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Rounding the Bases Faster, With Math
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.'"
Kind of obvious when it's pointed out to you. :)
Of course if you're only trying to get to first, a straight line might be advised.
1st page of the proof:
Consider a spherical runner in a frictionless vacuum.
So there's a single, precise path for this?
It doesn't vary even slightly based on one's mass, the length of one's legs, or anything?
Is that model presumes that the batter's immediate intention is to round all the bases. That is certainly not the fastest path to run a single.
If you leave the accepted line of travel too far, they call you out. Its a judgement call, but I wouldn't want to push my luck if I was a player.
God spoke to me.
If the majority of hits are singles, does this still apply? It only mentions hitting a double in that you can round the base faster. It would look pretty funny if the batter used this for a single and it took them much longer.
Carl Sagan quotes get you an automatic +5 on all posts.
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.
I don't believe in time. It's a grand conspiracy designed to sell watches.
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 are more based on information that isn't known when the player first hits the ball. As such, the action will be to take the fastest path from the current base to the next base.
So that swooping path can't be slower than the straight path or the player risks giving up a lot of singles and allowing double-plays. These are often determined by fractions when the fielding team is efficient.
Does this not seem like a round-about answer to anyone else? *hides under a desk*
Once you start despising the jerks, you become one.
Runners can be called out for running outside the basepath, which is 3 feet to either side of the baseline. It usually only comes up on plays where the runner is trying to avoid a tag, but that's also usually the only time anyone ever goes very far from the baseline. It's quite likely a runner would get called out well before they got 18.5 feet away from the baseline.
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.
I would have been called out for running a line like that.
All I'm hearing out of you is "watching tall lanky guys", "bouncing balls", "putting it in a guy's hole", "playing with a guy's stick", and "left hand tugging a guy". It makes me think that you might be a user of Apple products.
...its against the rules. Awww. (just noticed pashyM's comment
The players must run the base-lines, to allow the team on defense a reasonable expectation of where the path they will run from one base to another in order to apply a tag for an out.
Really though, I'm glad they did this research to show that humans can't turn 90 degrees at an all-out sprint.
"You said 'Run Home', so he did!"
but I'll try it if it stops those morons in Boston from rioting.
Come on. Admit it. You're a Philly fan.
none of the researchers or verifiers actually got off their ass and ran bases to test
Unbeknownst to those cricket-playing islanders off the coast of Normandy, Time Lord and wander Doctor Who is the one who's on first. (Surprised he plays baseball? I was.)
Could I get this in a car analogy?
LOL troll.
Nah, you have a good point. Baseball was the only sport to require an organist 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 that's being played every 5 seconds over the PA.
Robot Wars - now that's a motherfuckin' sport!
Calculus of Variations! Seriously, it's a fascinating subject. See Brachistochrone. It also ties in closely with optimal control and such subjects. There are some fascinating, counterintuitive results. A professor described a researcher who had used this to calculate the optimal (in some sense) ascent trajectory for a jet aircraft after takeoff. For the specific case, it wasn't even a monotonic climb!
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!
Well, they sorta did... I believe it was last week's episode where Lisa used calculations to get her players to play the game. I normally don't watch the Simpsons but it was 10/10/10 and I wanted to see if they would do something special for that day, which they did.
The rules of baseball do not allow the runner to swing outward of 18.5 from the first and third base lines, so one can not run in a circle.
With respect to first base it makes no sense to run anything other than in a straight line to first base as any other distance would be longer and hence for a runner's greatest speed would be slower increasing the probability he would be called out as it gives fielders more time to throw the ball to the first baseman tor the force out. With respect to third base it would create all kinds of potential difficulties to the rules, such as a runner heading home instead he could head for the restroom near the hotdog stand and then sneak up behind the catcher after he thinks he is continuing the game. It simply wouldn't make any sense to allow a circular route along the first and third base lines.
"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.
No amount of math and analysis will change the fact that baseball is a pretty poor excuse for a "sport"
Baseball is the only game left for people.
To play basketball, you have to be 7 feet 6 inches. To play football, you have to be the same width. ~Bill Veeck, 1975
Baseball is almost the only orderly thing in a very unorderly world.
If you get three strikes, even the best lawyer in the world can't get you off. ~Bill Veeck
More than any other American sport, baseball creates the magnetic, addictive illusion that it can almost be understood. ~Thomas Boswell, in Inside Sports
Ninety feet between home plate and first base may be the closest man has ever come to perfection. ~Red Smith
Baseball
with meth.
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.
Once I was a four stone apology. Now I am two separate gorillas.
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 to do).
Also, to clear up the rule question everyone's asking (I've been an ump for >10 years): so long as no one is trying to tag you out, you can go out as far from the diamond as you want. What you can't do: go inside the diamond. (Also: if you overrun first, even if you curve to the left (or right) as you run past the base, you can't be tagged out unless the ump thinks you've made a break for second, so even fewer worries with this strategy.)
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, Baseball Think Factory, the Society for American Baseball Research (SABR), and the writings of Bill James, 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 ...
There's something deliciously ironic about math helping people get to 3rd base quicker.
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.
I wonder if really good base runners have a left leg that is shorter than their right leg. Like all the tennis players with one arm that's like three times as big as the other one.
"I assumed blithely that there were no elves out there in the darkness"
But like in most real-time decision-making scenarios, a lot of it is gamed out and optimized ahead of time. Check these out:
http://www.amazon.com/Physics-Baseball-3rd-Robert-Adair/dp/0060084367
http://www.baseballcalculus.com/articles.php?name=brad
The authors " assume that regardless of a runner’s speed, he can speed up, slow down or turn at the same rate (more precisely, that his maximum acceleration vector is constant), which isn’t strictly true". Here are some complexities:
The faster you run the slower you can turn (meassured in degrees per second)
In order to turn left without falling you have start leaning your body to the left.. and this takes some time to do.
I thought it was about vector space bases.
Rule 7.10(a):
"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:
"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."
I agree with the guy a few posts back.
Even when it seems "obvious" (off the wall, etc) you almost always base the decision to go to 2nd from the 1st conference presentation. You make contact, start running at fast as you can, everyone starts looking, and you are basically over 1/2 way to 1st base before anyone figures out whether the result has merit. And a lot of the time you are not the only one running - you (and your faculty advisers) have to look out for other runners, figure out what they are going to do, and guess the composition of the peer review panel, etc, to know whether the paper will be accepted for publication.
Trying to plan for the exact base and route to it (beyond the usual wide turn that any little leaguer already knows) from the moment you make contact is about as useful as planning where you are going to swing before the pitch. Mathematics research is NOT a video game...
Now it all makes sense. The paper is actually a parody on outcome-based research investment as depicted in the red states.
Why nerds are not Jocks.... In a real game of baseball, there are only 2 instances where a runner tries to run the entire 4 bases: 1) a home run, in which case NO ONE is trying to complete the loop as fast as possible, heck its more aptly named the home-not-so-brisk-jog. 2) an inside the park home run. While aptly applied, the number of times this situation is attempted, much less completed is so infinitesimally small, if kinda makes this junk science. Furthermore, this idea assumes that the runner is aware of the necessity of obtaining an inside the park home run path (as opposed to say a straight line single) from the time he leaves the batters box. This is simply never the case, a typical inside the park home run is usually a stand up double or stretched triple and during the base running the runner must make 2-3 judgment calls as to the prospects of reaching the next base successfully and usually occurs through some unforeseeable bounce in the outfield or fielding bordering on an error. Therefore, in all but a fraction of a percent of plays, following this path will actually cost runners time, bases and outs. Furthermore, in the instance of a single, where from leaving the box the runner understands extra bases will not be an option, the straight line reigns supreme. The only instance where this applies is when leaving the batters box, where at least a stretched double is assumed. Again providing inside the park home runs occur so infrequently that a four base path should be completely omitted from calculations because it would disproportionately and adversely effect the 2 and 3 base runs. Basically apply the distance/speed algorithm used here to a triple and again for a double both will end up different from the 4 base version and each other, merge these two paths weighted based on the proportionality of doubles hit to triples hit. Thats is the path to be followed. furthermore, overlay the double and tripple paths ontop of the combined paths to allow the runner to deviate from the combined path at any point during the run to accommodate for an assumed more expected result which can be judged multiple times during the run. Now that would be applied science.
If all the players were't so fat. Seriously...
Who else read the article and thought it had something to do with rounding numbers in different bases?
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.
Any math teacher should know this:
http://en.wikipedia.org/wiki/Brachistochrone_curve
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 instead of equations.
Let me know when they finally jazz the game up!
If a baseball hitter is running 18.5 feet outside of the base path, he's running on grass, not the dirt of the base path. The surfaces are different, as are the mechanics, the drag, the effect on the cleats over time.
Even the huge dirt warning tracks in professional or college baseball stadiums are no more than 10 to 15 feet wide. It's thinner at lower levels (like Little League).
Better mathemeticians would have factored in these differences. They wouldn't just assume a constant running surface.
A big circular shaped run would undoubtedly be ruled as running out of the baseline.. engendering an automatic out.
Granted the Umpires allow some leeway, typically less the 6 ft from the actual line... but still ....
I navigation, it takes longer to make small course changes to account for the curvature of the earth so traveling a curved line is usually faster to avoid breaking the momentum.
Since when is a sport required to maintain a frantic pace to be entertaining? I think most people watch a sport based on what happens when there is action not how often those actions occur.
In the park home runs are very rare. And usually happen with only the swiftest runners or errors in the outfield(maybe both).
What really matters it what is the quickest way to get to second base.
When a batter hits the ball he knows quickly if the ball will go to the outfield or stay in the infield.
He will need to make a snap decision on how to run to first base. Infield, straight to the base. Outfield, half circle.
If this running in a half circle is truly quicker then every baseball player should consider using this method.
Also, no base runner does a 90 angle at first base. They round first base if the ball goes to the outfield.
I thought this said "Rounding the bases faster with meth"
And to play baseball all you need is the hand eye coordination of an ace fighter pilot (plus fast legs and a strong arm are nice).
I see what you mean though. If someone the size of Dustin Pedroia can win an MVP then at least the game isn't contingent upon a particular extreme body type.
"In America, first you get the sugar, then you get the power, then you get the women..." -H. Simpson
Thought that's what it said at first. I'm wrong.