⚾Baseball Physics: Does the Pitcher’s Mound Increase Velocity?

First published at 00:37 UTC on November 5th, 2017.

In this video I go over an interesting question regarding the baseball pitching speed and if the pitching mound adds to the ball velocity. This was a question forwarded to me on Twitter, and thus I look to get to the bottom of it. The pitcher’s mound is a circular hill located inside a baseball field, and has a rectangle rubber plate where the picture must start his pitching momentum from. According to the official Major League Baseball (MLB) regulations, the distance from the front of the plat to the rear point of the home plate is exactly 60 feet 6 inches (about 18.44 m). The mound height measured to the top of the rubber plate has a maximum limit of 10 inches. This max height was lowered on 1969 from 15 inches (and sometimes higher to 20 inches) because the pitching had become very dominant. This is because the mound height gives a higher downwards velocity and thus makes it harder for the batter to hit the ball squarely.

To understand how the velocity of the ball changes, it is first important to understand just how the ball speed is measured. The MLB uses a Radar measurement technique, which involves a Radar Gun that shoots electromagnetic radio waves (at the speed of light) towards the ball and measure the resulting waves that bounce back. Due to what is known as the Doppler Effect, the frequency of the waves that bounce back from the ball depend on the speed the ball is traveling. The higher the frequency, the faster the ball speed. While this is a good way to measure ball speed, it is difficult to indicate whether the velocity measured is the horizontal or absolute ball speed. But as I show later in this video, the theoretical differences in horizontal and absolute speeds are negligible for a typical baseball pitch.

Going over some baseball physics, trigonometry, and calculus, while simplifying some of the many unknowns such as pitcher height, air resistance, etc., I am able to obtain some basic formulas for the speed of the ball upon release and just as it reaches the home plate. Throwing all these into a Microsoft Excel Spreadsheet that I made, we can see how the speeds differ for different mound heights. The calculations show that the horizontal and absolute speeds are very similar at any mound height, and thus it is expected that the Radar Gun readings should remain the same; assuming pitching mechanics and human physiology is negligible for this slight downwards angle. Nonetheless what is significant is the downwards velocity as the mound increases. It appears that for every 10 inches in mound height, we expect roughly 1.6 miles per hour (mph) downwards velocity increase! Given that the major leagues is a game of inches, the mound height gives the pitcher a big advantage as it makes the batter worry not only about balls coming towards himself fast, but that it is moving downwards fast as well. This helps explain why 1968, the year before the mound heights were decreased, is known as “The Year of the Pitcher”!

This is a very interesting example on applying mathematics to the world of sports, of which Baseball is all about the numbers, so let me know what you think, and play around with the Excel sheet that made to see what cool statistics you can find!

Download the notes in my video:

PDF: https://1drv.ms/b/s!As32ynv0LoaIhvsC_9GQSBQgxYoRvg
Excel: https://1drv.ms/x/s!As32ynv0LoaIhvsDjym7tVJC4vSv9g

View video notes on the Hive blockchain: https://peakd.com/mlb/@mes/video-notes-baseball-physics-does-the-pitcher-s-mound-increase-velocity

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