Thursday, March 08, 2012
Z-Scores and Pitch IQ ScoresPosted by Dan Brooks
I thought it important to describe a new feature we've added to the PitchFX Player Cards over the last month or so. I’ve previously tweeted (@Brooksbaseball) about these features but haven’t described them in detail.
When the cards first debuted, we were asked by a number of people to provide average data for comparison, especially for the "Sabermetric Outcomes" table. For example, if Clay Buchholz got 45.96 percent whiffs/swing on his change-up, people wanted to know how good that was relative to other pitchers, and so they wanted some average number of swings and misses. They had a feeling it was good, but they wanted to know just how good.
The problem people don’t realize is that they really don’t want the average, because while it is useful in some contexts to know simply an average, it isn’t nearly as useful as knowing something about the distribution of scores. For example, if I told you that on some made-up metric Buchholz was a 7, and that the average was a 5, you’d know that Buchholz was above average but you wouldn’t know by how much. Maybe on this metric most good players score between 5-6, and so 7 is really outstanding. Maybe on this metric most good players score between 5-25, and so 7 is really not very exceptional.
So you can see, it would be nicer if I told you instead something about how far Buchholz was from the mean score as an expression of the distribution of scores. For that, we can use a Z-score.
The Z-Score is a simple concept in statistics. Simply, it tells you how many standard deviations a score is from the mean score. So, if you now scroll down to the “Sabermetric Outcomes” table on Buchholz’s player card, you can change “Percentages” to Z-Scores. This will contextualize the percentages that you see on the table (all of them, not just whiffs) so that you can better understand just how good the pitches are that you’re looking at.
It’s also important to think about which distribution is appropriate for comparison in this case. For example, we could compare Buchholz’s change-up to all other pitches, or, perhaps more appropriately in this context, compare the change-up to all other change-ups. We’ve chosen “all other change-ups” as our distribution. When you change the months or years on the player cards, it will change the numbers used for Buchholz’s data but won’t change the numbers used for calculating the Z-scores, because we didn’t want to get too fine with the comparisons that we made.
There’s also a problem in this dataset that arises when pitchers throw a very small number of pitches, because this makes their whiff numbers artificially high or low (luck plays a larger role). So, we’ve left pitches (e.g., Player X’s change-up) out of the distribution that didn’t get thrown at least 100 times. You can still look at those pitches as a function of Z-score, but they won’t be particularly meaningful. Even with these omissions, we’ve still got a very large sample to work with for each pitch in this case (except Knuckleball, which is a special case on its own).
You can also change the scores into “Pitch IQ Scores.” You can think of the “Pitch IQ Scores” exactly like you would think of Z scores, except, some people don’t like Z scores because it requires explaining basic statistics to people, and IQ scores are a sort of intuitive thing that we use in everyday life. The formula here is simply 100+15*Z (just like it is for IQ). We also often use the 100+/- system in baseball, for describing things like ERA+ or OPS+, so describing a pitch as having a 124 Whiff/Swing (pretty damn good) or a 64 Whiff/Swing (worse than useless) seems like something that could catch on, and might be easier for your readers to grok than numbers like “1.6” and “-2.4”.
Have fun, tab through, figure out which representation of the data you like best. I hope you enjoy the new features and we look forward to hearing additional feedback as the season begins.
Dan Brooks is a Neuroscientist at Brown University. He operates BrooksBaseball.net and eats Fried Chicken during every Red Sox game, especially in September. Come follow him @brooksbaseball.