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Monday, September 28, 2009

Optimal running path

By Tangotiger, 10:44 AM

The academicians are giving us this:

A couple of points which seemed confusing (to me) when I read the blog post:
- Frank Morgan, the blogger, writes in the third person
- the first study mentioned (22.2 seconds) is specifically about “station-to-station” ball, where you do not overrun the base, and follow the baseline in a straight line, starting/stopping at each base
- the circular-type of optimal paths presumes you are going for an inside-the-parker from the outset
- it’s hard to tell what the maximum velocity is attained in each leg (base-to-base), and how much slowing down occurs (if any), as the runner steps (or sets himself to step) on the base

Anyway, I’m looking forward to reading the full study, as my interest is piqued.

When we talked about hustling a few months ago, I guessed:

I will guess a fast player would have an inside the parker in 13 seconds.  I reason 3.1-3.2 for each base, plus an extra 0.5 or so “startup”.

Another way to calculate is to imagine he’s running in a circle with diameter=127 feet.  That gives us a circumference of 400 feet, or 122m.  Olympic runners do 100m in 10 sec, and the other 22m would take 2 sec, for 12 sec.  So, it seems reasonable that very fast, but non-Olympic runners, with not ideal track conditions will take it in 13 sec.

I will guess that a slow runner (by MLB standards) would run around the bases in 18 seconds?  Pure guess here.

The Guiness record according to the blogger is 13.3 seconds (set 70 years ago, which tells me no one is seriously making a run at this record, for whatever reason).  All to say that the sanity-check model (my model) sorta supports the numbers we see.

Glove-slap to Neyer.


#1    salb918      (see all posts) 2009/09/28 (Mon) @ 11:47

I haven’t read the study yet, but at first blush this is a pretty standard engineering optimization problem.  But the graphic you excerpt is a very academic way of looking at things.  I would do the following:

1. Time to run straight through first base.
2. Time to run to second base while maintaining a straight line path to first base.
3. Time to run to first base in the optimal path for running from home to second.
4. Time to run to second base in the optimal path for running from home to second.

Then you could compare 1 vs 3, 2 vs 4, and do similar pairings for double/triples, etc.  That would be a pretty interesting study that could make suggestions about the path runners should take on groundballs through the infield or down the line, liners into the gap, etc.


#2    Mike Fast      (see all posts) 2009/09/28 (Mon) @ 12:01

The FIELDf/x play that I studied over the winter had Miguel Cairo scoring from second base on a drive to the left field wall.  It wasn’t clear whether the left fielder would catch the ball, so Cairo tagged up at second.

He then ran from second base to home plate in 7.06 seconds, taking a path 180 feet long, with a maximum forward acceleration of 13.3 ft/s^2.  His maximum speed was 30 ft/s.

His path was not quite as round as the one shown in the Carozza paper.  Of course, he started at 2B already.  The reason his path is only 180 feet long is that he started with his back foot on second base and cut the corner to just touch the inside of the bag at third (and, to a smaller extent, he only needed to touch the front corner of home plate, not the back point).

You can see the demo we put together for this play at the NY Times in video attached to this article:
http://www.nytimes.com/2009/07/10/sports/baseball/10cameras.html?_r=1&hpw

If I dug through the whole data set for that game, I’m sure I have more interesting baserunning plays.  No inside-the-park home runs or triples, though.


#3    Peter Jensen      (see all posts) 2009/09/28 (Mon) @ 12:02

Sounds like the big factor that they left out of their “simplified model” is the time advantage of having the base as a fixed pivot point to change lateral direction.


#4    Mike Fast      (see all posts) 2009/09/28 (Mon) @ 12:07

it’s hard to tell...how much slowing down occurs (if any), as the runner steps (or sets himself to step) on the base

In real life, little or no slowing down occurs as runners rounds a base.


#5    Peter Jensen      (see all posts) 2009/09/28 (Mon) @ 12:36

Mike - How much time did he lose rounding third?  That is, from the time he began decelerating before third base to the time he regained his previous maximum speed.


#6    Peter Jensen      (see all posts) 2009/09/28 (Mon) @ 12:38

Sorry, crossed posts.


#7          (see all posts) 2009/09/28 (Mon) @ 12:57

Hm.  I can’t call up the original post for some reason, just hangs up - so I’ll ask the dumb question here.  Was that Guinness WR under game conditions, or was it line up at home plate, wait for the whistle, and see how fast you can run around the bases?  It makes a difference if you have to hesitate or look for a sign from the third-base coach.  Also, in game conditions a player may only rarely find himself in a position to go for the inside-the-park homer.

I for one can imagine that Crawford, Granderson, Reyes, or even a guy like Bloomquist or Pierre could circle the bases in 13.5, maybe a bit less, depending on the conditions.  From there it could just be random variance that gets any of them under 13.3.


#8    Tangotiger      (see all posts) 2009/09/28 (Mon) @ 13:20

I seem to have this memory, and maybe it’s completely made-up, that the Expos used to run this on-field promotion where they’d have kids run the bases, and show the time of Tim Raines on the scoreboard doing it in 13.2, while they’d show the kids’ numbers be 20-25 seconds or something.

For whatever reason, I had that number (13) in my head, and when I worked it out, I was surprised how well I could justify it.


#9    Brian Cartwright      (see all posts) 2009/09/28 (Mon) @ 14:44

Sometimes I have a stopwatch application open while I am watching mlb.tv.

All the times to first that I measured were from 3.9 to 4.9 seconds. Nyjer Morgan 3.9, Andrew McCutchen 4.0, Jeff Cirillo 4.9 on the ball that hit off the base and Murphy made a circus play.

I meausred a McCutchen double at 7.4 IIRC. 4.2 to 1b (0.2 extra to round the base as opposed to running straight through) then 3.2 1b to 2b. 3.2x3+4.2=13.8.

I can agree with mid 13 for very fast runners.


#10    KJOK      (see all posts) 2009/09/28 (Mon) @ 19:17

Tom - That’s an interesting memory, because I have a very vivid memory of the Cardinals broadcasting crew in 1974, after talking about how fast Bake McBride got down the line to 1st base, starting using a stopwatch on him each game.  Then, one game he hit a GROUND BALL on the hard Busch Stadium turf past the Montreal SS into Left-center field which split the LF and CF, and he circled the bases for an Inside-the-park HR.  They had the stop watch going, and claimed that he circled the bases in 13 seconds.


#11    Brian Cartwright      (see all posts) 2009/09/28 (Mon) @ 20:49

Ober the past 5 seasons (2005-2009) my Gameday db reports 61 regular season mlb inside-the-park HRs. I’ve made a list of gameid, inn, half and name, and when I have time (or if anyone else wants to volunteer to help) I can look up the game on mlb.tv and check the video with a stopwatch.

Carl Crawford leads with three, David DeJesus, Chase Utley, Clint Barmes, Curtis Granderson, Grady Sizemore, Mark Teahen and Price Fielder! with two each.


#12          (see all posts) 2009/09/29 (Tue) @ 04:10

Mike, post #2 is great, and I recommend the video at that link to everyone.  It’s a really impressive application of technology.

Cairo’s asymmetric path from second to home makes me think his first priority was getting to third, and then trying to score.


#13    cdm      (see all posts) 2009/09/29 (Tue) @ 09:41

Wow. The video in Mike/2 is incredible. I don’t like watching GD for pitches, but I think I’d prefer to watch that model play defense than watch the live players.  Is that too geeky?


#14    BenJ      (see all posts) 2009/09/29 (Tue) @ 11:38

For what it’s worth, Scott Podsednik’s inside-the-parker a few weeks back was just over 15 seconds.  I timed it myself and saw that the mlb.com article reported the same time. 

I don’t have the video in front of me, but I think he hesitated just slightly out of the box, maybe delaying his final time by half a second or so at the most.


#15    Tangotiger      (see all posts) 2009/09/29 (Tue) @ 11:52

Pods is fast, but not super fast:
http://tangotiger.net/scout/index5.php?sortid=11

He’s on page 5/6 of a 34 page list, so at the 85th percentile.

I’d like to see the running time for the “no doubters” (Crawford, Gomez, Nyger, etc) fastest players in baseball.


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