A Factorial Design for Baseball

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## A Factorial Design for Baseball

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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 !**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**• leftie vs. rightie (pitcher vs. batter) • Pitcher days between starts • Maximize runs - sacrifice, hit and run, swing away**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**• If statisticians invented baseball instead of baseball inventing statisticians… • “Build it, and they will come”**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**• # 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 ?**• 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**• 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**• 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**• 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 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**• 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**• 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?