Category Archives: Science

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

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Instant replay in tennis

This afternoon, I tuned in for the last two games of the Wimbledon semifinal between Andy Murray and Jo-Willy Tsonga. Andy Murray won the match, making him the first British male finalist at Wimbledon in 74 years (no pressure, Andy!).

The winning point was a bit strange, however. Murray hit an aggressive shot that was a tough call for the umpire. The crowd exploded, but then quickly realized the ump called it out. No matter. Murray put a finger in the air and challenged the shot. Under tennis replay rules, players can challenge in or out calls, and the disputes are decided by the Hawk-Eye ball tracking system. Hawk-Eye uses high frame rate cameras to map the trajectory of the ball. The Hawk-Eye trajectory showed the ball nicking the outside of the line, and Murray was through to the finals!

I asked my buddy Tony, a staunch replay opponent, whether he would have felt bad if Murray had lost the match in the absence of replay review. He said no, because he guessed the tennis replay system faces precision issues. This is his standard “blades of grass” complaint. On extremely close plays, there is no way to tell whether a ball (or player, in other sports) is in or out, because it comes down to the deformation of the ball on impact, individual blades of grass, and lack of precision in painted lines.

I set about to prove him wrong, under the premise that a computer-driven system like Hawk-Eye would have definable precision. In one way, I was right. Hawk-Eye’s average error is 3.6 mm. But if that’s the case, why is it used to make calls that are well within it’s margin of error? Continue reading

Basketball endgame

The Thunder and Warriors played a very entertaining game last night. All the stars showed up (Monta Ellis, career high 48 points; Kevin Durant, 33 points, game winning shot, close to a triple double). The defense wasn’t terrible — the Warriors especially made a bunch of tough shots. Close games like this are generally decided by luck, but there were two interesting decision points in the endgame where each team affected the odds:

Down one, should you shoot early or late?

With about 22 seconds left, down one point, the Thunder had Durant drive right to the hoop and go for a quick shot — air ball, but the Warriors knocked it out of bounds. On the next inbounds play, Durant pulled up immediately and banked in a (relatively) open jumper to take the lead with 16 seconds remaining. This gave the Warriors plenty of time for a rebuttal, and the Warriors announcers were confused that the Thunder didn’t run down the clock to take the last shot.

The Thunder clearly wanted to shoot quickly. Did this help or hurt their chances of winning? It gives the Warriors another chance Continue reading

Adventures in clock operation

The Kings got a little hometown boost from the clock operator last night and scored with (supposedly) 0.4 seconds left to beat the poor Blue Jackets. If you watch the highlight video from the 25 second mark to the 35 second mark, you’ll see that the clock freezes with 1.8 seconds left. The NHL has admitted that more than 0.4 seconds elapsed during the freeze (so the goal probably shouldn’t count), but they aren’t going to change the outcome.

What was the Kings’ defense? From Kings’ GM Dean Lombardi (written to ESPN):  Continue reading