182. Baseball Pain (4). The Pythagorean Number

 
-->

When you're a fan you become so focused on your own ballplayers that you get to thinking they're the cause of everything.  The other guys don't "get" three hits; your pitcher "gives them up."  He "gets" batters to swing at bad pitches, hit the ball on the ground, pop up, even line out.  When your guy comes to the plate and does that it's all his fault.

Other teams are known mainly by what they have done to you. The Phillies beat us up in the first two series we played with them in 1964 and after that they were "the mighty Phils," kept on their eminence by memory — and, of course, the numbers in the won-lost column.  That's why I referred to them (in the preceding post) and the Giants as the two "really talented" and "strong" teams, up there battling for first place.  Well the Phils weren't nearly as strong as they appeared, as I recently found out.

One number in one of those genius statisticians' columns, called "the Pythagorean number," made it all clear.  The number is the percentage of wins a team "should have," given their talent, measuring talent by the differential between number of runs scored and number of runs allowed up to that point (see note, below).  You can see right away whether or not a team is "playing over its head" — that is, beyond its basic talent — or not.  If it is, you're not so surprised at a fold.  Class will tell.

Well, on September 21, the day Ruiz greased their skids, the Phils had a Pythagorean number of  .561.  Their won-lost percentage at that point was .600.  They had been playing "way over their heads."

What a useful number!  How much it tells us about past pennant races.  Knowing that on the 21st the Phils were playing .39 over their heads I check the Reds and see that their Pythagorean is .564 while their actual won-lost is .557.  They're playing a little under their heads.  If there had been a Pythagorean number in '64 I'd have been saying, "Yeah, man, we'll catch 'em.  We got the class."  To a Philly fan after the fold I could have said, "Don't take it so hard, buddy.  It was in the cards.  Class told."

In the cards.  In the cards.  Easy to say but when I think about that old fatalist expression, especially during a game, it troubles me.  In my seat I don't for one moment believe that Brandon Phillips' game-changing break for third base (see Post #172) was in the cards.  It was a decision he made, and it came out of his character.  Everything my players do is a manifestation of character.  I see it in every action on the field.  I can't help it.  That's the way I watch and that, I think, is the way most fans watch.  Do the numbers show that we're fools?

If we are fools some of us, the nuts for whom "in the cards" will suggest simulated games, should know it well by now.  Robert Coover, the novelist, certainly should know it.  One of his heroes matches every percentage event in a baseball game to a comparable percentage throw of the dice.  Most nuts use playing cards (jack for a single, queen for a double, and so on) with the proportion of cards in an arranged deck adjusted for event (only one ace for a home run, for example) and player (more face cards for sluggers).  Play that game over the winter and you'll have no doubt that "in the cards" refers to a mathematical outcome independent of human agency.  Or, where the shoe pinches, that winning a pennant has nothing to do with character.

A cynical, illusion-smashing statistician could really drive this home.  "Oh sure, you can find parts of a season — winning streaks, losing streaks, sudden turns — that appear to be character-driven, you can use words like 'confident' and 'demoralized' and 'momentum.'  You can talk about 'psychological advantage' and a player 'choking.'  But those are just you, constructing something dramatic and intelligible." 

And you know, as you learn more about statistics you begin to wonder if that killjoy has a point.  Do you know that 100 random win-lose tosses will produce, more often than not, at least one six-game winning streak?  Look at that streak in your winter game and try not to make up a story about it.  Hell, that's the point of playing the game, to trigger your imagination.  Turn over one card and a team boards the train home fired up, turn over a different one and they're in the dumps.

If you upped the technology and had ballplayers running on batteries wired to a talent program that cranked out their performance would the season they produced be in any way distinguishable from a season produced by human ballplayers?  Might you produce the 1964 season this way?  How, to go Cartesian with this, do I know that the 1964 season wasn't produced that way, by some all-powerful demon?

What a prospect!  Every team's line on the graph wobbling toward its Pythagorean number, every player's line showing more and more accurately how much a victim or beneficiary of his basic talent he is.  But then there are those streaks at the end of 1964, by all three teams we're interested in.   Once you acquire the statistician's view you can't get rid of it.  So, fair warning.  The drama in the rest of this narrative could have no basis in nature.  An evil demon could just be playing with my mind.

Note: The Pythagorean number was first obtained by dividing runs scored² by the sum of runs scored² and runs allowed².  The exponent was then changed to 1.83 in order to bring the number closer to results in the world.