*Edit: Please see my later post as well, which corrects an omission here.*

Miguel Cabrera has a shot at the Triple Crown this year. No one has done it since Carl Yastrzemski. Is it really possible that he could win the Triple Crown and not win the MVP? Well, yes. Every advanced stats guy out there is trumpeting Mike Trout for MVP, with his “wins above replacement” (WAR) above 10 (next best in the majors is 6.8) and his 13 “total zone total fielding runs above average” (basically, this is the number of runs he has saved with his fielding, compared to an average fielder).

The discussion is eerily similar to the AL Cy Young conversation in 2010. Felix Hernandez won because he led the AL in innings pitched, ERA, and, most importantly, WAR, even though his win-loss record was a mediocre 13-12.

The 2010 Cy Young was a victory for sabermetricians. Pitchers can’t control how many runs their offense scores. All they can do is put up a low ERA and stick around for as many innings as possible. Strikeouts help too, since they reduce the risk of errors, and walks hurt, since fielders can’t do anything about a walk. There might be some cases where pitchers rise to the occasion in a close game to get a win, but for the most part, getting a “win” has little to do with pitcher skill after accounting for pitchers’ direct performance statistics.

**2012 MVP: the Saber-Men After Party?**

This time around, sabermetric thinking is stacked heavily against Cabrera (and the media is paying attention):

**RBIs are meaningless**After accounting for total bases and on base percentage in some way, RBIs have little to do with individual skill*.***Cabrera LEADS THE AL IN DOUBLE PLAYS**with 28, which is not captured by any traditional stat (granted, he has Austin Jackson’s high OBP in front of him, so he has lots of chances)**Trout steals lots of bases and never gets caught**(46 for 50 this year), which also isn’t captured by traditional metrics**Cabrera is a poor fielder**(10 runs worse than average at third base), Trout is a good fielder (mentioned above)

All these factors lead to Trout’s 10.4 to 6.7 WAR advantage over Cabrera. If voters take these numbers seriously, it seems that we’ll be looking at another win for the number crunchers.

**But What is WAR Anyway?**

Four extra wins is a lot and WAR is widely accepted as meaningful, but before I leap on the Trout-wagon, is WAR actually a good statistic? Here’s a snippet from Baseball Reference’s WAR explanation:

There is no one way to determine WAR. There are hundreds of steps to make this calculation, and dozens of places where reasonable people can disagree on the best way to implement a particular part of the framework.

Uh oh . . . hundreds of steps is never a good sign, especially when people can easily disagree on many of them. Increased complexity is not always better! Whether accurate or not, this is guaranteed to get you a stat that is (a) very hard to understand, (b) impossible to reverse engineer, and therefore (c) difficult to evaluate. Loosely, WAR tells you how many wins a player generates above what a “replacement player” would generate (i.e., a pretty good Triple A player that is readily available). It would add 500-1,000 words to this post to explain how it’s calculated, and I probably wouldn’t get all the details right because it’s nearly impossible to cover every assumption.

**A New Saber: True Runs**

I’ve been suspicious of WAR and other complex wins measures for awhile, and since I’m a Tigers fan, I figured this is as good a time as any to try an alternative. I’ll stick to the offensive side due to data constraints for now. I just want a measure of how many runs a player accounts for over the course of the season with his bat.* There will be none of this “replacement player” business, which introduces another parameter to be estimated (read: more obfuscation and error) with no clear improvement in determining the MVP.

Here’s the procedure:

- Using the last 20 years, regress total runs scored by each team each season on total singles, doubles, triples, homers, stolen bases, caught stealing, walks, strikeouts, double plays, and hit by pitches in that season
- Take the coefficients from this regression, multiply them by each individual’s stats, and add up the result

Two steps, that’s it. The team stats are readily available at Baseball Reference with 20 copy-pastes. I’ve made a few assumptions where “reasonable people can disagree,” so I’ll mention those:

- I included all outcomes of an at bat that are directly under a player’s control, with perhaps the exception of sacrifices (not very common, and many of these are probably accidents)
- I excluded all outcomes of an at bat that are outside a player’s control, with the exception of double plays, which are partially due to player skill (fleetness of foot, ground balls vs. balls in the air), but partially due to teammates and luck (who’s on base)**
- Due to data constraints, I don’t account for base running apart from stolen bases and caught stealing***

In honor of my True Wins football measure of team quality (which awards a half win for close wins *and *losses and a full win for blowout wins), let’s call the resulting measure “True Runs.” Like True Wins, True Runs is designed to be simple and understandable. True Runs has a regression in it, but the intuition is clear: the regression tells you how many runs are generated by each action on average, which I then apply to each individual’s stat line.

**Who’s the Real MVP?**

It’s the moment you’ve been waiting for . . . who’s the MVP according to True Runs? Here are the numbers for Cabrera and Trout, along with the regression coefficients (which I also find very interesting):

So, Cabrera has generated about 15 more runs on offense than Trout. It’s worth noting that Cabrera has 67 more plate appearances (Trout started this year *in the minors*, if you can believe it), giving them nearly identical 0.2 and 0.19 Total Runs per plate appearance. For MVP consideration, I think total True Runs is more important.

Cabrera has an advantage offensively, but I don’t want to ignore defense completely, because Trout is clearly better. For that, I’ll have to resort blindly to the Total Zone Total Fielding Runs Above Average mentioned at the outset. Cabrera is 10 runs worse than average third basemen and Trout is 13 runs better than average center fielders, so Trout seems to be 23 runs better on defense, overcoming his 14.6 True Runs deficit. However, these defensive measures are position-specific, and it’s unclear whether average runs attributed to center fielders and third basemen are the same or different. It seems likely that third basemen face more situations where fielding skill matters, though I have no hard evidence to back that up.

The long and short of it: it’s a close call. With defense (sloppily) included, Trout is about 8 runs better — less than one win using the usual approximation of about 10 runs per win. Maybe it wouldn’t be so bad if traditionalists got their way (I think they will if the Tigers make the playoffs and the Angels miss), and maybe the saber-men should reflect more on these incomprehensible stats before they use them to argue about the MVP.

**Bonus Round**

A couple interesting notes from the table above:

- A single (0.38 True Runs) is worth more than a walk (0.35 True Runs) and a walk is worth more than a steal (0.16 True Runs) because singles and walks can advance existing baserunners.
- The benefit of a steal (0.16 True Runs) and the cost of a caught stealing (-0.23 True Runs) suggest that running will increase True Runs whenever the guy has at least a 59% success rate. This is for the average situation. It does not make sense to send a 60% guy with Cabrera or Trout at the plate.

Below, I calculated True Runs for 19 top AL players. I’m pretty confident I got the top 10, though after that there might be some others that I missed (I listed offensive WAR for comparison):

There are some curious differences here. A quick glance suggests that True Runs rewards homers more than oWAR (Adam Dunn!), but I’ll have to investigate further. Also, looking at Cabrera’s and Trout’s oWAR, it’s hard to figure how Trout ends up so far ahead in total WAR. Yes, Trout is somewhat better than average on defense, but is he 2.5 wins better? Cabrera is worse than average by a similar amount and his WAR is only 0.7 lower than his oWAR. I wish I could tell you what’s going on here, but I’ve given up trying to understand the WAR spider web.

*I could convert the runs stat to wins in some way. Most wins stats divide by 10 or do something more complex, but that’s more steps and more parameters. I can’t think of a good reason why this parameter should be different for different players (I don’t believe in “clutch hitting”), so it adds nothing but unnecessary complexity.

**I included double plays in part because Cabrera has so many. I don’t want to discount that since I’m a Tigers guy, even though there’s never anyone on for Trout’s first at bat.

***Trout is surely a better baserunner than Cabrera, so this will hurt Trout, but it’s very hard to quantify without additional data. Using more data might help accuracy, but it also makes things more complicated, which I’m trying to avoid.

Reblogged this on Stats in the Wild.

Great post! Fun reading. I love regressions.

Cabrera saved two runs and the win tonight at third base.

Indeed, I was tempted to shore up Cabrera’s defensive numbers a little bit after tonight!

Errors would be easy to add to your model but would penalize players who get more chances. Players who get more defensive chances are probably more valuable, so adding throw outs (assists) and solo put outs would be nice, if accessible.

Right – this might be better than a fielding stat that is very difficult to understand, despite the weaknesses (e.g., it won’t do a good job of capturing range). I think the way to set it up is to run another regression with runs allowed as the dependent variable. I’ll have to think about what exactly to include, but it will be something like strikes outs, walks, hit by pitches, balks, hits allowed, errors, double plays, assists, etc. Would be interesting to compare to existing defensive measures at least.

here is a fact for you. Cabrerra gave up 1st base to 3rd sacrficiing so Prince Fielder would come to Detroit and play here , without that the Tigers would be in 4th place. BTW, only 5 people in history have achieved the triple crown and miguels runs and rbi’s and such have actaully clinched many of the games they would ahve otherwise lost and WAR is a meaningless BS stat that is useless.

I totally agree – Cabrera’s move to third is huge. He’s been more of an average first baseman in his career, as opposed to a below average third baseman. And you’re right that only 5 guys have achieved the Major League Triple Crown, but Cabrera won’t get that because of batting average (Posey in the NL is going to beat him for sure). He’s still got a good shot at the AL Triple Crown of course. The purpose of my post was to address whether the Triple Crown is truly valuable (scarcity isn’t so important if the stats are meaningless, and RBI are pretty meaningless, especially after accounting for home runs). I agree that WAR has problems, and hopefully my True Runs alternative provides something more meaningful.

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Uh, pretty sure park matters if you are trying to compare true player value. The actual raw numbers you post are pretty meaningless (totally biased toward those hitters in friendly parks). Also, you would never create a rate stats as per AB. It’s per PA.

Yes, I should have used PA (I changed this now), though it doesn’t make a huge difference for these two. The point here is to create something simple and understandable. I could have adjusted each stat to be park neutral by multiplying by (league-wide average for stat X)/(weighted average for stat X based on where you played your games), but this is not perfect either because it doesn’t account for opposing pitcher quality. You’re welcome to discuss park factors in relation to these statistics. My idea is to give a more meaningful aggregate stat to start with so that people don’t have to argue about whether Cabrera’s 44 homers or Trouts 48 steals and 8 triples are worth more. There’s often a complexity/simplicity trade off. I’m trying to start at the simpler side of that since baseball stats have gotten a bit out of control.

A better critique would have been that True Runs/PA is probably more important than I suggested, since the same number of True Runs will lead to more wins when accumulated over a shorter time frame. I’m going to do another post on this after the season is over, where I tweak things a little.

Park is simply huge. Any metric that compares players from different teams must adjust for park. I would be like, I dunno, doing a study on mortality without adjusting for age.

By a reasonable estimate of park factors, a player changing teams from Colorado to San Diego would expect to see his “True Runs” go down by a whopping 20% with no change in underlying skill.

In the case of the two players and the inidivdual season you are focusing on, you’d want to add 4% to Trout’s synthetic runs created, and subtract 2% from Cabrera’s. You end up with Cabrera 126.9, Trout 119.5 — an 8-run gap instead of a 15-run gap. Add in the defense (and yes, there is a reason why CFs are almost never great hitters — it’s a very difficult position to play), and Trout is a no-brainer. Certainly you could use indiv. stat park factors instead of general park factors but that would add complexity and frankly too much error with low freq. events like triples.

I agree that adjusting for quality of opposition is missing piece in this analysis but one that it is fairly complex to incorporate. But I don’t see the rationale for ignoring basic park adjustments.

Interesting – could you share your source for the park factors? My experience with these is that they are variable from year to year due to small samples, hitter quality (the “build your team for your ballpark” theory is part of this), and pitcher quality (as you note).

Though it’s not the goal of my stat to capture everything, I understand that parks matter – clearly some guys made careers out of Coors Field. An alternative way to quantify this in the MVP debate specifically would be to estimate how much more valuable a run is in Trout’s games vs. Cabrera’s (basically, convert the runs measure to a wins measure adjusted for what it takes to win in your average park). Your estimates above would put Trout ahead by almost an additional run, but again the difference seems smaller than the gap of four suggested by WAR, and I’d rather have the park discussion after the main, comprehensible stat is presented (it would have helped to mention this in the post), as we’re doing now.

I’m not sure I buy that CFs are not great hitters (though I’m also not sure this is important). Trout, Josh Hamilton (not always in center, granted), Austin Jackson, and Adam Jones are all in the top 20 in OPS in the AL. This doesn’t mean center field is easy – most likely, the fact that it’s hard attracts a few extremely talented guys that are good at everything.

Tyler, why aren’t you including outs other than GIDPs and Ks in the regression? Are you saying those outs aren’t within a players control, but other hits are? It seems like that exclusion would bias things in Cabrera’s favor.

I thought the fangraphs article was a pretty good WAR-free case for Trout

http://www.fangraphs.com/blogs/index.php/mike-trout-miguel-cabrera-and-measuring-value/

Yes indeed – that’s the tweak I mentioned in an earlier comment. Right now, I’m implicitly assuming that non-strikeout, non-double play, non-caught stealing outs are worth zero runs. A better way to go about it would be to assume that strikeouts are worth zero runs. I’ll post an update soon, but the upshot is that “usual outs” are worth about 0.13 runs themselves (since they often move runners), so it actually helps Cabrera a bit to include them (since I’m counting them as zero right now).

The fan graph article is interesting – their final conclusion rests on a runs contribution measure that I presume is similar to mine, but as is often the case with these things, I can’t find their calculation method on their website. Do you know how they’re doing it? Since it purports to be doing the same thing as me (albeit with a replacement level subtracted out . . . ), it should be easy to compare.

Ah ok, I thought you might have normalized regular outs to zero.

Yes, I had the exact same reaction to the fangraphs piece — I was hoping to tell you exactly what the difference was. It’s clear one difference is that they took into account more baserunning measures, but I can’t believe that would be it. And yes, even if there’s some complicated structural probability model in play, you should still be able to pick up a good first-order approximation with your methods.

I know it’s unfair to judge a player based on the team’s value (like King Felix in 2010). However, are there any stats that account for situations in games that actually matter? For example, BA when the game is within 5 runs. I don’t buy into “clutch hitting” stats either, but oWAR doesn’t account for fact that the value of a HR for when a game is out of reach is much less than in a close game.

It would be like comparing Jim Sorghi or Brian Scalabrine’s garbage time stats to an actual starter…

I definitely see your point on this. My usual approach is to ignore things like scenario (as most of the sabermetrics culture does) until someone proves to me that there’s something consistent about scenario-specific performance. E.g., if it’s possible for a guy to hit/field better in important situations, then that seems important.

However, as you mention, the Scallywag’s points are actually easier, because the other team isn’t trying as hard and he’s going against other scrubs. It’s the same in baseball. Guys pitch to contact with big leads (allowing more hits but getting quicker outs in the process), weaker pitchers are in the game, and guys put in lower effort (most likely).

Some of this is true even in a close game. Cabrera and Trout likely face better pitchers on average than guys at the bottom of the lineup. Teams also pitch around them, but not as much as they pitch around Prince Fielder, who’s protected by the enigmatic Delmon Young. If we truly want a measure of skill/performance independent of other players, it should account for all of this.

I guess it’s easy to see why WAR etc get so complicated, but I think that rather than trying to put everything in one number (WAR guys are always backtracking and talking about how imprecise it is), it’s better to start with something simple and then layer on some additional discussion.

I wouldn’t say most of the community totally ignores it, because Win Probability Added would implicitly take into account performance in clutch performance. At the very least it’s better at looking at a couple of handpicked arbitrary situations like “avg. with runners in scoring position and 2 outs.” I’d been ignoring baseball most of the year (thanks Red Sox) and went into this Trout-Cabrera with the same prior as you, that Trout’s advantage must be due to some lame WAR methods based on strange replacement player estimates. But seeing that Cabrera had no significant edge in WPA (and actually trailed) persuaded me to the Trout side.

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Nate Silver’s take on the argument: http://fivethirtyeight.blogs.nytimes.com/2012/11/14/the-statistical-case-against-cabrera-for-m-v-p/

Interesting – Silver is far more trusting of some of these advanced stats than I am, which surprised me a little. I have a few other nitpicks, but I think the general conclusion is hard to refute (and similar to what I find here): Cabriera and Trout had pretty similar value at the plate, with Trout looking a little better if you look at value/plate appearance, since he had fewer games (this could be considered good or bad). Beyond that, It’s hard to argue that Cabrera matches up with Trout on defense and baserunning, but I’m just not as confident as Silver that new statistics value these contributions accurately.

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