Associated Topics || Dr. Math Home || Search Dr. Math

### Stolen Base

```
Date: 08/29/97 at 04:29:46
From: MINH VU
Subject: Modeling the stolen base

I need to create a mathematical model for a stolen base, identifying
all variables and stating all assumptions. Initially the model should
be as simple as possible; the complexity may be increased once a
reasonable model has been created.

The baseball diamond is a square 90 feet on a side. A player on first
base (the runner) can 'steal' second base if he can run to the base
before the ball is thrown to second base. The typical sequence is that
the player at first base walks a short distance toward second base,
staying close enough to get back to first base if the pitcher throws
to first; then when the pitcher (in the center of the diamond) begins
to throw the ball to home plate the runner begins running to second
base. The catcher at home plate then throws the ball to second base;
the runner is 'safe' if he reaches second base before the ball, and he
is 'out' if the ball reaches second first.

```

```
Date: 08/29/97 at 17:49:04
From: Doctor Barney
Subject: Re: Modeling the stolen base

Pretend that you are the runner on base. Think about all of the
decisions you would have to make, in order. Try to identify all of the
information that you would use to make these decisions. For each
decision, consider all of the possible outcomes, making further
decisions as necessary. For criteria that are beyond your own control
(pitcher tries to throw you out, for example) assign an estimated
probability for that criteria. For example:

1. You are on first base. Where do you stand? This decision
depends on:
a. who has the ball
b. what other bases have runners on
c. where the first baseman is standing
d. where the pitcher is looking
e. what the catcher is doing
f. what the score is, the number of outs, the count as in
strikes and balls

I've never stolen a base so I'm sure there are many I can't
think of.

From this smaller model you will formulate a decision to stay on
base, lead off a little, or lead off a lot, probably up to some
easily estimated maximum.

2. Now you must decide when to stay there, when to run quickly back
to first, and when to try to steal. For this decision try to
identify all of the factors that will influence this decision.
Many of the same factors we used above will apply, some will not,
and some new ones will.  You decide what's important
a.
b.
c.

3. In the rare event that you decide to try to steal, there are many
other actions you need to model. For example:
a. Does the second baseman move to the base?
b. Does the catcher signal to the pitcher?
c. Does the pitcher or the catcher (or anyone else) throw to
second?
d. Does the throw beat you there?
e. Does the second baseman catch it?
f. Does he tag you?
g. Does the ump call it right?

Try to think of everything you can.

Get a BIG piece of paper or use a chalk board or white board and write
down all your ideas and how they relate to each other. Don't worry
about putting any numbers in until after you have the overall process
identified. Then just guess at a numerical probability for each of the
factors you identify. Based on your personal experience, how often
does the second baseman drop the ball?  half the time? 10 percent of
the time? less?  Does he drop it more often when the throw is from the
catcher than when it is from the pitcher?  Eventually you can start to
write some equations for how these factors relate to each other. At
this point you will need to find out from the instructor what kind of
format he wants it in, but this should get you started.

Have fun, and keep your eye on the ball!

-Doctor Barney,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Probability

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search