Why Do We Use MPH? by Brad Johnson November 16, 2013 The Hot Stove is still pre-heating, so while we wait on the oven timer, let’s reflect on a topic that we rarely question. Provocative title aside, why do we use miles per hour, more commonly referred to as mph, to talk about velocity in baseball? After all, it’s a game of feet, inches, and seconds. It’s 60 feet, six inches from the rubber to the back corner of the plate. Home to first is 90 feet. Home to second is 127 feet, three and 3/8’s inches, which can also be expressed as 90 times the square root of two (h/t Pythagoras). The outfield fence is typically somewhere between 310 and 410 feet from home plate. A really long home run will travel 500 feet in about four to six seconds. Billy Hamilton can steal second base in 3.1 seconds. When Jose Fernandez hits a home run, it takes him about 28 seconds to wander around the bases. In other words, no other single activity in baseball is meaningfully measured using miles or hours. A simple googling of the topic reveals nothing helpful. In fact, the search phrase “why does baseball use miles per hour?” never appears. Tinkering with that search phrase reveals very little useful information. We can intuit that the widespread use of mph in baseball has much to do with available technology. Radar guns, which were invented in the late 1940s, are still the primary method for measuring pitch velocity. According to Wikipedia, they were originally invented for military purposes, but the most popular application of the technology is to measure the velocity of cars. You knew that. Baseball Reference traces the origins of the radar gun in baseball to the 1960s. Danny Litwhiler and John Paulson invented the JUGS gun in 1974, which measures pitch velocity from when the ball leaves the pitcher’s hand. It is still the gun of choice today. We can guess why the first guns used mph, but it’s harder to understand why it has remained the unit of measurement for pitch velocity. When Justin Verlander follows a 95 mph fastball with a 98 mph fastball, we know that he’s throwing gas, but it’s not obvious how the hitter’s reaction time is affected. If Verlander were then relieved by Jamie Moyer’s 78 mph fastball, how much more time would a hitter have to react? It would seemingly be more intuitive to use feet per second (ft/s) as these are units that translate directly to the activities on a baseball diamond. Below is a conversion from mph to ft/s with time to plate added for fun. *The time to plate column is based on 60 feet, six inches for simplicity and uniformity. To accurately measure time to plate requires knowledge of the exact release point of each pitch, which is generally between 52 and 55 feet. It’s also worth noting that the velocity diminishes fairly rapidly once the ball is released, so actual pitches will take slightly longer to travel 60 feet. As you can see, one mph equates to about 1.467 ft/s. Put another way, 15 mph equals 22 ft/s. Ostensibly, those of you out in Readerland are waiting for an explanation as to why the above chart is groundbreaking. Well, it’s not. In fact, ft/s is scarcely more intuitive than mph. Let’s face it, if ft/s was a groundbreaking change, saberists would have been all over it years ago. There are, however, a couple simple advantages to ft/s. The relationship between velocity and reaction time is immediately obvious. Anyone can take 60 feet, mentally divide by the observed ft/s, and have a rough estimate of how much time the batter had to hit the pitch. The measure also allows for slightly greater precision, but that is of dubious value. Besides, anyone analyzing PITCHf/x or Trackman data will have precise information regardless of the unit of measure. It’s generally accepted that a one mph increase in velocity results in fewer runs allowed. Combining these results with the above chart shows that a hitter’s ability can be strongly disrupted by a pitch that travels only a few thousandths of a second faster than the previous pitch. Hitters are already operating at the extremes of a human’s ability to accurately track and interact with an object in flight, and even the most marginal of changes could tip the scales in favor of the pitcher. For example, the difference between a 98 mph Verlander fastball and Moyer’s 78 mph slowball is just a single tenth of a second. The chart also tells us why there has never been a groundswell to convert from mph to ft/s. Most baseball fans learn the relationship between an impressive pitch and its velocity pretty quickly. Announcers are usually capable of filling in the gaps for more casual fans. Thinking in thousandths of seconds remains an esoteric concept for most people, so being able to immediately convert velocity to a rough measure of reaction time has no practical purpose. All told, it’s hard to dispute that ft/s is qualitatively more useful to a baseball fan. You can intuit more information from ft/s, however the value of that information remains limited. The time to make the change was probably back in the 1970’s, shortly after the JUGS gun was invented. Today, a change would require an uphill battle against tradition. Simply put, it is not worth the effort.