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A Factorial Design for Baseball. Dr. Dan Rand Winona State University. When it was a game, not a poorly run business. How was baseball designed? Abner Doubleday in Cooperstown, or Alexander Cartwright in Hoboken, NJ? Baseball is a beautifully balanced game !.

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a factorial design for baseball

A Factorial Design for Baseball

Dr. Dan Rand

Winona State University

when it was a game not a poorly run business
When it was a game, not a poorly run business
  • How was baseball designed?
  • Abner Doubleday in Cooperstown, or Alexander Cartwright in Hoboken, NJ?
  • Baseball is a beautifully balanced game !
look at balance of baseball that developed in 1800 s
Distance to bases (infield single)

Catcher's throw to catch a base stealer

Diamond - why not pentagon or oval?

Irregular dimensions - home run fences

How many outs ?

How many strikes ?

How many bases ?

Foul ball areas

Look at balance of baseball that developed in 1800’s:
baseball strategy is optimization
Baseball strategy is optimization
  • leftie vs. rightie (pitcher vs. batter)
  • Pitcher days between starts
  • Maximize runs - sacrifice, hit and run, swing away
balance through product modification
Balance through product modification
  • 40 years of trial and error experimentation, then
  • Ball changed in Babe Ruth's time
  • Mound raised in 1968.
  • Designated hitter in 1973.
  • Home run totals of 1996-2001
we could do it all in 1 experiment
We could do it all in 1 experiment
  • If statisticians invented baseball instead of baseball inventing statisticians…
  • “Build it, and they will come”
baseball design factors
Baseball Design Factors
  • A - Infield shape/ number of bases - diamond, pentagon
  • B - outs - 3, 4
  • C-Distance to bases - 80 feet, 100 feet
  • D - foul ball areas - areas behind first, home, and third, or unlimited
  • E - strikes for an out - 2, 3
  • F - fences - short, long
  • G - Height of pitcher’s mound - low, high
measurements trials are innings
Measurements - trials are innings
  • # hits walks, total bases
  • % infield hits (safe at 1B as % of infield balls in play)
  • % of outs that are strike-outs
  • % of outs that are foul-outs
  • % caught stealing
  • % baserunners that score
  • total runs
how many innings
How many innings ?
  • Test 7 factors (rules) one-at-a-time, say we need 16 innings at each level
  • 16 x 7 x 2 (levels) = 224 innings
  • At what levels are the other 6 factors ?
  • Full factorial experiment - every combo of 7 factors at 2 levels, 27 = 128 combos
  • Any factor has 64 innings at its low level, and 64 innings at its high level
a full factorial gives info about every interaction
A full factorial gives info about every interaction
  • Interaction = the phenomenon when the effect of one factor on a response depends on the level of another factor.
one trial of a full factorial
One trial of a full factorial
  • A - Infield shape= 5 sides, 5 bases
  • B - outs = 3
  • C-Distance to bases = 100 feet
  • D - foul ball areas = unlimited
  • E - strikes for an out = 3
  • F - fences = long
  • G - Height of pitcher’s mound = low
the power of fractional factorials
The power of fractional factorials
  • For 16 innings, each level, each factor: what can we get out of 32 innings?
  • Can't run every combination - what do we lose?
  • We can't measure every interaction separately.
the power of fractional factorials13
The power of fractional factorials
  • Needed assumptions:
    • 3-factor interactions don't exist in this model
    • 2 2-factor interactions can be pre-determined as unlikely to exist.
  • Then we only need 32 of the 128 combinations
  • Let’s play ball !
the power of efficient experiments
The Power of Efficient Experiments
  • More information from less resources
  • Thought process of experiment design brings out:
    • potential factors
    • relevant measurements
    • attention to variability
    • discipline to experiment trials
let s evolve an experiment design
Let’s evolve an experiment design
  • Link to this Power Point file on my Website http://course1.winona.msus.edu/drand/
  • Let’s develop this as a case study in the experiment design community
  • Needed – a Web site that would receive improved designs from anyone – Yahoo?
  • An academic exercise- any class group could access it
  • Simulation?