I just completed Russell Carleton’s new book The Shift: The Next Evolution in Baseball Thinking. It’s a great book and I’d recommend it for any quantitative/baseball fan. Carleton talks about current baseball thinking about shifts, in-game decision making and runs expectancy. He also talks about issues that may become more important in the future. For example, Statcast measures a lot of new things, but it doesn’t handle measurements of a player’s emotions like how a player handles being struck out. The book is light on the math, but it provides an interesting glimpse of what sabermetrics might look like in the future. Carleton add stories from his own life and these stories help in motivating the baseball statistical stories.
Although Carleton’s book is great, there is one aspect of the book that bothers me as a statistician. Carleton always uses tables in his book to describe statistical patterns in baseball data. Here’s an example. In Chapter 7, Carleton describes the value of foul ball statistics in measuring batting performance. As evidence of this “foul ball” value, he presents the following table that shows the average AVG, OBP, and SLG of nonpitchers in different two-strike situations. (I have added caps a few places to emphasize the differences between these situations.)
The first row gives the average AVG, OBP, SLG in all plate appearances, the second row gives the average AVG, OBP, SLG for all PA’s with two-strikes, the third row gives the average measures for 2-strike counts where there was at least one foul ball, etc.
Although this table has the information, it is hard to read — why?
- One has to look carefully at the table to see any effect.
- If you scan the AVG column from top to bottom, you are surprised that the last four rows (0.193, 0.172, 0.187, 0.204) are not monotonically decreasing. But then looking more carefully, you realize the situations (at least one foul, no foul, just one foul, more than one foul) are not presented in a monotone manner in the table.
- Are the changes from one row to another large? It is hard to quickly tell — one needs to compute differences and decide if they seem large or small.
The point I’m trying to make is that tables are hard to quickly decipher to get the meaning. The casual reader might as well ignore the table and believe the conclusions stated in the text.
Why Not a Graph?
If you have read any of my posts, you know that I always try to use graphs to display statistical patterns. To better understand how foul-ball statistics are helpful, I would like to use a graph to portray the averages displayed in Carleton’s table.
Here are some decisions to make when I create my ggplot2 graph.
- Type of graph? Since we are displaying averages for different situations, a Cleveland-style dotplot seems reasonable.
- How to treat the three different averages? Since AVG, OBP, and SLG are different measures on different scales, it doesn’t make sense to compare AVG, OBP, SLG for a particular situation. Instead I will create three graphs, one for each type of average.
- Ordering of situations? When I plot an average against different situations, I check if ordering of the situations is relevant. Here I see a natural ordering in terms of fouls (no fouls < one foul < at least one foul < more than one foul) and I’ll use this ordering in my graph.
- Other graph aspects? I decide to use a larger size dot so it is more visible. Since the situation labels are long, I’ll put them on the y-axis. I’ll add an informative title to make the graph more readable.
Here are my three graphs from Carleton’s table. What do I see from the AVG graph?
- We see clearly that the average AVG is an increasing function of the number of fouls on two strikes. Quickly we see that an additional foul on 2-strikes adds about 0.01 to the AVG.
- The mean AVG with two-strike counts with no foul is very low — under 0.180.
- All of these two-strike means are much lower than the mean AVG for all plate appearances — this shows the significance of a two-strike count.
The OBP graph tells a different story. When one repeatedly fouls a two-strike pitch, it is making it more likely to walk. So the mean OBP, with two strikes and more than one foul, is close to the overall mean OBP. Again, one can measure the effect of one more foul on the average OBP.
Here is the same type of graph for SLG. This resembles the AVG graph more than the OBP graph.
- Why not graphs? I’d be interested in learning why Carleton decided to use tables instead of graphs in his book. In writing Curve Ball, Jay Bennett and I tried to use graphical displays throughout.
- Andrew Gelman, on April 1 (note the date), wrote an interesting article “Why tables are really much better than graphs.” This article eventually was published with discussion in The American Statistician.
Here are some reasons to prefer tables quoted from Gelman’s article:
- Reason 1: The best quantitative research has an underlying clarity and a substantive importance whose results are best presented in a sober, serious tabular display.
- Reason 2: It’s much more important to put in the exact numbers, as these represent the most important summary of your results.
- Reason 3: The time you save not agonizing over details of graphs can be instead be used to think more seriously about your research.
- I hope you realize by now that Gelman doesn’t believe that tables are better, but he was trying to initiate a discussion about the value of graphs.
- Several things stand out when I read Gelman’s article and the discussion in the journal article. First, statisticians aren’t all graph people — Michael Friendly and Ernest Kwan describe the general public as either “graph people” or “table people” and perhaps Carleton is one of the “table people.” Second, both tables and graphs can be viewed as forms of acts of communication. They pose these questions for this communication (either table or graph): (1) what is the communication goal, (2) who is the intended audience, and (3) was the communication effective? Any type of display, graph or table, should be evaluated from this perspective.