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A Factorial Design for Baseball Dr. Dan Rand Winona State University

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When it was a game, not a poorly run business How was baseball designed? How was baseball designed? Abner Doubleday in Cooperstown, or Alexander Cartwright in Hoboken, NJ? Abner Doubleday in Cooperstown, or Alexander Cartwright in Hoboken, NJ? Baseball is a beautifully balanced game ! Baseball is a beautifully balanced game !

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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 Irregular dimensions - home run fences How many outs ? How many strikes ? How many bases ? Foul ball areas

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Baseball strategy is optimization leftie vs. rightie (pitcher vs. batter) leftie vs. rightie (pitcher vs. batter) Pitcher days between starts Pitcher days between starts Maximize runs - sacrifice, hit and run, swing away Maximize runs - sacrifice, hit and run, swing away

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Balance through product modification 40 years of trial and error experimentation, then 40 years of trial and error experimentation, then Ball changed in Babe Ruth's time Ball changed in Babe Ruth's time Mound raised in Mound raised in Designated hitter in Designated hitter in Home run totals of Home run totals of

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We could do it all in 1 experiment If statisticians invented baseball instead of baseball inventing statisticians… If statisticians invented baseball instead of baseball inventing statisticians… “Build it, and they will come” “Build it, and they will come”

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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

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Measurements - trials are innings # hits walks, total bases # hits walks, total bases % infield hits (safe at 1B as % of infield balls in play) % infield hits (safe at 1B as % of infield balls in play) % of outs that are strike-outs % of outs that are strike-outs % of outs that are foul-outs % of outs that are foul-outs % caught stealing % caught stealing % baserunners that score % baserunners that score total runs total runs

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How many innings ? Test 7 factors (rules) one-at-a-time, say we need 16 innings at each level Test 7 factors (rules) one-at-a-time, say we need 16 innings at each level 16 x 7 x 2 (levels) = 224 innings 16 x 7 x 2 (levels) = 224 innings At what levels are the other 6 factors ? At what levels are the other 6 factors ? Full factorial experiment - every combo of 7 factors at 2 levels, 2 7 = 128 combos Full factorial experiment - every combo of 7 factors at 2 levels, 2 7 = 128 combos Any factor has 64 innings at its low level, and 64 innings at its high level Any factor has 64 innings at its low level, and 64 innings at its high level

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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. Interaction = the phenomenon when the effect of one factor on a response depends on the level of another factor.

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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

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The power of fractional factorials For 16 innings, each level, each factor: what can we get out of 32 innings? For 16 innings, each level, each factor: what can we get out of 32 innings? Can't run every combination - what do we lose? Can't run every combination - what do we lose? We can't measure every interaction separately. We can't measure every interaction separately.

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The power of fractional factorials Needed assumptions: 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 !

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The Power of Efficient Experiments More information from less resources More information from less resources Thought process of experiment design brings out: Thought process of experiment design brings out: –potential factors –relevant measurements –attention to variability –discipline to experiment trials

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Let’s evolve an experiment design Link to this Power Point file on my Website Link to this Power Point file on my Website Let’s develop this as a case study in the experiment design community 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? Needed – a Web site that would receive improved designs from anyone – Yahoo? An academic exercise- any class group could access it An academic exercise- any class group could access it Simulation? Simulation?

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