Thanks to a topic raised by my favorite Padres blog (www.ducksnorts.com), I have been thinking a lot about what is “luck” in baseball.  After thinking about it quite a bit, it is pretty hard to define.  The best way I can describe luck is making the metaphor to blackjack.  This is not original, I am pretty sure I read in Moneyball that Billy Beane thinks about baseball as blackjack.

Anyway, with blackjack, you go to the table, get horrible cards, people say “bad luck”.  Vice versa, you get great cards, people say “good luck”.  I think of it slightly differently that the people getting the bad cards are getting worse than expected outcomes.  But I have a hard time calling it luck, because it is a mathematical certainty that this type of outcome is going to happen for players (same with the hot streak).  So, I think of it as just part of the game.  Now, if a player, over their lifetime, consistently gets better or worse cards, the label of “lucky” or “unlucky” seems to fit better, but it stills feels like a mathematical function.  I think of the scatter plot of distribution of black jack players, one roughly shaped like a bell curve.  The dots are the lifetime win rates of people playing blackjack (with some minimum sample size threshold).  So the bulk of the dots are going to be around the mean (winning 48% of the time), but there are going to be some dots above and below the mean, some (but much fewer) substantially away from the mean.  This also feels like a function of the probabilities.  For a dot (person) well above or below the mean, people will call them “lucky” or “unlucky”, and by conventional understanding they are, but I still feel like their outcomes and behavior are ruled by the random application of statistic probabilities.  So, they feel very “predictable”, albeit for the individual it will feel very lucky or unlucky.

What does fall into luck, though, is the size of the bet.  I envision someone at a blackjack table, getting good cards and bad cards, but if they happen to be betting more when they got good cards (and this is random; they are not counting cards), that is lucky.  There decision to bet more or less was random and not subject to statistical probability.  I actually have a friend like this.  When we play together, it seems like whenever he places a massive wager, he wins.  That is lucky.  Good, bad cards, feels “lucky” or “un-lucky”, but is a product a statistical probability that will even out, if not for players, for the casinos.

So this conversation was prompted by the bottom of the 8th inning of the Padres-Giants game on June 26, 2007.  Scott Linebrink, the pitcher for the Padres, had two outs and two strikes on Kevin Fransden when Linebrink made a good pitch that Fransden fought off for dribbler that was an infield hit.  The next batter also fell back 0-2, only to get jammed on a high inside fastball that flaired over the shortstop for single.  The next hitter knocked in the tying run from second.  Many people on the blog said that “Linebrink got unlucky”.

One way to think of baseball players is as stacks of cards.  You could think about it outcomes (for a pitcher:  walk, strike out, single allowed, double allowed, etc) but I view it with even more granularity:  good pitch, bad pitch.  So Scott Linebrink is stack of cards comprised of good pitches and bad pitches.  Based on scouting and statistics, you have a pretty good idea of the make up of his deck (in his case, mostly good pitches) but you cannot really control which one is going to be dealt at a given time. 

And you have to consider he is pitching to a player who is also a stack of cards (good swing, bad swing).  Some players are going to give you a lot more good swings (or takes) than bad ones, but you really don’t know what is going to happen next.

And then, when you factor in the variation on the outcome of the interactions:  good swing on a bad pitch may result in a line out to the 3B, while a bad swing on a good pitch may result in a dribbler for a single.  When you add all the variation together, it is hard to predict any individual match up, but generally have to rely on the variation oscillating around the expected outcome.

So, what is luck in baseball, using my blackjack metaphor?  The best I have come up with is that Fransden got the equivalent of winning a hand despite having a 15 into a dealer’s face card, and the deck is full of face cards, but he still wins the hand.  “Lucky”?  By conventional means yes, but, to me, part of the statistical probability.  Some count of times this is going to happen.  Now, if Scott Linebrink gives up more than his share of those kinds of hits or Fransden gets more than his share, they might be considered lucky or unlucky hitters or pitchers, but, again, they feel like one of the dots who plays blackjack who consistently comes out ahead or behind on the game.  They may appear individually lucky or unlucky, but still part of the broader distribution.

What feels like luck in this case is that it was a pretty high leverage situation, meaning the outcomes have a big impact on the game’s outcome.  This feels like the betting equivalent.  The Giants (and the Padres) both had a lot of chips on the table, but the Giants are the ones that got the good outcome.  So, it was not so much that Fransden got the dribbler (predictable if infrequent) but that he got it during an important time in the game.  Fransden’s hit was compounded by the next batter also getting an improbable hit.  So getting these favorable (or unfavorable) but improbable outcomes during important times, feels like luck.  I will have to think so more how well this works.

Getting away from this specific example, I can think of other cases I feel are “lucky”:

Jeff Weaver and Cardinals
Last year, Jeff Weaver got on a roll, propelling the St. Louis Cardinals to a world championship.  It is not that unusual that a mediocre pitcher pitches really well for awhile, but the Cardinals were very lucky that Weaver got this hot streak just when it counted the most:  the playoffs.

The reverse luck may be the Giants (with Bonds’ historical flailing) and the Yankees (with Alex Rodriguez having very bad post seasons thus far). 

This seems to fit within my way of thinking about probabilities vs. luck.  It is just probability that players get hot or cold, but it is the luck (good or bad) for the team that these key players get hot or cold during “high leverage” times.

Arizona Diamondbacks
On Baseball Prospectus’ adjusted standings, the Arizona Diamondbacks, sporting a 46-35 record, are the luckiest team in baseball.  First of all, looking their runs scored vs. runs allowed (346 vs. 347), they actually have a negative run differential but are 11 games over .500.  With a run differential like this, teams typically are .500, so they should be 40-41 instead of 46-35.  So, they have gotten the runs when it really helps them and allowed runs when it has not hurt them.  This is not skill, this is luck.  Then, when you look at the “second order” standings, this adjusts for how the team’s batting lines and pitching lines translate to runs.  For Arizona, based on their batting performance, one would expect them to score 343 runs, very similar to their actually 346.  No big deal.  For their pitching, however, one would expect them to have allowed 367 runs, twenty runs more than they have allowed.  So, they are not only getting lucky in the timing of getting and allowing runs, they are getting lucky in that they are allowing far fewer runs than would be expected.  This, again, is not skill.  You put these two factors together, and the Diamondbacks ought to 38-43, not 46-35.  That is a difference of 8 games, the largest in all of baseball right now.

How does this fit into my blackjack model?  I think it is the parallel that the Diamondbacks keep getting key runs scored and meaningless runs allowed, as well stranding a lot of base runners when they are pitching.  This is somewhat the equivalent of them winning a lot more of their blackjack hands when they raise their bet than when the bet is lower.  If they are counting cards, fine, but they are not.  They are getting lucky.

Summary
I am trying to separate the randomness of baseball events from the timing of those events.  So Scott Linebrink was not necessarily unlucky to give up the dribbler, but the Padres were unlucky that this low probability event (a positive outcome on a good pitch and bad swing) came at a critical moment.