative ethics aside, it’s impossible to measure the moral character of a man—but we can measure, or at least attempt to quantify, the impact he has on his teammates.

Intrigued, I set out to determine whether Inge, patron saint of chemistry and all-around good guy, really made such a gigantic difference to his teammates’ performance. Mine is not the first investigation into this topic—Baseball Prospectus’ Russell A. Carleton examined the same issue in March of 2013, and there have been numerous attempts to place a valuation on chemistry over the years. But as you’ll see, there are some methodological differences to our approaches, and the differences expose some interesting conclusions.


There is no ironclad way to assess Inge’s potential effect on his teammates, short of cloning entire teams of players, randomly assigning Brandon Inges to some of them, and having them play a large number of seasons.

In order to determine Inge’s value as accurately as possible, I can’t simply measure his teammates’ performance—I’d just be concluding that Inge played with good or bad teammates. Instead, I need to develop a counterfactual, or a method of estimating how we could’ve reasonably expected Inge’s teammates to play in his absence. Fortunately, an excellent one already exists—a ZiPS projection. ZiPS, to my knowledge, does not have a ‘played with Brandon Inge variable,’ so it should be unbiased. Carleton instead used an AR(1) covariance matrix to try to adjust for player talent, but given that ZiPS explicitly incorporates past performance with a view to projecting, as accurately as possible, how a player will perform in the upcoming season, I believe it is a suitable tool.

I chose wOBA as the dependent variable for our study—while Carleton looked at multiple indicators (BB%, K%, etc), one, all-encompassing measure of players’ offensive performance seems best suited to answering the question, “Do players perform better with Brandon Inge on their team?”

In order to develop the requisite dataset for this analysis, I downloaded every player-season since 2006[1] from FanGraphs’ leaderboards and filtered the data to include only those players who amassed at least 200 plate appearances. This yielded 3130 player-seasons. Next, I created a binary variable called ‘IngeTeammate,’ with a value of ‘1’ if the player was on Inge’s team during the given season (and not Inge himself), and ‘0’ if he wasn’t. For the 2012 season, the only one in which Inge played for multiple teams, I counted Inge as having played for the Athletics, with whom he spent the majority of the season.

The next part was a bit tricky—bringing in the ZiPS projections. The latest years, the ones for which ZiPS has been featured on FG, were easy—data was readily available, wOBA already calculated, and records already associated with a player id. But wading deeper into the past unearthed some issues—in order to match records, I had to manually match player names (including the two Chris Carters, and, apparently, two Abraham Nunezes . . . Nunezii . . . who knows?) and hand-calculate ZiPS-projected wOBA for older player-seasons using the weights provided on the FanGraphs Guts page. One potential issue with some of the oldest data is the lack of projections for things like intentional walks and sacrifice flies.

However, forging through all of the record-matching and manual wOBA-calculating eventually yielded ZiPS wOBA projections matched to 3088 of the 3130 player-seasons. Of the 42 unmatched seasons, only one was an Inge teammate (2010 Brennan Boesch). 81 of the 3088 matched seasons were Inge teammates. So unless you think ZiPS would have pegged Boesch, a relatively unknown 25-year-old at the time, for a significantly better performance than the .322 wOBA he posted in 2010, the unmatched records probably didn’t have a huge effect.

What we’re left with is data that look like this:

Year Name Team Age PA IngeTeammate ZiPS wOBA wOBAdiff wOBA
2010 Jose Bautista Blue Jays 29 683 0 0.322 0.100 0.422
2010 Jim Thome Twins 39 340 0 0.343 0.096 0.439
2010 Wilson Betemit Royals 28 315 0 0.302 0.084 0.386
2010 Josh Hamilton Rangers 29 571 0 0.365 0.080 0.445
2010 Chris Johnson Astros 25 362 0 0.286 0.067 0.353
2010 Carlos Gonzalez Rockies 24 636 0 0.350 0.063 0.413
2010 Justin Morneau Twins 29 348 0 0.387 0.061 0.448
2010 Paul Konerko White Sox 34 631 0 0.361 0.056 0.417
2010 Joey Votto Reds 26 648 0 0.383 0.055 0.438
2010 Danny Valencia Twins 25 322 0 0.299 0.052 0.351
2010 Giancarlo Stanton Marlins 20 396 0 0.305 0.051 0.356
2010 Miguel Cairo Reds 36 226 0 0.288 0.051 0.339
2010 Will Rhymes Tigers 27 213 1 0.288 0.050 0.338
2010 Tyler Colvin Cubs 24 395 0 0.301 0.050 0.351
2010 Michael Morse Nationals 28 293 0 0.328 0.049 0.377
2010 Adrian Beltre Red Sox 31 641 0 0.343 0.048 0.391
2010 Ryan Hanigan Reds 29 243 0 0.321 0.048 0.369
2010 Yorvit Torrealba Padres 31 363 0 0.279 0.044 0.323
2010 Matt Joyce Rays 25 261 0 0.321 0.043 0.364
2010 Aubrey Huff Giants 33 668 0 0.344 0.043 0.387
2010 Drew Stubbs Reds 25 583 0 0.295 0.043 0.338
2010 Andres Torres Giants 32 570 0 0.316 0.042 0.358
2010 Corey Patterson Orioles 30 341 0 0.274 0.042 0.316
2010 Austin Jackson Tigers 23 675 1 0.288 0.041 0.329
2010 Brett Gardner Yankees 26 569 0 0.306 0.040 0.346
2010 Colby Rasmus Cardinals 23 534 0 0.329 0.040 0.369
2010 Andruw Jones White Sox 33 328 0 0.323 0.039 0.362

In the above table, wOBAdiff refers to the amount by which the player outperformed his ZiPS wOBA projection. A negative number would indicate that a player underperformed his projection. So Jose Bautista outperformed his 2010 projection by .100—multiplying by 1000 tells us that this was 100 points of wOBA. It was good to be Joey Bats in 2010.


If we look at the mean wOBA deviation (in terms of points of wOBA) Inge teammates and non-teammates experienced from their ZiPS projections, we see the following results:

  Player-Seasons Total PA Mean Weighted Diff. (wOBA pts)
Mean Unweighted Diff. (wOBA pts)
Non-Teammate 3007 1,378,732 -3.09 -4.62
Teammate 81 37,965 4.30 4.24

In other words, if we weight by plate appearances, Inge teammates outperformed their ZiPS projections by an average of about 4.30 points of wOBA. All other players underperformed their projections by an average of about 3.09 points. Which might not seem like a lot, but if you were to apply that 7.4 wOBA difference to an average-hitting team over a 6000 PA team-season, that’s roughly 34 runs. So 3.4 wins. Which is, you know, quite a bit. The unweighted version is even more extreme, suggesting that players with lower numbers of PA have outperformed their projections even more when teamed with Inge.

If we simply run a regression including the independent variables IngeTeammate (binary) and age and the dependent variable wOBAdiff (unweighted), we can express the story another way:

wOBAdiff = 0.0127064 + (IngeTeammate* 0.0090544) + (age* -0.0005993)

I included age as a control because ZiPS projections, as you can see from the model above, tended to slightly overproject older players in comparison to younger players, and therefore I needed to consider the possibility that Inge simply benefitted from playing only with young players (he didn’t).

Note that in the model above, 0.001 corresponds to one point of wOBA (i.e. a hitter moving from .323 to .324 would have gained a point of wOBA). The r-squared of the model is absurdly low (0.006), but that’s to be expected—after all, I’m not trying to assert that Brandon Inge is responsible for all or even a significant part of the variation between MLB players’ expected and actual performance. More importantly, the variable ‘IngeTeammate’ is significant at a 98.4% threshold.

Considering the possible influence of aging is interesting, as the Inge difference is even more pronounced among younger players, or those whom he allegedly mentored while playing with the A’s. If we filter the data above to include only players 27 and younger, the table looks like this:

  Player-Seasons Total PA Mean Weighted Diff. (wOBA pts)
Mean Unweighted Diff. (wOBA pts)
Non-Teammate 1241 568,944 -0.50 -2.09
Teammate 30 14,298 16.58 17.27

We’re starting to run into some serious sample size issues that make me uncomfortable drawing any particularly bold conclusions, but young players who play with Inge have done really, really well, collectively knocking the snot out of their ZiPS projections. There are problems with extrapolating this to a 6000 PA team-season, given that presumably an entire team won’t be composed of young players, but if one did so the result would be a ridiculous 78.6 runs of additional value.

The table below lists every 27-and-under player season for which the player was an Inge teammate:

Year Name Team Age PA ZiPSwOBA wOBAdiff wOBA
2008 Matt Joyce Tigers 23 277 0.275 0.084 0.359
2011 Alex Avila Tigers 24 551 0.308 0.076 0.384
2013 Jordy Mercer Pirates 26 365 0.282 0.051 0.333
2010 Will Rhymes Tigers 27 213 0.288 0.050 0.338
2012 Chris Carter Athletics 25 260 0.319 0.050 0.369
2011 Brennan Boesch Tigers 26 472 0.300 0.048 0.348
2007 Curtis Granderson Tigers 26 676 0.344 0.044 0.388
2010 Austin Jackson Tigers 23 675 0.288 0.041 0.329
2012 Yoenis Cespedes Athletics 26 540 0.328 0.040 0.368
2010 Miguel Cabrera Tigers 27 648 0.399 0.032 0.431
2013 Jose Tabata Pirates 24 341 0.308 0.032 0.340
2012 Josh Reddick Athletics 25 673 0.296 0.030 0.326
2013 Andrew McCutchen Pirates 26 674 0.365 0.028 0.393
2013 Starling Marte Pirates 24 566 0.317 0.027 0.344
2006 Omar Infante Tigers 24 245 0.306 0.016 0.322
2008 Curtis Granderson Tigers 27 629 0.358 0.015 0.373
2009 Clete Thomas Tigers 25 310 0.302 0.015 0.317
2012 Josh Donaldson Athletics 26 294 0.286 0.014 0.300
2011 Andy Dirks Tigers 25 235 0.297 0.011 0.308
2013 Neil Walker Pirates 27 551 0.328 0.005 0.333
2013 Pedro Alvarez Pirates 26 614 0.327 0.003 0.330
2006 Curtis Granderson Tigers 25 679 0.335 0.000 0.335
2009 Miguel Cabrera Tigers 26 685 0.407 -0.005 0.402
2010 Alex Avila Tigers 23 333 0.306 -0.007 0.299
2011 Austin Jackson Tigers 24 668 0.315 -0.010 0.305
2012 Jemile Weeks Athletics 25 511 0.304 -0.028 0.276
2012 Derek Norris Athletics 23 232 0.304 -0.029 0.275
2006 Chris Shelton Tigers 26 412 0.380 -0.033 0.347
2013 Travis Snider Pirates 25 285 0.310 -0.039 0.271
2008 Miguel Cabrera Tigers 25 684 0.419 -0.043 0.376

It’s not as if one year is hugely skewing the results—pretty much every year, whichever young players happen to be playing with Brandon Inge outperform their projections. The graph below illustrates the mean wOBA differential younger Inge teammates exhibited each season. I would’ve imagined, prior to viewing these results, that Inge’s positive ‘effect’ might’ve been almost entirely a product of the 2012 Athletics, but this doesn’t seem to be the case—outside of the 2006 Tigers (when Omar Infante, Curtis Granderson, and Chris Shelton collectively underperformed their ZiPS projections by a modest average of ~5 points of wOBA), Inge’s younger teammates have outperformed ZiPS every single year in the sample.

Perhaps, one could say, Inge has simply benefitted from playing on teams run by intelligent front offices. After all, the Tigers, Athletics, and (more recently) the Pirates all have reputations as relatively savvy management teams. Maybe they’re just collectively able to out-forecast ZiPS.

When we look at ZiPS wOBA differentials by team, however, the Tigers (+1.36 points of wOBA), Athletics (+0.11) and Pirates (-0.31) all had weighted mean differentials less than the Inge gap. The average over all teams was -2.89, so while all three front offices ‘beat the market,’ so to speak, they still don’t explain the huge Inge effect. It looks as though there’s something here.

After observing the results for Inge, I was curious about whether other veteran players might also exhibit similar correlations—while we’d expect to find no correlation with ZiPS wOBA differential for most players, it might be the case that, as with Inge, patterns emerge. Specifically, I looked at two players with diametrically opposite reputations—A.J. Pierzynski and Jonny Gomes. Below, I replicate the initial summary table used for the Inge analysis and note the magnitude of the effect:

A.J. Pierzynski

  Player-Seasons Total PA Mean Weighted Diff. (wOBA pts)
Mean Unweighted Diff. (wOBA pts)
Non-Teammate 3004 1,375,450 -2.75 -4.29
Teammate 84 41,247 -7.65 -7.87

The game’s most hated player didn’t fail to disappoint, as his teammates collectively underperformed their ZiPS projections by an additional of 4.9 points of wOBA when compared to non-teammates, an effect worth -22.6 runs to the team over the course of a full season. I should note that I assigned Pierzynski to the 2014 Red Sox (with whom he spent considerably more time) instead of the 2014 Cardinals—both teams underperformed their ZiPS projections, but the Red Sox did so by a larger margin.

Pierzynski’s unweighted results, while still negative, are less damning, and using a regressed model reflects this:

wOBAdiff = 0.0128794+ (AJTeammate* -0.0033689) + (age* -0.0005939)

The intercept and coefficient for age are, understandably, almost identical to those I observed in the Inge model. The significance level for AJTeammate, however, is only 64.1%, suggesting that we can’t really conclude much of anything with the same level of confidence as for Inge.

Still, twenty-plus runs is a non-negligible amount, and Pierzynski’s numbers have been negative across all four teams for whom he’s played (White Sox, Rangers, Red Sox, Cardinals). It may be that more historical data would reveal a broader trend, given that we’ve limited our sample size to only the latter half of Pierzynski’s career.

Jonny Gomes

  Player-Seasons Total PA Mean Weighted Diff. (wOBA pts)
Mean Unweighted Diff. (wOBA pts)
Non-Teammate 3000 1,376,613 -3.05 -4.56
Teammate 88 40,084 2.58 1.52

The phenomenally-bearded Gomes, Inge’s running partner in the Brandon McCarthy quote that triggered this analysis, also appears to be a potential chemistry star, though his results are less extreme than Inge’s. His teammates outperformed non-teammates by 5.6 points of wOBA, worth an estimated 26 runs per season.

wOBAdiff = 0.0124387+ (GomesTeammate* 0.0055032) + (age* -0.0005873)

The effect, as with Pierzynski, is not statistically significant—the significance level is 87.4%.


We can’t make firm statements about causality from this analysis, but we can say pretty conclusively that being on the same team as Inge during the last nine years correlates positively with hitting better than ZiPS projects you to hit.

Maybe you don’t believe Inge should get credit for the extra 3.4 wins of value each year. We don’t have a ‘chemistry above replacement’ metric to account for the fact that some other player with a modicum of veteranosity might plausibly have a positive effect if analyzed the same way. And there’s no feasible way to develop one on the horizon—you can only start to do this sort of analysis retrospectively, and it requires a large number of plate appearances and player-seasons before we can conclude that any pattern has emerged. I’m not really arguing that Inge deserves all the credit for his teammates’ overperformance, only that we have reason to believe a nonzero effect may exist.

But let’s entertain, for a minute, the possibility that the 3.4 win-per-season gap we see *is* entirely attributable to Inge. That maybe all the minute, unnoticed interactions between players over the course of a season can add up to improved performance at the plate. The effect could even be greater than 3.4 wins—I didn’t examine pitching and fielding at all. After all, everything we know about human psychology suggests that happier workers are more productive, and I’ve yet to hear any compelling reason that ballplayers constitute an exception. We sometimes, in the analytics community, fall into the trap of assuming that because we can’t measure something accurately, it doesn’t deserve a meaningful place in our analysis. And yet our inability to measure a phenomenon is not proof of its nonexistence—just ten years ago, we lacked meaningful metrics for catcher framing, for instance.

Perhaps Inge contributed more hidden value over the last decade than anyone this side of Jose Molina, and Brandon McCarthy’s twenty-four wins were, if still hyperbole, grounded in a subtle truth. 3.4 wins currently has a market value north of $20M, making Inge a substantially underpaid man over the course of his career.

It’s a shame, on some level, that it’s only after he’s retired that we recognize the unheralded Inge for who he might secretly have been: Brandon Inge, Superstar.


[1] Before 2006, I struggled to find ZiPS projections in a readable format to develop the counterfactuals.

Data retrieved from FanGraphs and Baseball Think Factory.

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9 years ago

Would love it if you could share your data set

9 years ago

Interesting. Did you happen to look at the results for each year in the data set? Were they consistent? Did the gap grow (or shrink) as Inge aged?

ZiPS appears to be biased, which I found odd. Perhaps this has something to do with the 200 PA cut off. Regardless, I don’t think this affects your analysis directly.

Inge’s teams were overall very good teams (from 2006 on). Inge may have helped, but you could simply be measuring the effect of being on a good team. I know you don’t have the data, but 2003 would be an interesting case study, considering Inge was on the worst team in modern history.

Overall, my guess is that there may very well be an Inge effect, but I don’t think it was quite 3.4 wins a year. Nonetheless, this was a good starting point.

9 years ago

The idea of using actual vs. projected performance was ingenious. Even with the difficulties of culling out possible biases in the projection system, at least you have a fair chance of doing that objectively. Which is very cool.

I wonder if chemistry is itself very dependent upon the makeup of the remainder of the team. Here are some possible dimensions of this:

– Whether there are other “plus-chemistry” guys already on the team (as you and Carleton both note)

– The age/experience distribution of players on the team

– The number and severity of clubhouse “cancers” on the team

– The number of “cardboard cutout” personalities on the team

It wouldn’t surprise me if analysts working for some teams have already taken information on player personalities, which they could probably categorize fairly well, and studied the impacts of different mixes of team personalities. This might mean that some baseball insiders might have a fairly good handle on the true value of chemistry, something that analysts on the outside can only guess at.

9 years ago

Really cool article. Can you run this for every player and find the ‘leaders’ of leadership?

A wacky theory:
Is it possible that Inge’s utility status itself helps the team? A player who can play many positions allows other players to perform a bit better by gaining the platoon advantage in more situations, get rest when needed, etc.

What does Ben Zobrist look like in this context?

This Is My Post
9 years ago

This is fascinating. Would love to see research into what happened to projections/results after, say, Inge or AJ left their respective teams, what they did the next year without them. Great article though.

Mike Magazine
9 years ago

Very interesting Joshua…i will share with my class at uc…who says chemistry is distinct from analytics…

9 years ago

This is a very interesting concept. It reminds me of conversations about the value of a quality ace on a pitching staff, like a Greg Maddux, and the affect he has on other pitchers. It would be great to apply this same theory for pitchers to see the value of a pitcher on his days off. Good stuff!

Ian Sales
9 years ago

Love the article! Email me!

9 years ago

a few other thoughts:

you mention that there is an optimistic bias in the zips projections, but do you correct for it in your reported values?

since you are always dealing with players from one team, i think the effect of an unbalanced schedule is potentially significant, and so you would really need to address quality of competition

also, another aspect of always playing on good teams is the whole “exponential nature of offense”. teams with above average hitters overperform the average wOBA of their lineup. see this link. I think this must be accounted for as well if you decide to continue with wOBA

9 years ago

thanks for the responses, some more thoughts

if you notice a population bias, wouldnt it be more rigorous to just remove it from the population than to assume youve identified the only variable that may have an asymmetric affect?

in addition to the age asymmetry, we know that zips is less accurate for players that had less prior data to project on. perhaps another worthy control is service time/prior career PAs. if inge consistently played with players that had below average prior data to work with, the projections would have more variability, increasing the chances of finding extremes like the one you found here.

i still think quality of competition is really important and on the same order of the effect found here. i went through the data for 2006. The tigers played 19 teams and the weighted average (by # of games played) of their opponents ERA was about 2 % worse than average, which would have been good for an additional 12 runs. I dont think its likely that opponents will get baked into the projections simply because even without player turnover, pitcher performance and TBFs/season has high year to year variation.

another thought: for the years where no projected woba was provided, you said that you were calculating woba using each year’s constants as reported on fangraphs. however, those constants are derived from each of those season’s actual data, which occured after the projection. For 2013, the end of season constants applied to the projected wOBA components resulted in wOBAs on average 0.002 higher than the actual preseason projected wOBAs. the wOBA constants change at different rates so could have an asymmetric affect on different types of players. For instance, the HR constants change by the greatest rate year to year and the hitters projected to be in the top quartile of HR rate had a wOBA calculated from end of season constants of .003 greater than the projected wOBA (a difference from the mean effect on the same order of the effect you attribute to inge). Perhaps the cepesdes/Reddick/mccuthen type seasons are being overrated.

Adrian Carnelutti
9 years ago

Good article. If you get time I would be interestede to see a statistical look at the effect that AJ Burnett has had on the Pittsburgh pitchers