A Black Belt steps up to the plate with Six Sigma confidence.

Bill had a problem. His company’s baseball team wasn’t doing that well, and he was part of the reason. Bill was in a long slump. Frankly, he stunk at the plate.

But Bill is a Six Sigma Black Belt. He decided to approach his batting problem just like he would approach any process problem at work–by conducting a designed experiment. First, Bill determined which factors are important. He wrote up a lengthy list and then winnowed it down to four experimental variables (see Table 1).

FactorNameUnitTypeLevel 1Level 2
AFoot positionAngleCategoricalSquare45°
BChoke on batInchesNumeric02 in
CPosition in boxN.A.CategoricalForwardBack
DSpeed of pitchmphNumeric60 mph80 mph
Table 1: Experimental Variables for Hitting

Bill decided to spend a few evenings and weekends on the practice field swinging at 100 pitches for each of the 16 combinations of the four variables needed to conduct a full-factorial experiment. The field was equipped with a pitching machine that could be programmed to throw pitches at either 60 mph or 80 mph. Bill decided to count any ball that went past the infield in fair territory as a hit. Over a two-week period Bill was able to complete the experiment, producing the results shown in Table 2.

145°2 in.Back60 mph13
2Square0 in.Forward60 mph28
3Square2 in.Forward80 mph14
445°2 in.Forward60 mph38
5Square2 in.Back80 mph27
645°0 in.Back60 mph11
7Square0 in.Back60 mph13
8Square2 in.Forward60 mph40
9Square0 in.Back80 mph19
1045°0 in.Back80 mph23
1145°0 in.Forward60 mph34
1245°0 in.Forward80 mph5
13Square0 in.Forward80 mph2
14Square2 in.Back60 mph23
1545°2 in.Forward80 mph9
1645°2 in.Back80 mph31
Table 2: Bill’s Batting Experiment

The analysis indicates that factors B and D, and especially the C-D interaction, make big differences in Bill’s performance. Factors A and C do not have a significant effect on Bill’s batting average. The analysis in Table 3 shows the details.

FactorCoefficient Estimate95% CI
B-Choke on bat3.752.035.47
C-Position in box-0.63-2.351.10
D-Speed of pitch-4.38-6.10-2.65
Table 3: Significant Factor Effects

The 95-percent confidence interval for C (position in the batter’s box) includes zero, meaning that C is not statistically significant as a main effect. (C is included because the significant C-D interaction term requires it for statistical reasons.) However, the other factors in the table–B (choke on the bat) and D (speed of the pitch)–are statistically significant. The most important factor is the C-D interaction, which has an impressive effect of more than 9 percent. The coefficient estimate tells us what happens to Bill’s batting average as we go from one level of the variable to another. For example, when B is at the high level (choke up on the bat two inches), Bill’s batting average improves by about four percentage points.

The analysis indicates that when Bill is facing a pitcher with real heat (80 mph isn’t too bad for an amateur pitcher), he can improve his batting average from 8 percent to 28.75 percent by standing near the back of the batter’s box (see Table 4). Conversely, when Bill is up against a 60-mph hurler, he’s better off in the front of the batter’s box (38.75 percent in front hits vs. 15 percent in back). Combining all of these results, Bill’s strategy is to always choke up on the bat and position himself in the batter’s box depending on the expected speed of the pitch.

Pitch SpeedBatter’s Box PositionAverage
Table 4: Bill’s Results

Bill may not be ready for the majors with this strategy, but he’s hitting a lot better than the .206 (20.6%) he’d been getting without a strategy. In the meantime, Bill, work on hitting that fast ball!

One response to “Design of Experiments and Baseball”

  1. RickABQ Avatar

    I’ve always had a secret desire to become a sports Black Belt to do exactly what you’ve described in this article!

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