MVN: Most Valuable Network

A few weekends ago, I was enjoying a leisurely dinner with a friend of mine from high school.  He hit on the waitress, like he usually does, and we spent a good three hours talking about old times (including that one time when our friend Steve... oh nevermind), work, and of course, the Indians.

A brief transcript, that might have been slightly altered from the original, but not by much.

Friend: Pizza, you're the world's foremost expert on baseball, not to mention incredibly smart, debonaire, and otherwise better than me.  What do you think will happen this off-season with the Indians?
Pizza Cutter: Not really sure yet.
Friend: Oh, come on, you are the smartest guy I know, and your knowledge of baseball is un-matched.  Surely, there's something brewing.
Pizza Cutter: It's really hard to tell.  They might, they might not.
Friend: Do you think that the Indians will trade Kelly Shoppach?
Pizza Cutter: Funny that you mentioned Shoppach.  I just happened to be doing some research that is pertinent to this very issue.  In fact...

Shoppach is one of the more interesting names on the hot stove this winter.  He's a catcher, and everyone needs one of those, lest (as Casey Stengel reminded us) you have too many passed balls.  But Shoppach, in addition to strapping on the tools of ignorance, is also good at something else.  He's one of the most purely powerful hitters in baseball.  In fact, when I ran my power scores for the 2008 season, Shoppach rated as the 11th most powerful hitter in baseball (min 100 PA).  Well, that is when he actually hits the ball.  When I ran my plate discipline numbers for Shoppach in 2008, he came in near the bottom of that list.

Shoppach got his big chance in 2008 when Victor Martinez went down with an injury early in the year and didn't re-appear until late August.  In 403 PAs, Shoppach hit 21 HR, to go with 27 doubles, and... 133 strikeouts.  He'll be 29 next year, and with Martinez back and healthy, Shoppach is a backup that would probably make some team looking for an upgrade behind the plate rather happy.  Throw in the fact that the Indians still have a few needs here and there, so perhaps a trade could be worked out.  Then again, maybe they shouldn't.  V-Mart is an injury risk and there's been talk of a permanent move to first base, and so it would be nice to have a guy like Shoppach around just in case.  You can never have enough pitching.  Or catching.

But oh my, what to do about those strikeouts!  Shoppach does hit about 20% of his fly balls out of the yard (nice!), but is that worth a strikeout rate over one third?  It's the curse of a power hitter to strike out a lot... but then again young players do learn things.  Maybe since he's only 29 this coming year, things might get better?  If Shoppach could cut back on his strikeout rate by even five percent, the Indians would have a monster hitter on their hands.  And at that point no matter what they get back, in hindsight, trading Shoppach would probably look about as silly for the Indians as a team trading away Brandon Phillips... oh right...

Does plate discipline really improve with age?  We know that as players age, they walk more, but that has less to do with their plate discipline skills than the fact that they simply swing less often.  Still, there might be something to be learned as players grow up.  They've seen more pitchers and pitches over the years.  Maybe, just maybe, there's hope for Kelly Shoppach.

I took this opportunity to break out a new statistical tool called mixed linear modeling.  It's not really new since it's actually the process that gives me intra-class correlation, which I reference quite a bit, but MLM is a more fully developed case of intra-class correlation.  It's regression-based, but allows for the use of repeated measures, as well as covariates.  It also allows for fixed and random effects to be used (and if I wanted to, hierarchical terms).  If you don't understand that last sentence, just nod and say, "Ooooh, pretty!"

What intra-class correlation tells you is how much of the variance is accounted for by factors within the player himself.  What we're going to try to do is to "steal" some of that variance by adding additional variables and wrinkles into the model to see if some of that variance will wash out.  If what was once explained by ICC can be explained by controlling for other factors, then perhaps players aren't simply doomed to repeat their past performances.  We simply need to install other skills in them.  Easy enough, yes?

I took all player-seasons from 1993-2008 and calculated the player's age and his sensitivity rating using my plate discipline measure.  I restricted the sample to those who had more than 100 PA, which had the nice side effect of getting rid of (most of) the pitchers batting.  (Somehow, Randy Johnson logged 104 PA for the Diamondbacks in 1999.  He was easy to spot... it was the worst season for plate discipline in the whole sample.)  I looked at the ICC for sensitivity over a player's whole career (with age as the repeated measure) and it came out to .75, which is really really high.  That means that a player will be very consistent from year to year of his life in terms of his plate discipline.

However, the good news for Shoppach is that what small trend line for change that there is does point upward.  (I ran a simple linear regression looking at age predicting sensitivity.)  The bad news is that it points upward ever so slightly, to the point where it's a negligible effect.  A player would have to play for 20 years to get anything remotely resembling a decent effect out of it.

But then we have a very wide and heterogeneous sample in looking at all major leaguers.  We need to cut down the sample to those who are more like Kelly Shoppach.  Shoppach debuted in the majors when he was 26 years old.  This is important.  The players who get "the call" at 23 are a different set than those who get "the call" at 26 or 28 or 30.  Shoppach has also survived to play until age 29, meaning that he was not a "cup of coffee" guy.  I looked for guys who debuted at 26, and were still playing at age 32, which seems a pretty safe bet for a guy like Shoppach.  In that sample, the ICC budged downward to .73.  Oh dear, no luck there.

Well, let's try some other tricks.  Let's add some covariates to the model to see if that helps.  In MLM, there are two types of effects: fixed and random.  (Warning: technical lecture follows)  A fixed effect is much like the regression equations that you are used to.  Everyone's data points get thrown into a big hat and the program tries to find a line that shoots roughly through the middle.  A random effect, on the other hand, treats each person as if they are their own regression line over time, with its own slope.  Clearly, it won't be able to tell me what the slope of the overall line is, but it will be able to tell me whether those slopes are consistent or inconsistent, and how much of the overall variance in each case is accounted for by the variability in the slopes.

I added in pitches per PA in as a covariate, first as a fixed effect.  I added in swing percentage.  Neither got me below .70.  Then, I tried contact percentage.  That dropped the ICC down to .64, which is a small, but significant effect.  This says that plate discipline is, in some small part, the ability to make contact, which of course, surprises no one.  The problem, of course, is that contact percentage is pretty stable over time too, and we haven't explained all of plate discipline by a long shot.  I took all three (PPA, swing%, contact%), and put them into the same regression, plus all possible interaction terms.  The ICC was still at .60.  Even allowing the covariate effects to be random, the lowest I could get the intra-class correlation was down to .52.  Even controlling for all of these factors, the intra-class correlation, which is a measure of how much of the variance in the dependent variable (plate discipline) is related to factors specific to the individual, just won't go away.

Originally, plate discipline had an ICC of .73, which has an R-squared value of 53%.  After controlling for all the factors I mentioned, it dropped to 27%.  So, half of the repeatable variance can be accounted for by controlling for those other variables, although these variables have also been shown to be remarkably stable.  Batters who see more pitches per PA, swing less, and make more contact have better plate discipline ratings.  Considering that my plate discipline measure is a strike-avoidance measure, that's probably not a surprise.  So, perhaps the Indians might counsel Shoppach to be a bit more patient and not swing as much and practice hitting more often for contact.

There's a problem.  We know that swinging for contact and swinging for power seem to be two ends of the same spectrum.  You can aim to hit for power, but will sacrifice contact.  You can aim to hit for contact, but will sacrifice power.  So, while the Shoppach might be able to learn to hit for contact (and no one's done studies on how teachable these skills are), but he'd probably lose some of that pure power.

Then there's the issue of extending his at-bats out more.  This can be done by fouling more two strike pitches off or taking more pitches in the hope that some of them are balls.  The former is a contact skill, which is good to have, but again, we don't yet know if it can be taught.  The latter wouldn't be wise in Shoppach's case.  My plate discipline measure has a companion measure called response bias.  It gives us a rough estimate on whether a player is more likely to push the "swing" button or the "take" button.  The perfect number is 1.00.  Higher than 1.00, and the player would actually have fewer strikes on him if he swung less.  Lower than 1.00, and he's not swinging enough.  Shoppach in 2008, was actually a .988 (which is really good!), although it means that if anything, he needs to swing a tiny bit more, but he's so close to 1.00, that I wouldn't tinker with that aspect of his game.

The moral of the story appears to be this.  Yes, players do get ever-so-slightly more disciplined as they age, but the ones that have the A-ha! moment are few and far between.  Plate discipline and the skills that go with it are pretty well-wired into a player, at least by the time he makes it to a major league roster.  Kelly Shoppach probably won't learn to strike out less, or at least he's not a really good bet to do so, not without sacrificing some power in the process.  He'll probably always be a guy who's a member of the Russell Branyan school of "swing real hard in case you hit it."  Now, given what Shoppach did last year, in terms of results, that's not a bad player.  As frustrating as the strikeouts were, the value that he added with all the doubles and home runs was also worth a lot to the Indians.  (There's a difference between a player being frustrating and a player being valuable.  The game is about winning, not pleasing the eyes.)

Should the Indians trade him?  Well, a trade should always be evaluated based on what you get back (Shoppach for Pujols and Lincecum?  Deal!), but the Indians probably wouldn't be trading away a player about to emerge from being a grubby caterpillar to a beauiful butterfly if they decided to part ways with Shoppach.  He's probably going to continue to do what he's been doing and should be valued accordingly.  And a catcher who has a bit of pop, even if inconsistent, ain't a bad commodity to hold or to trade.

Let's start out by stipulating to something.  Barry Bonds* would have made at least one team in baseball (and probably a lot of teams) better on the field.  Word on the street was that Bonds* was willing to play for the MLB minimum, and as the season progressed, it was clear that there were teams that could have used a good power-hitting DH, or maybe just a guy to stick into LF once in a while, even if he was inching into his mid-40s.  Sure, some teams wanted to go with a youth movement, and others already had a dandy DH.  But, no one wanted him?

It's not hard to figure out why teams were shy on signing Barry in 2008.  After all, he might have inhaled.  And so last week at Hardball Times (on Christmas Eve... which is when I basically checked out of society for a few days...), a gentleman named Jack Marhsall posted a piece looking at the question of "Why not?" from an ethical perspective.  The article generated a bit of discussion, sadly, more of it heat than light.

Marshall's argument rested on a psychological concept called cognitive dissonance theory, which talks about what happens when someone faces up to the fact that they hold two contradictory views and has to reconcile that.  As a psychologist myself, I don't recommend reading his explanation of the subject, as he missed some technical, but important details.  Equilibration, which is what he proposes, isn't the only defense mechanism that one can use against cognitive dissonance.

Basically, his argument goes something like this.  That queasy feeling that you would have gotten in the pit of your stomach because Barry Bonds* was playing for your team would make you feel more negatively about your favorite team.  Even if Bonds* were hitting a home run every 3 PA, it would still be hard to reconcile the fact that your team might very well win a World Series championship on the back of a cheater.  It might raise your opinion of Bonds* to see him in your team's uni.  But a team would be dealing itself a self-inflicted wound by signaling that they were willing to sink to Bonds* (alleged) level.  So, therefore a team would have no incentive to sign Bonds*.  Makes sense on the surface.

Let's stick with the equilibration argument, and suppose that there were a team that really didn't have a lot going for it to begin with (aka, nothing to lose.)  They hadn't won a championship in a while, but Barry Bonds* might well have been the difference-maker between a legitimate shot at a championship and another season in third place.  Yeah, signing Bonds* might have had a negative effect on the team's perception, but perhaps it would spark some interest in the team itself, whether for reasons of making the team better or sideshow curiosity.  People would go from being un-interested to very interested, and even given the debit from the bad Bonds* karma, the team might just come out ahead in those stakes for having signed him.  Cognitive dissonance is not a static process.

Marshall says that if his beloved Boston Red Sox had signed Bonds (and after David Ortiz was injured mid-season, a few people in the media floated the idea), he would have forsworn the Red Sox until they brought in new management.  I guess the queasy feeling would just be too much for him.

The real question is why is that queasy feeling there to begin with?  For that, I turn to another psychological theory, this one by Abraham Maslow, on the hierarchy of human needs.  Maslow's theory says that human being are ultimately striving for what he termed "self-actualization", a term that he reserved for such "peak experiences" as mystical commuinion with the divine.  Interpreted more broadly, and in the context of baseball, we might say that the peak experience in baseball is winning the World Series.  Not coincidentally, that's everyone's stated goal at the beginning of every season (and I don't believe them for a minute... but that's another chapter).  Before getting to those peak experiences, humans have to take care of other needs first, and in a specific order.

The first needs are for things like food and air.  The second is for safety, both immediate (no one around trying to hurt me) and future (financial security).  Then, comes the need for love and then respect and admiration.  The needs have to be filled in this order, according to Maslow's theory.  Only after fulfilling all four can those peak experiences be pursued.  Think about it.  If you don't have food, you don't care what it looks like to other people, you find food.  But if you do have food (and security), you begin to think more about what other people think about you.  All 30 teams surely wanted to win a World Series last year, but apparently all of them decided that the loss of respectability wasn't worth it.  So teams actually did the strangely counter-intuitive action of refusing to sign someone who would have brought them closer to their stated goal and the fans celebrated them for it.

Perhaps under different circumstances, a team owner/GM/decision maker might have figured that they had enough esteem from elsewhere that they wouldn't mind the bad press.  It didn't happen, clearly.  But it might have.  And certainly some of the fans of the team would have decieded that rooting for a cheater just wasn't something that they could have their friends catch them doing (although I'm guessing that there would have been a lot of subterranean fans ...)  Some of them, on the other hand, might not have felt that their needs were being threatened and cheered openly and proudly.

I suppose that whether winning at all costs is ethically permissible is a question for the philosophers.  Frankly, I was never much on the subject of philosophy... it always seemed to be a game that ended in a standstill with both sides having large words to justify their positions and their upset stomachs.  But I would put forward that teams weren't thinking about their duty to the American culture.  It's much more base than that.  I'd say that they were more thinking with their stomachs, and it was simply a matter that none of the teams who would have benefitted from Bonds*'s presence could stomach having Barry Bonds* on their team.

There's been a lot of talk around the net the past week or two about positional adjustments. Everything that a player does is relative to the production of those players around him. Both his offense and defense are compared to average and replacement levels in order to calculate that player's relative worth. Defensively, a shortstop is compared to other shortstops but offensively, shoudl he be compared to all players in the league, or only other shortstops? How are the adjustments determined and how are they applied?

Things got going at Rob Neyer's blog at ESPN where our own Eric Seidman was quoted trying to explain Tom Tango's system of defensive adjustments. The idea is, to get a players total, add their offense above league replacement, defenase above position replacement, league adjustment and position adjustment. More discussion took place at Baseball Primer.

Most of Neyer's readers had problems grasping the concept of what is labeled a "defensive" adjustment, not sure if it means players higher on the defensive spectrum are valued more because they are playing a more difficult defensive position, or if it has something to do with the offense. Tango has done studies of players at multiple positions to see, for example, how much better a shortstop who moves to second may play.However, in another thread, he calculates the average at each position by decade in order to determine the offensive differentials between the defensive positions.

This is the approach I have favored. A players value is in how hard he is to replace. At age 30, Rafael Furcal projects to hit 282/345/415 next season, a 335 wOBA, fourth highest among major league shortstops, behind only Hanley Ramirez, Derek Jeter and Jose Reyes. Furcal was highly coveted on the free agent market, and re-signed with the Dodgers for $39m over 3 years. Meanwhile, Lyle Overbay projects at 269/340/424, for an almost identical 336 wOBA. However, that puts Overbay ahead of only Mike Jacobs and Sean Casey offensively among major league first baseman. Furcal is a precious commodity at short, but if he is moved over to first base, his bat is very replaceable. There are a good number of players who can hit as well or better than Furcal, but only three of them also play shortstop.

Therefore, when calculating a player's value, compare his defense to others at the same position, and likewise compare his offense to others at his position. An argument against this method is that if a few teams put a high offense player at a traditionally low offense position (Aaron, Mays, Mantle Snider is centerfield) that it make everyone else look less valuable in comparison. They seek a more stable baseline than a yearly average. In addition, offensive levels have changed over the years. The major leagues combined for a 295 wOBA in 1968, then rising to 348 in 1999 and 2000. I believe the answer is in a Marcel, rolling weighted mean model, where I weight the most recent season at 1.00, the year before at 0.70, the one before that at 0.49, etc. That way, the baseline is modeled on the same years, with the same weights, at the stats to which it is being compared.

I first calculated the wOBA for each position, and for all players, for each season from 1954 to 1978. Starting in 1956 (the first season with three years of data), I used Marcel to calculate the expected wOBA for each position. (Table 1). Then for each season, I took the wOBA for each position, subtracted the league mean, divided by 1.15 (to convert to runs per PA) and then multiplied by 700 to get the plus/minus run values for each position (Table 2).