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## Rounding the Bases Faster, With Math212

Posted by timothy
from the suh-wing-battah-battah-battah dept.
An anonymous reader writes "The fastest route around the bases, mathematicians show, is one that perhaps no major-league ball player has ever run: It swings out a full 18.5 feet from the baseline, nearly forming a full circle. 'I would definitely experiment with it,' says former American Major League Baseball outfielder Doug Glanville, who last played with the Philadelphia Phillies. 'There's no question in my mind that runners could be more efficient.'"
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## Rounding the Bases Faster, With Math

• #### Re:Hitting the brakes slows you down. (Score:3, Insightful)

<dc-7@@@charter...net> on Saturday October 23, 2010 @10:25PM (#34001240) Homepage
Well, yeah, always obvious in hindsight, but I'm just waiting for someone to say, "If that really worked, everybody would be doing it already."
• #### Re:Hitting the brakes slows you down. (Score:5, Insightful)

on Saturday October 23, 2010 @10:36PM (#34001300) Homepage

If that really worked, everybody would be doing it already.

And indeed, baseball players typically do this: They run straight along the baseline at the beginning and then, if they think they’ve hit a double or more, they bow out to make a “banana curve. ... Carozza noticed that even when the ball heads straight for a pocket between fielders, making a double almost certain, runners almost never curve out right away.

The researcher seems to expect ball players to gamble with every such run, betting their play on what the researcher thinks is "almost certain". That means that, while trying to hit the ball, the player must know the tactics and maximum speeds of all the opponent fielders. I don't think that's going to happen.

• #### Re:Hitting the brakes slows you down. (Score:5, Insightful)

on Saturday October 23, 2010 @10:46PM (#34001346) Journal

Players don't run in a big circle because there is no reasonable expectation they can round all four bases. They're lucky to get one.

You get a hit, you run straight for 1st. If after arriving you can keep going, you curve over to second. Unless you belted it out of the park (and are therefore in little hurry) it's unlikely you can get further than that, but anybody going on to 3rd will make another wide curve.

In general, if a runner thinks he can clear two bases, he'll make a wide curve. Otherwise it's just a beeline for the next base.

• #### very telling (Score:4, Insightful)

on Saturday October 23, 2010 @11:25PM (#34001510)

none of the researchers or verifiers actually got off their ass and ran bases to test

• #### Re:Baseball is still a shitty sport. (Score:4, Insightful)

on Saturday October 23, 2010 @11:59PM (#34001652) Homepage Journal
LOL troll.

Nah, you have a good point. Baseball was the only sport to require an organist [voanews.com] to fill in the boring parts.

Modern baseball games are even worse. Even live, only a fifth of the game is actual baseball. The rest is filler provided by the jumbotrons and sound systems. The only redeeming qualities of going to meatspace MLB games are getting really drunk and laughing inside about how our kids don't fully understand the meaning of the popular song Hey-oh [songfacts.com] that's being played every 5 seconds over the PA.
• #### Re:Maybe for a home run... (Score:3, Insightful)

on Sunday October 24, 2010 @12:05AM (#34001678)

I would guess that *most* mathematical research is done without any expectation of a "useful" outcome. On the other hand, how much of our modern world would be possible without that exact type of "I wonder..." research?

• #### Re:very telling (Score:2, Insightful)

on Sunday October 24, 2010 @12:26AM (#34001760)
Do you want some engineer that designed something to test it out to see if it improves professionals performance half a percent?

Please. This is to help real baseball players who really run bases. If the math guys could suddenly outrun the professionals, fine, but this is a clear fraction of a fraction gain, not a leap forward.

You don't get non-runners to do a running test. How is this insightful? Seems more "funny" to me.

• #### Wrong answer, but the truth is easy to derive (Score:5, Insightful)

on Sunday October 24, 2010 @12:32AM (#34001778)

"At first you might think that a very slow, awkward runner should just walk directly from base to base, except that he'd likely fall down trying to make the sharp turn at first.."

I would like to point something out.

Making a 90 degree turn is physically impossible without coming to a complete stop. If a person immediately applies a force orthogonal to their current velocity, it would not result in a 90 degree turn in the path (but it would probably cause them to fall down). The only way to make a 90 degree turn is to come to a complete stop, then turn, then accelerate in the new direction. There would be no reason for the runner to fall down under these circumstances.

Because our muscles exert a finite amount of force, and force is the time rate of change of momentum, and momentum is mass times velocity, the time required to come to a stop must be proportional to the velocity of the runner.

This confirms the obvious fact that for a walker, the time that it takes to go from walking speed to a full stop is a fraction of a second, and hence there is no measurable time wasted in making a 90 degree turn, and no reason to walk anything other than the shortest path if you are walking.

We know that the optimal path for a faster runner involves some overshooting, and this proves that there is a continuum of optimal paths that is dependent on velocity. It is also clear from Newton's first law, as I showed above, that running faster befits reducing curvature of the path. This applies to any velocity. Thus, in the limit as velocity goes to infinity, curvature becomes ever increasingly important, and hence in the limit the optimal path must be a circle.

• #### Re:Hitting the brakes slows you down. (Score:4, Insightful)

on Sunday October 24, 2010 @01:53AM (#34002028)

Exactly. He takes visual queues from the opposition players and coaches. Do I keep going, or do I stop. The decision for all four bases can't be made as soon as he contacts the ball. He hits it, he runs for 1st. Is it safe to go for second? Continue on, but that decision is made at or near 1st base.

Why does everyone keep repeating this? It's not true. I'm not a major league player, but after watching a good number of games, I assure you that I, most fans, and every major league player knows, very likely, what base they will reach when it becomes apparent where the ball will land. Sorry to repeat myself:

* Over the centerfielder's head: Triple
* Reaches the wall elsewhere: Double
* Doesn't make it past the outfielders: Single

If the defense tries to make a play on another runner, you might take an extra base, and there are a few other variables, but the above is pretty reliable. Think how many times a major leaguer has hit a ball: It's not like they have no idea what is going to happen, or that they won't make it past first when they hit it a line drive off the wall in left-center.

• #### Slashdotters talk baseball (Score:5, Insightful)

on Sunday October 24, 2010 @02:50AM (#34002204)

This is pretty funny. If we were talking about Halo, we wouldn't see so many naive claims and theories, and so many of them moderated up! Instead of replying to each one, let me clarify a few points:

A major league batter knows the base he'll likely reach as soon as he knows where the ball will land. Having seen many thousands of hits, he can make a pretty good judgement pretty quickly. I've merely watched the games, and I can tell you well before the ball lands. It's all done without any math or calculations, if you can believe it, just rules of thumb based on experience:
* Over the center-fielder's head is a triple
* Reaching the wall elsewhere: a double
* Doesn't get by the outfielders: a single.

There are variables from that 'baseline': The defense could make a play on another baserunner, giving the batter the chance to get another base. Fielding mistakes, and sometimes a hard hit, a very fast/slow runner, or a very good/bad arm can make a difference of a base, but it's rare.

For the other question, I really don't know for sure. Baserunners are regularly outside the baselines, but I've rarely seen a baserunner go that far out unless he was avoiding a tag, taking out a fielder in a double-play, or over-running first base. But they sometimes round bases pretty widely without being called out. The rules are more complicated than they appear and the umps have discretion. I don't know for sure, but I doubt they'd be called out unless they were avoiding a tag or interfering with a fielder. I wouldn't depend on an answer that didn't come from an umpire.

I'm just a long-time avid baseball fan. I'm surprised I don't see more on /.; baseball depends heavily on a very controlled environment (batter vs pitcher) and is accessible to extensive statistical analysis. For those interested, I recommend Baseball Prospectus [baseballprospectus.com], Baseball Think Factory [baseballthinkfactory.org], the Society for American Baseball Research [sabr.org] (SABR), and the writings of Bill James [wikimedia.org], the great modern popularizer of the statistical analysis of baseball (I think of him as the Bruce Schneier of baseball -- very insightful, clear analysis). Now, back to your regularly scheduled News for Nerds ...

• #### Actually, quite a bit of science is involved. (Score:1, Insightful)

by Anonymous Coward on Sunday October 24, 2010 @03:56AM (#34002408)

But like in most real-time decision-making scenarios, a lot of it is gamed out and optimized ahead of time. Check these out:

• #### Re:Maybe for a home run... (Score:3, Insightful)

on Sunday October 24, 2010 @04:27AM (#34002482)

t just shows the difference between the exact science of mathematics, and the heuristics of game theory/statistics, etc.

I think the problem is that no _serious_ mathematics has been applied. This is just two guys running with an idea and a bit of very imprecise computer simulations and then put up an article on the internet. Their model of a runners' speed and accelleration is very imprecise. You'd have to take factors like exhaustion and ability to accelerate running in a curve vs. a straight line into account. Then game theory and statistics (which both fall under the exact science of mathematics) have not been applied at all. The problem isn't that mathematics doesn't work, it works just fine, but you have to do it seriously. These guys haven't.

• #### Re:1st page of the proof: (Score:5, Insightful)

on Sunday October 24, 2010 @06:06AM (#34002844)

These days? Have you seen a picture of Babe Ruth?

• #### Re:Baseball is still a shitty sport. (Score:3, Insightful)

on Sunday October 24, 2010 @07:47AM (#34003264) Homepage
One fifth is still better than the NFL, which I believe hovers around one eighth. That's half of the reason I watch hockey - play is always moving when the clock is running. Even when the clock isn't running, stoppages rarely take more than 30 seconds.
• #### Re:Hitting the brakes slows you down. (Score:3, Insightful)

on Monday October 25, 2010 @09:44AM (#34012110) Journal

Not to mention "hits the wall near Pesky's Pole and before the fielder can react it's scuttled like a rat all the way to the bullpen." Inside-the-park home run in that case if you're a decent runner.

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