This is the second in the series of blog posts inspired by the 2004 Ken Ross book entitled A Mathematician at the Ballpark. The first one is here. In this post, again, we illustrate all these notions using the Baltimore Orioles’ 2022 season.

For an experienced baseball fan, baseball is a game of patterns. We “know” what a well-executed pitch looks like, how a double play is to be executed, how a pop-up is to be fielded, and so on. Because of these expected patterns, we know the plays which should emerge and so the desire to track their occurrences should come as no surprise. It’s been done since professional baseball started in the 1870s.
This week we discuss a pitching statistic you see on televised games, WHIP. WHIP is short for “walks plus hits allowed per innings pitched”.

Earned run average

We start off with the most basic pitching statistic, the Earned Run Average or ERA. This is the number of earned runs per 9 innings pitched:

ERA = 9·ER/IP,

where 

• IP, the number of Innings Pitched,
• ER, the number of Earned Runs allowed by the pitcher. That is, it counts the number of runs enabled by the offensive team’s production in the face of competent play from the defensive team.

It is possible to have ERA = ∞, since innings are measured by the number of outs achieved (so if the pitcher doesn’t get any batters out, his IP=0). The lower the ERA the better the pitcher. In the 2022 season, right-handed Félix Bautista, who entered late innings as either a closer or a reliever, had an ERA of 2.19. Left-handed closer Cionel Pérez had an ERA of 1.40.

WHIP

We define walks plus hits allowed per innings pitched by:

WHIP = (BB+H)/IP,

where (as in the previous post) BB is the number of walks and H stands for the number of Hits allowed by the pitcher (so, for example, reaching base due to a fielding error doesn’t count). WHIP reflects a pitcher’s propensity for allowing batters to reach base, therefore a lower WHIP indicates better performance.

When we plot the ERA vs the WHIP for the top 20 Orioles pitchers in 2022, we get 

Again, the line shown is the line that best fits the data. As the line of best fit doesn’t fit the date too well, this tells us that these two statistical measurements aren’t too well-correlated. In other words, low ERA indicates a good pitcher and low WHIP indicates a good pitcher, but the values for “average” pitchers seem less related to each other.