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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

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

by Anonymous Coward on Saturday October 23, 2010 @10:33PM (#34001284)

1st page of the proof:
Consider a spherical runner in a frictionless vacuum.

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

on Saturday October 23, 2010 @11:23PM (#34001500) Journal

Consider a spherical runner...

Baseball players are approaching that these days.

• #### 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: (Score:2)

This is the funniest thing I've ever read in /.

Bravo.

• #### Re: (Score:2)

I'll be interested to see how they make turns in a frictionless vacuum. Maybe with an RCS [wikipedia.org]?

• #### Re: (Score:2)

I'll be interested to see how they make turns in a frictionless vacuum. Maybe with an RCS [wikipedia.org]?

It didn't say it was tractionless vacuum. Frictionless just implies that no energy (as heat, sound etc) is lost to friction.

• #### Re: (Score:2)

Traction relies on friction.

However, I don't know if the op was being pedantic or funny. I'm just bored and pointing out the obvious even though your comment was obvious.

• #### Re: (Score:2)

Traction relies on friction.

I see what you are thinking, but a pendulum swinging in a vacuum still follows a curved path..

• #### Re: (Score:2)

What? Since when are baseball players attached to a pendulum? I'm pretty sure they have to rely on traction to round those bases.

• #### Re: (Score:2)

Traction relies on friction.

I guess the dictionary definition does. I was actually referring to more general concept, which would include things like frictionless gears (which would still transmit power to connected gears) or maglev train propulsion (I think it's generally called propulsion and not traction), and (since we're talking about a spherical runner moving in a vacuum) even Star Trek tractor beams.

• #### Re: (Score:3, Interesting)

They charge the runners and apply a magnetic field perpendicular to the playing field? Synchrotron baseball. Cool.

• #### Re: (Score:3, Interesting)

1st page of the proof:

My good friend and neighbor, the mathematician G.V. Ramanathan has an article in this weekend's Washington Post that seems a little bit relevant to this discussion. It's called "How much math do we really need?"

I recommend you take a look. He makes a very interesting point. [See? I told you I'd find a way to promote it on Slashdot.]

• #### Maybe for a home run... (Score:5, Interesting)

on Saturday October 23, 2010 @10:42PM (#34001332)

The main reason why they've calculated a circular path is because of the delays that sharp turns introduce. As far as I can tell, this path makes sense if and only if you're trying to run from home to home. If you're going for a single, or a double, or a triple, you'd have different ideal path.

So even in theory, this doesn't really pan out: nobody in MLB makes it to home-plate on an outfield hit. You could probably come up with more effective routes for doubles and triples, but on the other hand, it's probably hard to tell if you've hit a triple right as you start running. If you make a hit that would be a triple, but follow a route like it's a single and then change your mind as the ball gets played, you'll probably still end up with a single or a double. If you start running for a triple on a base hit that's only really going to get you a single, it could slow you down enough to get you out. I'm more in the hedge-your-bets camp, and I'm betting that, on that basis, this isn't an effective way to go.

• #### Re: (Score:3, Funny)

On the other hand, if it works, maybe high school jocks with start to find it counterproductive to bully the math geeks.

• #### Re: (Score:2)

Or perhaps, this is some math geek's way of getting back at the jocks by making them run in silly circles and loose the game. If we ever get a scientific report that the best route is in fact skipping from base to base, then we'll know for sure.

• #### Re: (Score:2)

"silly circles and loose the game"

And the grammar geeks will pick on the math geeks for using the wrong word instead of 'lose'.

Ignore my "beginning a sentence with 'and'" and putting the period outside of the quotes; that's how I write.

And yes, I probably put a mistake in here too.

• #### Re:Maybe for a home run... (Score:5, Funny)

on Sunday October 24, 2010 @12:16AM (#34001724)

Well, if the math geeks can find a significant increase in efficiency, and they don't tell the jocks, then guess who gets the ladies?

(The jocks. But it was worth a try.)

• #### Re: (Score:3, Informative)

TFA addresses this. The ideal path for a double still curves quite a bit, going about 14' off the straight line path instead of 18 for the home to home path.

It is amusing to think that the only time you know when you leave the plate that you're running back to home for sure is the same time when it doesn't matter how fast you go.

• #### Re:Maybe for a home run... (Score:5, Informative)

on Saturday October 23, 2010 @10:52PM (#34001380) Homepage

As far as I can tell, this path makes sense if and only if you're trying to run from home to home. If you're going for a single, or a double, or a triple, you'd have different ideal path.

As the article notes, the authors are aware of this. They also are aware of the fact that runners seldom adjust to more efficient paths even when they know they've hit doubles, not singles. This was, in fact, the motivation for the study.

I think you're confusing their point: they're quite clear that they don't think that this helps in reality (at least, not much). It's an exercise in "I wonder..."

• #### Re: (Score:2, Funny)

when they know they've hit doubles

Right. The players will hit the ball, then watch carefully and verify its path, do some quick back-of-the-envelope calculus to verify the fielders' maximum speeds, apply their doctorate-level psychology knowledge to anticipate the fielders' actions, then once they know it's a double, they'll start running a longer path that's faster if their bodies work according to various assumptions.

Or, they'll just run, and figure out what's best as they go.

It's baseball. It's not rocket science.

• #### Re: (Score:2)

Modded, funny, but should be modded insightful (since it's what I was going to post ;)

The whole point that makes this article useless is that the optimal path requires perfect knowledge of the target base from the start, and that's just not how baseball works.

It just shows the difference between the exact science of mathematics, and the heuristics of game theory/statistics, etc. The average (ok slightly above average) player hits maybe 25 doubles and a couple of triples, vs over 150 singles. So, statistic

• #### Re: (Score:3, Insightful)

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

• #### Re: (Score:2)

So its like Philosopher's football? [youtube.com]

• #### Re: (Score:3, Interesting)

Right. The players will hit the ball, then watch carefully and verify its path, do some quick back-of-the-envelope calculus to verify the fielders' maximum speeds,[...]

Or, they'll just run, and figure out what's best as they go.

Those are the same thing. Brains are smart and very good at prediction, especially given the training a pro ball-player goes through. It's 3 seconds to first base - that's a lot of time to predict and adapt. Ball players do it intuitively; the physicists have just quantified it (and probably failed to account for a dozen parameters that a ball player's brain will accommodate without their conscious awareness.

• #### Re: (Score:2)

It's an exercise in "I wonder..."

Great. I wonder how many of my tax dollars this year were spent so that mathematicians can indulge in "I wonder..." studies where there is no expected useful outcome?

• #### Re: (Score:3, Insightful)

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: (Score:2)

Duh, you must be new here. That's why it's called mathematical research and not physics or some other specialty. The main difference is that with math you're focused on the mathematical challenge rather than the what actually happens stuff.

Not that there's anything wrong with it or that it never gets applied, it's just not usually referred to as mathematical research if it has a direct and obvious application.
• #### Re: (Score:2)

Maybe I've been drinking too much...I missed that line.

I haven't played baseball since Little League, certainly not on a professional level, but I would think that a runner would have to pay attention to what the outfielders are doing, and adjust on the fly. If so, it's probably better to aim on the side of caution.

But of course, none of what we're talking about right now is reality, reality is the Rangers in the World Series (I've now lived in Dallas long enough that I probably have to become a fan now), w

• #### Re: (Score:2)

It could be potentially useful though, too. Baseball is home to a lot of "we do it this way because we've done it since the 1800s", as well as a lot of "I'm doing it this way because I think I'm clever". This is in frequent contrast to the actual evidence.

For Chrissakes, there are runners who still slide/dive into *first* because they inexplicably think it's faster (and no, not just to avoid a tag).

• #### Re: (Score:3, Interesting)

Additionally, they discount the fact that you can use the base to apply extra side-force to cut the corner faster. - the fastest path around the bases is to curve a little but mostly to use the inside corner of the base, with your outside foot, to push off in a new direction. Baseball has been played for 150 or so years,and has been studied to death by both the finest minds in sports and some of the best athletes, in real life. The ideal path has been known for more than a century, and coached accordingly.

• #### Re: (Score:2)

"So even in theory, this doesn't really pan out: nobody in MLB makes it to home-plate on an outfield hit."

There are numerous inside-the-park home runs every season. Common? No, not really, but they happen often enough that to say that "nobody..." does it leads me to believe that you (and those who modded you) don't actually watch baseball. That's fine; it's not for everyone. Kindly refrain from commenting on it if you don't actually know what you're talking about. I know, I know, this *is* /.

• #### This misses the point (Score:2, Informative)

by Anonymous Coward

No one cares about how fast you can round _all_ of the bases. There are only two times when it is applicable -- a home run or an in-field home run. The first makes the speed unimportant. The second really doesn't happen frequently.

The player will hit the ball, and then attempt to get to first base. If conditions look good, they will try for second base. At this point, third base will only be attempted in rare cases, mainly when an error has been made by the fielding team. The double/triple attempts ar

• #### Guess I'm confused (Score:4, Funny)

on Saturday October 23, 2010 @10:58PM (#34001412)
I thought a 'home run' was something else entirely. Involving a girl. A naked girl. I didn't know running in a circle was part of the process. Or running at all, for that matter.
• #### Re: (Score:3, Informative)

I thought a 'home run' was something else entirely. Involving a girl. A naked girl. I didn't know running in a circle was part of the process. Or running at all, for that matter.

Meat Loaf [youtube.com] can explain the connection.

• #### 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: (Score:2, Insightful)

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.

• #### Re: (Score:2)

If the math guys could suddenly run at all, fine...

There, fixed that for you.

• #### Re: (Score:2)

From the article:

A path that follows a circle turned out to be a whopping 25 percent faster.

That's a pretty big performance boost. It'd need to get to 33% faster to turn a 3rd base run into a home run every time, but there may be times when 25% is all you need.

• #### Re: (Score:2)

funny, for most of human history everyone knew how to run. Now only paid specialists can do it. I see.

Those that marked you *insightful* are a pathetic part of modern society's health and mind problems

• #### Stand Back! (Score:2)

Stand Back! I'm going to try SCIENCE! ...

so if you're standing within about 14 feet of the baseline, I might run you down. Seriously. Stand back!

• #### 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.

• #### Tagging up on 3rd (Score:2)

I often wondered why, if a runner is on say, 3rd and the batsman hits a long fly ball (but not a homer), why does the runner wait at 3rd to tag up, instead of backing up a few paces so that he can hit 3rd base at full tilt just as the fielder catches the ball. This would easily give him 2 or 3 if not more strides jump and he should be safe at home more frequently. In a game of fractions of a second, this would be a clear advantage.

• #### Re: (Score:2)

That might make sense if they were certain the ball is going to be caught, but usually they advance a little bit so they're that much closer to home in case the ball isn't caught.

• #### Re: (Score:2)

Doesn't make sense...if they hit 3rd running at the instant the ball is caught or dropped, they still have a jump from a stationary start.

• #### He can be called out on appeal, that's why. (Score:4, Informative)

on Sunday October 24, 2010 @05:56AM (#34002806)

Rule 7.10(a): [mlb.com]

"Any runner shall be called out, on appeal, when --
(a) After a fly ball is caught, he fails to retouch his original base before he or his original base is tagged;
Rule 7.10(a) Comment: "Retouch," in this rule, means to tag up and start from a contact with the base after the ball is caught. A runner is not permitted to take a flying start from a position in back of his base."

In case you're curious about the relevance of comments, there is this note in the Official Rules Foreword: [mlb.com]

"The Playing Rules Committee, at its December 1977 meeting, voted to incorporate the Notes/Case Book/Comments section directly into the Official Baseball Rules at the appropriate places. Basically, the Case Book interprets or elaborates on the basic rules and in essence have the same effect as rules when applied to particular sections for which they are intended."

• #### Re: (Score:2)

To gain the maximum effect, you would need to know how far to back up, since different flight paths of the ball take different times. More importantly, you can't be wrong by even a fraction of a second the wrong direction or you will not have "tagged up" after the ball was dropped. This latter bit is probably the most important point, especially since you must be seen tagging up after the ball is dropped.

My supposition is that the error involved is greater than amount of time gained on the trip towards home

• #### Liners should always be run as doubles+ (Score:2)

A lot of commenters seem to think this is a bad idea, but once you're sure you hit the ball over the infield, you should be running as if you've got at least a double, as your single is essentially guaranteed regardless of how you run (unless they catch your fly ball, in which case you're out anyway). Most ball players can immediately tell the difference between hitting the ball into the infield and hitting it over them (and if it goes through on the ground, the first base coach should be telling you what

• #### 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 ...

• #### What about momentum from the swing? (Score:2)

Take a right-handed batter. The swing will turn the batter toward third, making the run toward first naturally start toward the inside of the diamond. On the other hand, a left-handed batter will naturally start on a more outward trajectory. I wonder if this is a quantifiable advantage in doubles statistics for left-handed batters after accounting for factors like the shorter distance to first base from the left-handed batter's box.
• #### intuitive (Score:2)

Any math teacher should know this:
http://en.wikipedia.org/wiki/Brachistochrone_curve [wikipedia.org]

In brief, the Brachistochrone problem asks: what is the shortest time between two points. I'm simplifying a bit. It isn't always a straight line!

It should be fairly obvious to anyone in academia that the solution presented intuitively makes sense. Assuming that the goal is only to round the bases as fast as possible.

I do have to add that it seems sad that professors these days solve problems with mathematical modeling ins

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