Sunday, December 5, 2010

Context Indepedent Statistics

It is my belief that the single biggest reason for the reach and speed of baseball's statistical revolution is the existence of context independent statistics with sufficient sample size.  That is not to say that context does not matter in baseball; far from it.  A pitcher at Coors Field will appear, based on everyday statistics, to struggle where a pitcher at Petco is an All-Star, even though the Coors Field pitcher might be better.  Likewise - and an even simpler example - a pitcher for a terrible team may accumulate a crappy W-L record despite pitching well, while a mediocre pitcher on a World Series winner will put up 20 wins.  Context absolutely, positively, without a doubt, matters.

Which is why sample size is so important.  Any one event on a baseball field - or even a week of events, or even a month, or, in some cases, even a season - is too small to really tell us much about actual player abilities.  There are enough events, however, over the time and space of a season, or multiple seasons, that we can start to determine things like park factors, home field advantages, player aging curves, and expected batting averages on balls in play.  What all of those statistics let us do is normalize, meaning that the .263 your favorite player hit this year may not be an indication of his actual ability as a player, but that, combined with linedrive rate, on base percentage, and a variety of other real numbers can be normalized to provide a context independent statistic that may not tell us exactly how good a player is, but will get us pretty close.

Now a lot of people don't trust that process, and rightfully so.  It's complicated, it's mathematical, and it is not always predictive.  No advanced statistic predicted Andres Torres of the San Francisco Giants to succeed as well as he did this year, for example.  But that misses the point.  Individual outliers are a part of any statistical sample; a little good luck, and anyone can end up in that third standard deviation away from the normal curve.  Even in a full season - even in a full career - no player will play exactly to his ability, and some will, simply by chance, vastly overperform or underperform expectations.

The point here, however, is not to argue in favor of baseball statistics, or to explain how and why they work.  There are dozens of great websites and articles out there that can do that for you.  No, I'm writing to make a simple observation about baseball statistics relative to statistics in other sports.  In short, I want to argue that the ability to come up with context independent statistics, I believe, means that baseball will always be far ahead of every other major sport in its ability to quantify player performance.

Of course other sports can normalize their numbers to some degree, based on factors like home field advantage, weather (in the case of outdoor sports), or other external factors.  What makes basketball, football, and soccer so hard to quantify, however, is the interdependence of the success of one player on the success of others.  The context independent statistics in baseball depend on the ability to limit or remove external influences on data, but they also benefit from the non-interference of internal influences.  That is, Albert Pujols may drive in more runs with a good leadoff hitter in front of him than with a bad one (which is part of why RBI is a useless statistic), but it will have a negligible effect on his ability to get on base or to hit home runs.  His actual ability is unchanged by his teammates.

Consider, in turn, each of the other three major sports.*  This year's Miami Heat - though the sample is still small - are demonstrating that three players with tremendous individual skill do not necessarily result in greater success.  Certainly, and this likely goes without saying, that individual skill is not additive in the way it is in baseball.  What I mean is, if Pujols is worth 9 wins and the Cardinals added, say, Alex Rodriguez at 6 wins, the addition of Rodriguez would not make Pujols any worse, and the Cardinals would be expected to win 6 more games with A-Rod than without.  In basketball, on the other hand, you can't just add a 6 Win Shares player to a 4 Win Shares player and get 10 wins.  Why? Because there aren't any context independent statistics at play, and there can't be.  What LeBron does cannot be separated from what Wade does, and there's no two ways about it.  If LeBron takes a shot on a given possession, that's a shot that Wade doesn't take, and vice versa.

* Yes, I'm elevating soccer over hockey, and not just because of international appeal.  It seems to me that the MLS is very close to catching the NHL in national popularity.  Maybe I'm wrong about that.  After all, the Stanley Cup still has larger viewership than the MLS Cup.  However, comma, the Seattle Sounders averaged over 30,000 fans a game this season, and the league is expanding, and I think it's only a matter of time.  Then again, I'm biased, because I don't particularly like hockey.

Anyway, regardless of the status of hockey and soccer in America, it's no contest in the rest of the world (except for Russia and Canada).  Soccer wins, hands down.

One could argue that baseball is effected by this to a degree.  If Pujols is surrounded by an amazing lineup, he'll naturally get more chances to hit over the course of the season because the Cardinals will bat around more.  But that's a poor proxy, because the effect is minimal, and what counts most is still Albert's rate stats, not his counting stats.  Rate stats matter in basketball too, of course, but even the rate stats (shooting percentage, points per 48 minutes, even player efficiency) depend heavily on the rest of the roster.  Last year LeBron, Wade, and Bosh were 1,2, and 4 in player efficiency.  It's safe to say they're all great players.  So far this year, however, they're number 9, 18, and 34 respectively.  Still plenty good, but - ironically - it's hard to be as efficient a scorer with other teammates who are also efficient scorers.

In the NFL the case is even more stark.  Almost every NFL fan can tell you who's a good quarterback and who isn't, and we keep a strange and esoteric statistic called "Quarterback Rating."  Quaterback rating, however, is anything but context independent.  Indeed, in a sport as specialized as football, there's really nothing that is context independent.  Whereas an MLB player can get traded from the AL East to the NL West and still hit cleanup the next day, even a quarterback as gifted as Peyton Manning would struggle if he suddenly had to lead the Seattle Seahawks next week, and not just because the Seahawks are inferior to the Colts.  The systems are completely different; Seattle doesn't run the same - or even a similar - offense, the offensive lines block differently, the receivers run different routes.  The context is entirely different, and even Peyton Manning would have to learn the new system.

So how can we measure the true skill of a quarterback, when systems differ, when some offensive lines block better than others, when teams don't play balanced schedules, when the season is too short to really tell?  We can't.  We can use scouting - and, in fact, this is what teams do - and we can try to maximize the success of a player by adapting gameplans to the player's skillset.  But that just goes to show that there's no single objective measure for quarterback skill.  And if not at quarterback (the position that touches the ball most), at what position could we possibly generate a context independent statistic of real meaning?

Soccer is in the same boat.  While the soccer world has done fascinating work on player aging curves (by position, no less), and some teams have learned how to identify and pursue (or sell) under or overvalued players, it remains difficult to calculate some underlying ability.  I don't think it's impossible, because there is a wealth of information available and, while context does matter, soccer is has less variability in roster construction and approach than football or, I would argue, even basketball.  In other words, context is controlled more naturally.

Nevertheless, it's a difficult sport to quantify, because it has one of the same problems as baseball defense: player spacing and positioning is probably as important, if not more important, than player skill levels, and a lot of that has to do with coaching.  Moreover, there are so many different kinds of skills and players that a singular scale may not work to assess player values.  Some teams, for example, are built on speed and strength, neglecting skill or technique, while others are filled with wily veterans who cannot outrun their opposition, but rely on being in the right place at the right time.  Successful soccer - and soccer is undoubtedly a sport where success and failure walk a razor's edge - depends upon coherent roster construction as much, if not more, than skillful players.  Much like the Heat, a soccer team filled with great players (like England's World Cup roster) may crash and burn while inferior players who work well together (like Uruguay or Holland) may succeed.

All of this is not to say that other sports should not be asking questions about how to quantify - or at least understand - player ability and contribution to team success.  Rather, it is to say that baseball will always have a leg up here, because the unit of action is so easy to measure by comparison.  Maybe it comes down to that, above all: baseball is a turn-based game, while soccer, football, and basketball are all real time.  Or at least closer to real-time.  Football in particular strikes me as a turn-based game with real-time tactical battles.

Anyway, the point remains: baseball actually has units of action that generally revolve around two players: the batter and the pitcher, with ancillary support from the catcher and whatever fielder the ball is hit to.  Even the smallest unit of action in basketball, football, or soccer involves the entire team, by necessity, because there's so much inextricable context.

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