Means don't tell the whole story
Data rule: Know the distribution
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As I write this, I know some of you will go baseball—great—and others will groan, but there is an overall data point here that makes this worth reading even if you don’t like baseball (I do, so I had fun with this, and now I have more time with the Mets eliminated).
The Athletic article How fast could a human being throw a fastball? 106 mph, 110 mph—even 125 mph (6/28/2024) has a graph a lot like this one:
The section of the article this occurs in has the heading, The case for 110 mph, with this lead paragraph.
The study of biomechanics, or the mechanical laws relating to the movement and structure of living organisms, has unlocked velocity for a lot of today’s hard throwers. The average four-seam major league fastball, measured by the same technology and methodology, has increased in velocity every season since Major League Baseball started tracking it, all the way from 91.1 mph in 2007 to 94.1 now.
Looking at Figure 1, you could assume that pitchers will just keep throwing faster, so why not 110 mph? The point is that averages can rise without the maximum increasing significantly or at all. We need to take a deeper dive into Figure 1, which allows us to focus on the data rule: Know the distribution.
The data comes from the Baseball Savant Statcast Search page, which has about a million (well, a slight exaggeration) possibilities for data extraction. Despite all of these menu option boxes, you cannot get the maximum fastball velocity for each pitcher, but I can get close with the mean speed distribution by pitcher. The Athletic article contains statistics for every year from 2008 to 2024, but I needed more data, which was slow to download. In the end, Figure 1 has data every three years from 2009 to 2024 because I wanted a more sophisticated look at fastball velocity, specifically the mean 4 seam fastball distribution by pitcher. Let’s discuss Figure 2.
Figure 2 are boxplots by year of the average 4-seam fastball velocity by each pitcher. All pitches were included regardless of how many pitches they threw, and note that there were a few more low outliers for 2018 that were cut out of the graph.
The purple line is the average as in Figure 1. The numbers next to each box are the first quartile, median, and third quartile. The key thing to notice is that the distribution of mean fastball speed by pitcher is moving up but also compressing at the top.
From 2009 to 2024, the first quartile rose from 89.9 to 92.4, an increase of 2.5 mph, while the third quartile rose from 93.4 to 95.6, an increase of only 2.2 mph. More importantly, the top whisker has varied, but 2015 is the year where the top of the whisker is at it’s highest. 2024 is close and does have a few outliers, but the max on the whisker is no higher than in 2015, and the whisker itself is shorter.
Now, all of this is still average data, but it does suggest that we are already seeing limitations on the maximum velocity outside the occasional outlier. This makes sense as we increase our understanding of biomechanics and training. We can make the typical pitcher throw faster, but we bump up against physical limitations of the human body, which we already see in the increasing number of Tommy John surgeries.
Something would have to change to get to a 110 mph fastball, and 125 mph is just clickbait. We are close to 106 mph; in 2010, Chapman hit 105.8, but that is still the record 14 years later. A more honest title for the Athletic article would be Can someone hit 106 mph on the radar gun? The funny thing about the article is that they give a graph of the fastest 100-meter sprint time as an example of hitting a limit in speed, and the corresponding graph for pitching would look at the fastest fastball each year. Unfortunately, you can’t get that data from Statcast, which is good for the Athletic as it would make the article shorter.
One more graph. Figure 3 has the average speed of 4 seam fastballs over 99 mph per pitcher, again not maximums, but we do get to look at the fastest group of fastballs. While there are outliers, a lot in 2024, the boxplot themselves don’t show an increasing pattern. Maybe there are more pitchers in this category, but overall there is no increase in average speed over 99 mph from 2009 to 2024. Certainly nothing to suggest 110 mph is coming soon or even getting to 106 mph.
It will be interesting to update Figure 3 next year to see if we have the same number of outliers. I would bet not. These pitchers have the physical and mental capacity to throw a ball really fast, haven't slowed down with age, and are also having a great season. Notice how Aroldis was an outlier in 2012, 2015, and 2018 but then not in 2021 or 2024. The Athletic could have used data better in their article.
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Please point out if you think something was expressed wrongly or misinterpreted. I'd rather know the truth and understand the world than be correct. I welcome comments and disagreement. We should all be forced to express our opinions and change our minds, but we should also know how to respectfully disagree and move on. Send me article ideas, feedback, or other thoughts at briefedbydata@substack.com.
Bio
I am a tenured mathematics professor at Ithaca College (PhD Math: Stochastic Processes, MS Applied Statistics, MS Math, BS Math, BS Exercise Science), and I consider myself an accidental academic (opinions are my own). I'm a gardener, drummer, rower, runner, inline skater, 46er, and R user. I’ve written the textbooks R for College Mathematics and Statistics and Applied Calculus with R. I welcome any collaborations.