This post was written by Matt Cawse — a new contributor to microbrewdata which we are very excited to join our team. He holds an undergraduate degree in political science and is the proud and loving owner of two cats and a dog.
There Should be Crying in Baseball
Tom Hank’s character Jimmy Dugan says there’s no crying in baseball, but maybe there should be. Baseball as a sport is often inherently unfair. It’s a game where you hit a round ball traveling at (very) high speed with a round bat. You then hope the resulting collision leads to something good (or at the very least something not bad). A player’s worth (expressed in statistics that measure performance) is judged on the outcomes of these events. This is often regardless of whether or not you had much of an influence on the outcome.
(Sample) Size Matters
One of the simplest ways to make statistics that are unfair is to have inadequate sample sizes. Baseball has a system of minor leagues that feed players upwards into the major leagues through promotions. These are earned through performance and future promise. When a baseball player first gets called up to the majors, it’s often referred to as their “cup of tea” due to the fact that the amount of time you’re given before you get sent back down again. Each level is harder than the last, and the major leagues is the hardest of them all.
Using famous people as examples
Consider Billy Beane, who would later become famous through the book and movie adaptation (with Brad Pitt) Moneyball . His statistical performance can be found on baseball-reference.com. His first two seasons in the major comprised of 10 then 8 visits to the plate, that’s two full games. He almost hit 200 plate appearances in his third and longest season. He then only came close to 100 plate appearances once more at the age of 27 before he was done. His career total of 315 plate appearances isn’t even a full season for a regular player (Note: A plate appearance is every time you go to bat. An at bat is all plate appearances minus walks, errors by the other team, and a fielder’s choice. The difference is insignificant for the basic purpose of this article. Just don’t be confused when there is a slight difference between the two).
Before we consider his stats, we should quickly cover other relevant influences. His manager had a greater sample size of minor league performances to use in evaluations. They will also use the ‘eye test’ where experienced baseball talent evaluators can identify strengths and weaknesses based on observation divorced from statistical performance. There is also the aspect of Billy’s fielding and defensive performance which is not covered in these stats (or covered in any stats really, but that’s a whole separate article).
You must have this many at bats to qualify
Billy (used as an example for thousands of players over the years) realistically had a very short window of oppourtunity to create his batting statistics that would heavily influence his future as a baseball player. A single extra hit during his “cup of tea” could have heavily modified his stats and by extension his perceived value as a ball player. Even during his extended seasons a few instances of luck in his favour could have had a big effect.
When determining the player with the best batting average in a season (hits divided by times at bat, resulting in a percentage expressed to 3 decimal places) Major League Baseball requires that a player have 502 plate appearances ( 3.1 at bats per game in the season, for a 162 game season) to qualify for the award. Anything less in considered invalid due to small sample size. Billy Beane and other players didn’t even come close to this measure in their entire career.
Awards and Honours
Even if you get to have 500 plate appearances you are still not free from the effects of sample size. Here are the top 5 players for batting average for the American League (half of the full league) for the 2016 season.
First Last Avg At bats Hits
Jose Altuve .338 640 216
Mookie Betts .318 672 214
Dustin Pedrioia .318 633 201
Miguel Cabrera .316 595 188
Mike Trout .315 549 173
If Mike Trout turns two unsucessful at bats into hits he would instantly jump all the way to second place from fifth. This would be a significant boost to his prestige and recognition. (Note: he won the most valuable player award, given to the player deemed ‘most valuable’ by the selected media persons anyways but it still would have helped). Not pictured in the prestigious top 5 list is David Ortiz, who also hit .315 but is in 6th place. This is because he had fewer total hits than Mike Trout (total hits being the tiebreaker when the average is the same to 3 decimal places). By extension this means he had fewer at bats. Injuries, overall team performance, rest and lineup choices all influence Ortiz’s at bat totals. These variables are almost entirely out of Ortiz’s control.
It’s not all bad and arbitrary constantly. Jose Altuve significantly out performed the competition. He obtained 2 more hits in 32 less attempts than his competitor Mookie Betts. That difference can be potentially translated into a significant impact on the games that Jose Altuve played.
Over a career
To get better sample sizes we need to get a full career’s worth of stats. A full career can span over a decade and include thousands of instances of performance over the years. Most players (as seen with Billy Beane) don’t get a career in the major leagues, but those that do compile a significant amount of data.
Hall of fame
Recently the baseball hall of fame has inducted its latest batch of inductees. The hall of fame aims to celebrate “legendary players, managers, umpires and executives”(from baseballhall.org). The decision determining which players are legendary comes down to an organized vote by a selected group of baseball journalists. There’s a great deal of drama and politics in the vote due to things outside of pure performance, which we are going to ignore for now because they aren’t relevant to discussing statistics.
Let’s naively pretend that a player’s candidacy depends entirely on their statistical performance. Some players obtain the subjective legendary status by being an objective outlier of a baseball player. Consider the following box plot graph showing the distribution of strikeouts achieved by the top 50 pitchers every year between [1908, 1926] (data from ESPN).
Roughly speaking details located vertically above or below each individual box represents the following data
- (The Box) What is average (with inner horizontal line displaying median)
- (Black “Whiskers”) What is above or below average
- (Black Diamonds) Outliers of the distribution: what is considered amazingly abover or below average.
For the readers who took an intro statistics course a brief reminder of box plot heuristics is given to the right obtained from Wikipedia.
The red dashed line represents the total year strikeouts for Walter Johnson — widely considered one of the best pitchers of all time. When judging someone over the course of their career we might have an accurate idea of their worth. This is only after literally thousands of instances. To outperform the rest of the group like Walter Johnson did requires years of sustained excellence. Even then it only works on the phenomenon and the transcendent. Every year people discuss the hall of fame results and the difficulties of separating the very good from the legendary. Even with a career’s body of work it can still be very difficult to judge a player according to a certain standard.