Worth Reading: God and .500
I found Tangotiger’s most recent post on what if every player in the majors leagues was exactly the same as something anyone who has the slightest interest in baseball analysis should read.
Suppose that God herself came to you and told you that she was going to do something devious: for the 2011 baseball season, every team would have 25 players of identical talent, with all 30 teams being equals.
David Appelman is the creator of FanGraphs.
That was informative and fun. It’s really easy to forget what a big roll chance plays. Imagine what these numbers look like for a 16 game football season! As an interesting exercise for the math whizzes, how many games would each team have to play to get luck out of the equation and evaluate only talent. Wait, that’s impossible. There will always be some luck, even if it is just 1% of the outcome. So instead, can anybody post some numbers for how the standard deviation changes as the season gets longer? Maybe we should just play the WS every ten years to make sure that we are truly rewarding the only the best teams.
Which is what drives me nuts about almost all of football “analysis.” The writers and talking heads are willing to compeltely change their opinion of a team based on the results of a close game against another good team.
I agree. It’s maddening.
It is indeed maddening, and if James didn’t mean the ‘madden’ pun, then, unintentionally nice work. But when you’re dealing with 16 game seasons…you kind of *have* to change your opinion every week. I think this is why football is doing so well in today’s culture: they play once a week, and when they do play, the games are especially meaningful because they get so few chances to take the field. People get to form hyperbolic opinions and spout them off at top volume, and it somehow makes sense in the context of the game.
To be honest, I’m surprised Football Outsiders is getting the traction that they do; it seems like football is so poorly suited to advanced analysis, and yet they’re doing a remarkable job of it and getting recognized for it.
The standard deviation for a binomial distribution is sqrt(n*p*(1-p)), where n is the number of trials (games) and p is the probability of a certain outcome (the “true talent” level). So, the standard deviation is proportional to the square root of games played.
Solid read.
An important reminder that statitical analysis can only tell you what the best probability strategies are.
That’s what everything is “influence” and “probability”.
With all talent being equal, you could be certain that this is where managing, pitch sequences, and other factors would gain greater prominence.
As it is now talent trumps everything, and by a wide margin.
My problem with luck is how so many people use it as a crutch or an excuse AND the inherent problem with how random or indescribable it is to isolate what WAS actually lucky or unlucky.
In their hindsight they develop an acute sense of self importance and fail to grasp the full range of the necessary analysis by limiting it to the confines of their “unlucky” period of time, which to me is selfish and wrong.
Not just that, but the situation is “impossible” to account for variances due to “luck”. As soon as one event is different (say a base hit instead of a ground out), it changes everything. Pitch sequences will be different, pitch selection, managing strategy, etc.
We’re lumping ALL of those variables that have an impact (sometimes significantly) as “luck” or “randomness”. There is both luck and randomness in baseball, but there are also quite a few other factors that players and coaches can influence to alter probabilities (even if they are njot currently quantifyiable or predictable to the degree that we would prefer).
I just had a vision of 25 David Eckstein’s sitting in a dugout.
Would be fun trading in fantasy football. I offer a David Eckstein for….David Eckstein. Any takers?
I mean baseball, pardon me.
Maybe if you throw in a Eckstein to be named later.
Sounds like a METS fan! haha. I kid, but thought that article was a good read. Now if my Phillies could get back in the good graces of lady luck, they may make the playoffs. Its crazy to think that, after all of these injuries, they are only 2.5 out of the Braves.
As a Twins fan, I get sick thinking about 30 teams full of 25 Nick Punto’s.
Just thinking about an all-Punto (or, as a Tigers fan, an all-Laird) league…
If you replace 25 identical average players with 25 identical well-below average players, does the standard deviation in league wins shrink further?
Question:
Would the wins SD be the same if it were calculated from an at-bat level or a runs scored level? That is, if the probability of an out, single, HR, etc were simulated per at bat for each game for each match up, following the rules of baseball (extra innings, etc) would the SD on wins still be 6.4? Or if you randomly generated runs scored by each team and assigned wins accordingly, would the SD =6.4? Is that SD dependent on normal dist of runs?
My intuition says no, so I did the following:
Simulate a 162 game season 100 times with a normal dist of runs:
avg=81.3, stdev=6.4, as expected.
Simulate a 162 game season 100 times with a chi-sq dist of runs (more realistic since you can’t score negative runs):
avg=81.2, stdev = 7.6!!!!!!
This seems like a crucial distinction. Can a stats expert tell me what’s right or wrong here?
You could run the simulation for 92 seasons, and the team called “Cubs” still wouldn’t win the World Series.