THE BOOK--Playing The Percentages In Baseball

There are these two threads:

http://www.insidethebook.com/ee/index.php/site/comments/optimal_running_path/

http://www.insidethebook.com/ee/index.php/site/comments/fieldf_x/

In the second one listed (which was first chronologically), I said the following about Miguel Cairo’s speed/time from second to home on a base hit, where he tagged up because he thought the fly ball might be caught.

Cairo ran about 180 feet in 7.4 seconds, for an average running speed 16.6 mph.  (180 feet, because he ran a circular path, but he started with his lead foot already off second base, and he cut the inside corner of the third base bag.) He took about 2 seconds to accelerate to 17 mph.  The remainder of his run, his speed was between 17-20 mph.

Granted, Cairo was much faster than a typical player, but that gives you a benchmark from reality, as well as telling you what path a real player ran (if you look at the video in the NY Times article linked in the second thread).

Isn’t he saying that a curved path is 16.7 seconds?  Twenty-two seconds is for the current approach of running straight and then veering to the right as you approach the base.

On the preview, my CAPTCHA was “study.” It’s funny to me how often it picks a fitting word.//

You would only “veer” at first base, right?  You don’t veer on any of the other bases, certainly not if by that point you think you have an inside the parker.

1 mph = 1.47 feet per second.  So, 18mph is 26 feet per second.  400 feet would be 400/26 seconds (15 seconds).

No discussion of this can be complete without reference to the Tater Trot Tracker… although what would make someone watch every home run in MLB with a stopwatch in their hand, I can’t imagine…

http://www.wezen-ball.com/site/tater-trot-tracker/

I’m guessing if Matt Kemp takes 22.53 seconds to round the bases on a walk-off homer (June 1st), the typical inside-the-parker ought to be a bit faster than 22 seconds even…

180 feet:  Mike, I guess I’ll haev to plot that myself to believe it.  You are saying that even though it’s 180 feet from base to base to plate on a straight line, that because:
- Your lead foot is starting about 3 feet off 2B, and you are cutting the inside of 3B, that those extra feet of savings will cancel out for the non-straight line path you are taking

Where is the base measured from 90ft?  That is, center of bag, start of bag, end of bag?  Home plate is measured by the “triangular point” I presume?

Excellent, Greg.

From the Tater Trot Tracker, the six inside-the-park home runs this year have ranged from 14.48 to 16.45 seconds.  Of course, those are not being accomplished by the typical player, though Aubrey Huff with the 16.45-second time should be close to typical, I would think.

Tango #5:

90 feet from apex of home plate to back right corner of first base. 

90 feet from back right corner of first base to center of second base. 

90 feet from center of second base to back left corner of third base. 

90 feet from back left corner of third base to apex of home plate.

Tango/5, I think I clarified later in one of those threads, that my measurement in the work for the video was 181.5 feet.  So you should probably use that number rather than my 180-ft estimate when I went back for a quick look at the data.

The second base bag is centered on the point 90 feet from each baseline.  But the first and third base bags and home plate are completely in fair territory.

From the article:

Morgan wonders if the big leagues will test out his group’s new study.

“We haven’t heard from the major leagues yet, but I don’t see why they shouldn’t give this more attention,” said Morgan. “We’ll see what happens. By the next World Series, maybe they’ll let me in the booth there with them. Sometimes, math takes thousands of years to catch on. I’m in no hurry.”

Mmmm.... stopwatch… is there anything you can’t do?

Tango/5, in addition to 1.7-foot diagonal of the the third-base bag, my data showed that Cairo was leaning quite a bit as he rounded the bag, on the order of almost two feet.  At least I presume that’s what it means.  I’m guessing that the recording technology recorded the position of his center of mass or torso moreso than his feet.

Why don’t y’all just go out to your local ballpark and run the bases both ways yourself.  Get your wife or girlfriend, or maybe both to time you around the bases.  My guess is that there is not a 5.5 second difference between the two methods if done properly.  Just make sure to stretch, hydrate and wear plenty of sunscreen.

"In real life, often a runner begins by heading straight to first base as the ball leaves the bat. Only partway down the baseline will he begin to veer right if he think’s extra bases are possible.”

What “real life” is he talking about?  Baseball players are taught to go straight for the bag if you do not know if you are going to advance to the next base and then veer off if it turns out that you are going to advance, and to start out with a big curve, as the article suggests, if you know that you are going to advance to the next base.

At least that is what I taught when I coached. 

For example, if you hit a ground ball and you don’t know if it is going to get through the IF, which is most of the time that you hit a ground ball, you start out straight in order to get to first as quickly as possible if the ball is fielded.  If you hit a fly ball to the OF or a clean base hit to the OF, you start out with a big curve.

I don’t think that major leaguers (or high schoolers for that matter) do anything differently than what the article says that the researchers suggest.

Adam Rosales takes his home run trots pretty hard, and ends up running 16 or 17 seconds.  22.2 seconds is ridiculous - that’s actually probably closer to the average out-of-the-park HR time, which according to the Tater Tracker range from 16 to 30 seconds.  What a bummer - how can I trust the rest of the article if he’s saying the average inside-the-park time is 22 seconds, while the tater tracker has nothing over 16.5 seconds?

As to Tom’s off-the-cuff calculation, a reasonably significant factor to remember is that time is lost when running a curved path. To keep it two dimensional and simple, when running a straight path, like a 100m track race, the runner exerts force 100% “forward.” To run a curved path, the resolved vector of motion is diagonal, meaning the runner applies his/her available force partly forward (tangent to the curve) and partly cetripetally. The body orientation needed to achieve this combination of forces results in the “lean” Mike mentions in #10.

Nowadays 200m sprints are always run with the 1st 100m on a curve and the last 100m on a straightaway, but before the 1960s it was fairly common for the race to be run on a complete straightaway. Separate world records were kept for 200m/220y “straight” and on a curve, and the straightaway record would be about a half second faster. Obviously that time was lost specifically on the 100m curved portion. And the radius of the curve controls how much force has to be applied centripetally to stay on the curve, reducing what can be applied “forward.” Thus on unbanked indoor tracks, where the curve arcs are fairly close to what is needed to run the bases, about another whole second is lost compared to an elite 200m time achieved on the larger outdoor track.

So I’d estimate that an elite sprinter would lose about 1.0 seconds compared to a straightaway 125m time, due to the curved path.

So I’d estimate that an elite sprinter would lose about 1.0 seconds compared to a straightaway 125m time, due to the curved path.

I can’t believe a full second.  That’s the equivalent of 10 meters.  I don’t see how that’s possible.  0.1, maybe 0.2 seconds.

What a bummer - how can I trust the rest of the article if he’s saying the average inside-the-park time is 22 seconds, while the tater tracker has nothing over 16.5 seconds?

If you ask me, the premise was pretty shaky even without the TTT data: how could someone (apparently a few someones) really think that after playing baseball for 150 years, the best players on the planet are somehow still running the bases 33% slower than they could if only they would embrace mathematics?

Credibility -1 (though not irreparably, I’ll read their next entry with an open mind...)

"how could someone (apparently a few someones) really think that after playing baseball for 150 years, the best players on the planet are somehow still running the bases 33% slower than they could if only they would embrace mathematics?”

As I said, as far as I know, they don’t.  Seriously, who runs straight at a base and then makes a turn when they get 10 feet from the bag when they know that they are going to advance the extra base?

For example, I learned that when you are on second with one or no outs, you take your lead in the base path, because you might need to get to third as quickly as possible, such as on a ground ball out or if you are stealing or on a wild pitch or passed ball.  With 2 outs, you want to maximize your chances of scoring on a hit and you will not be thrown out at third on a ground ball (and you are not likely to steal or advance on a marginal WP or PB), so you take your lead a few feet back of the base path so that you can take that curves path to third anticipating scoring on a hit or an error.

So I think the entire premise of this article is faulty, unless I am reading it wrong.

Can’t we just look at video of players running the bases when they easily have the next base and might advance beyond it, like on a line drive or fly ball hit to the OF?

The NY Times/Sportvision video that is linked in the earlier thread I linked in Post #1 shows an example. 
http://www.nytimes.com/2009/07/10/sports/baseball/10cameras.html

Obviously Cairo, who we’ve already talked about, but also Johjima, the batter, who leaves the batters’ box and immediately heads into foul ground toward the dugout on a circular path toward first while running out his deep fly ball.  As he rounded first, Johjima had to hold up because LaHair couldn’t advance past second base, but Johjima left the box thinking he might make second base, so he ran a curved path from the beginning.

I wonder if the authors don’t know enough about baseball to know that sometimes the runners run a straight path toward the next base because they are initially unsure of their chances to reach it safely.

@MGL and others: My coach taught us to approach the bases in a modified question mark pattern. Nobody rounds the bases in a complete circle, nobody, period. There are several reasons for this.

1. With imperfect information you always have to hedge against the possibility of sliding into 2nd or 3rd rather than going the whole way. This means taking an arc path to the next bag can be detrimental if you might have to stop--it’s a longer path and it’s not conducive to a slide into that bag.

2. Running at a curve when you reach the actual base is actually rather treacherous. You exponentially increase the chance of a rolled ankle or just plain slipping.

@Tango: When you’re running an arc path the entire way around, you’re all the time fighting centrifugal force and the lack of friction provided by the playing surface before. You simply can’t run as fast in an arc as you can on a straight line, just as you can’t pilot an F1 car into a curve at top speed, even with a cornering capacity at 4Gs.

All that said, I was the fastest baserunner on my middle school and high school varsity teams (I couldn’t hit or field, but I could run). And I didn’t hedge against that risk--I just tried to run the whole thing as a perfect circle. I even took the bases on my inside foot, which is a fundamental no-no.

All that, and I never cracked 10 seconds. Nobody did.

I looked at the video for all three of the doubles hit in the Boston-Baltimore game tonight, and in none of them did the live camera or replays show more than a couple steps out of the box for the batter.

J-Doug/19, the data we have on Cairo’s run from Sept 20, 2008, shows that he did in fact run pretty close to a true circle path on his way from 2nd to home.  That kind of path means that you’re actually not turning when you cross the third-base bag.

So I’m not sure what you mean by “nobody, period.” Your point #1 is certainly true in many cases, but in some cases the runner will know that he is in no jeopardy of being thrown out or needing to slide at the next base.

@Mike/20: Yes, a runner’s path is going to better approximate a perfect circle when you either A) have the most confidence you can score the inside-the-parker and B) whether you decide to commit to that despite the risk, and this is most likely to happen once the runner passes 2nd and knows where the ball is and catches his 3rd base coach’s sign.

But I was specifically referring to the entire path from home to home, not just the second half of the journey.

Also, Miguel Cairo is exactly the type who would run close to the full circle. I’d imagine the more your offensive contribution depends on your speed advantage, the more you would discard the risks you incur by running that tight a path. This is actually rather testable.

Interesting thread.  Actually, if I’m looking at the right graphic from the NYT article, it sure doesn’t look like Cairo is running a circular path, especially on the part from 2nd to 3rd base.

Click on my name for a picture of the graphic, where I’ve overlaid a circle that goes through all four bases.  Cairo doesn’t run straight at 3B and then “veer to the right” as he approaches the bag, but he does start out in a rather straight line towards a point back of 3B and then goes into a circular trajectory about 20 ft. from the bag.

John/22, if you want to look at that more closely, here’s a more accurate graphic of his path without the artistic interpretation.

Re #23, never mind.

I decided I probably shouldn’t put that graphic up.  I don’t think it violated the terms of my agreement with Sportvision, but to be on the safe side, I have removed it.

Maybe someday some FIELDf/x data will public, and I won’t have to say, “trust me, that path was more circular than it looked in the graphic.”

I can’t believe a full second.  That’s the equivalent of 10 meters.  I don’t see how that’s possible.  0.1, maybe 0.2 seconds.

Actually I’m with Joe Arthur/14.  Having been a sprinter in indoor and outdoor track in HS, I can personally attest to the difficulty in maintaining speed while trying to hold a tighter curve.  Indoor tracks typically range between 160-200m compared to the standard 400m outdoors.  The 200m dash is the shortest sprint that is run on the curve indoors.  For comparison’s sake the indoor WR is currently 19.92, compared to 19.19 outdoors.  Looking at the WR progression, we eclipsed 19.9 outdoors as far back as 1968.

Now even indoors, half of the 200 is run on a straightaway.  If you make a 125m track that’s all curve, you’re fighting some serious centripetal forces.  Make it a dirt track and it’s even harder to hold.

Wes: wow good stuff.