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06-12-2009, 02:31 PM   #62
RedsManRick
Stat Wanker Hodiernus

Join Date: Dec 2004
Location: Chicago, IL
Posts: 15,674
Re: Willy Taveras or Chris Dickerson in CF?

Quote:
 Originally Posted by bucksfan2 If Wily Taveras is a true .330 OBP player why would his OBP average be hovering around the .300 mark? I do see your point with the Gamblers Fallacy bu there are too many variables with a baseball player than somewhat fixed variables in Gambling. There is no such thing as a "true" anything in sports. Averages in baseball aren't static, they are constantly moving. There are peaks and valleys in a given season. At time a player is hot and playing above his average, at others he is cold and playing below his average. Once you get enough at bats or a big enough sample size the average will regress to its mean.
Firstly, let's be clear about what "true" means. There is no way to know what a player's true skill level with absolute certainty. Our best guess of this true skill level is based on what the player has done in the past over a large number of plate appearances. If we have reason to believe his skills have changed since then, or that he has been particularly lucky or unlucky over that period of time, we might adjust our estimate accordingly. However, given that Taveras' OBP for his career is, if anything, higher than we would expect it to be based on his component skills, .330 is a fair estimate of his true skill level.

To your question, the reason his OBP is hovering around .300 is because .330 is an average over a theoretically infinite number of plate appearances. Just like if you toss a die an infinite number of times, you'll get a 6 on 1/6 of those rolls. However, if you only toss the die 6 times, you're not guaranteed to get exactly one 6. In fact, it's unlikely you'll get exactly one 6. What's more likely is that you'll get either zero 6's or two plus 6's. As the number of rolls increases, the proportion of rolls that are 6's will get closer and closer to 1/6. This is called the law of large numbers.

It works the same way in baseball. Take an established .300 hitter. In 10 at bats, he could hit anywhere from .000 (0/10) to .700 (7/10) and nobody would be surprised -- "small sample size". Make that number 100 and .000 (0/100) or .700 (70/100) would be quite unlikely. It's going to be more like .150 (15/100) and .450 (45/100). Make that number 500 and it's going to be more like .250 (125/500) and .350 (175/500). As the number of at bats increases, the tighter the range in which he might reasonably perform becomes. Make it 5000 at bats, and you probably have most of his career -- and he'll be pretty darn close to his "true skill".

So, why is Taveras' OBP hovering around .300? Because it is -- that's the sum of his performances this far. What you might call "streakiness" is exactly what we would expect to see if it was all happening randomly. If Taveras is a .330 OBP guy, there will be times when he goes 0-20 and times when he goes 10-20. He's not really shifting his skills from a great player to a bad one and back. He's just experiencing streaks in his results. Just like there will be times when you roll 3 6's in a roll. It doesn't mean you went through a period of being skilled at rolling 6's.

Streaks happen. Wild shifts in performance are expected over small samples -- and 200 at bats is a small sample in baseball. But they don't imply a wild shift in ability. Willy Taveras' most likely performance moving forward is the one based on his skill level -- a .330 OBP. He could be better than that moving forward. He could be worse than that moving forward. But .330 is the most likely. That estimation is based on his skill level, which doesn't change simply because he's got a .300 OBP so far this season.
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Games are won on run differential -- scoring more than your opponent. Runs are runs, scored or prevented they all count the same. Worry about scoring more and allowing fewer, not which positions contribute to which side of the equation or how "consistent" you are at your current level of performance.