One of the more subtle stories of the dawn of the statistical revolution in baseball was the case of Frank Thomas. Frank was a big slugger, but not exactly graceful in the field. Since he played in the American League for a long while, he often was slotted as the DH. On paper, this would make sense. A team could theoretically use his bat in the lineup while playing someone else in the field, to avoid his lack of fielding. Well, despite what current trends seem to say, baseball is not played on paper, and some factors that cannot exactly be explained can derail logical thinking, like the Thomas at DH theory.

What I mean by this is that for some reason, Thomas’ best seasons as a hitter came when he played in the field. In his two MVP seasons, he played only 17 games (about 5%) as the DH. In all five of his all-star seasons, he was voted in as a first baseman. This idea is further explained in Tom Tango’s *The Book*. For some reason, he was just not as good as a hitter as a DH. Maybe he was not as engaged, maybe he was “cold”, or maybe it was some other weird reason. I tried to dive into the splits to see the exact numbers, but could not get the exact data. Yet, the idea still remains: hitters may perform differently when placed in different spots in the field, or when they are not in the field at all.

I decided to apply this logic to the Minnesota Twins’ All-Star slugger, Miguel Sano. Like Thomas, Sano hits the cover off the ball, but isn’t as skilled in the field. Some would think that this means the Twins’ should play him as the designated hitter. Again, from a superficial level, this would seem to make sense, as his defensive liabilities would not come into play.

I looked into his splits for the 2017 season. With about 250 plate appearances as a third baseman and about 60 as a designated hitter or a pinch hitter, there were enough observations to perform a hypothesis test (specifically a Two Sample *t*-Test) on the subject.

My test criteria is as follows:

- Null Hypothesis: Batting Average/OBP/wOBA as 3B = BA/OBP/wOBA as PH/DH
- Alternative Hypothesis: Batting Average/OBP/wOBA as 3B ≠ BA/OBP/wOBA as PH/DH

My level of significance is 95% confidence, or *a* = 0.05.

For those who are not familiar with the two sample t-test for equal population means, or if you may have forgotten formulas for test statistics, degrees of freedom, point estimates, or anything else, you can find it here.

Here are Sano’s splits. One can note the obvious difference in his batting statistics, but is this difference statistically significant?

Let’s dive in. Well, here is my test:

It appears that the difference in means for batting average and wOBA are significant, meaning we can reject the null hypothesis that Sano bats the same when in the field and when off of the field. OBP was not significant, so we fail to reject the null for that metric, but the p-value was still relatively weak.

From this analysis, one can see that Sano does in fact perform worse when he doesn’t play 3B. Perhaps the Twins have already keyed onto this, as Sano has 4 times as many ABs as a third baseman than as a designated or pinch hitter. The Twins do have a few decent utility infielders, so maybe they are just squeezing in playing time for those guys when they move Sano to DH. But, in this case, the statistics don’t lie: please play Miguel Sano at third base.