Tag Archives: Evan

Billy Hamilton: faster than the optimal path

Cincinnati Reds minor leaguer Billy Hamilton is making noise with his speed – he set the minor league steals record on Tuesday, surpassing Vince Coleman’s 145 (though Coleman did it in fewer games). Hamilton was on my radar for the Portland Peskies awhile ago, after he clocked a 13.8 second in the park home run. In case you’ve forgotten, the Peskies are a hypothetical team built on undervalued baseball skills: speed, bunting, defense, and even knuckleball pitching. I’m convinced that you could build a decent baseball team for very little money by focusing on these skills.

Upon seeing Hamilton’s in the park home run time, I immediately started the mental math: 360 feet is about 110 meters, but you need to bow out to turn the corners, so maybe 120-130 meters is a good guess. The world record for the 100 meter dash is about 9.6 seconds, so a world class sprinter could do that distance in about 11.5 to 12.5 seconds — in a straight line.

But those corners complicate things. They slow you down, which makes it difficult to determine the optimal path. At one extreme, you could minimize the distance by running directly to each base and cutting hard. This is surely not the fastest way. At the other extreme, you can draw out the circle that touches each base. Again, surely not the fastest, since you don’t have to make a turn at home plate.

So, what’s the optimal path? A couple of math professors worked with a student at Williams College* to try to figure it out. The path they end up with has the batter bow out at a 25 degree angle, swing even wider than the circle from first to third, and aim for home on a relatively straight line. This path is far wider than most batters run.

Not a bad effort, but I’m not buying it. In order to prove Continue reading


The Prince Heavy Side Function

Here’s one potential career “arc” for Prince Fielder:

I call it “the Prince Heavy Side Function,” after the famous Heaviside step function. The graph above certainly has a “heavy side,” though Oliver Heaviside himself was not heavy at all.

Oliver "Not So Heavy" Heaviside

Thanks Brother Evan for suggesting the graph above!