Baseball team hitting statistics tend to focus on a single number, such as an overall batting average for the team. A single average may mask wide dispersion in batting averages across players. For example, two National League teams with identical .250 batting averages for their eight starters (other than the pitcher) can pose very different problems for opposing pitchers. A .250 team batting average can be achieved with half of the players hitting .200 and the other half hitting .300 or with all starters possessing a batting average of .250. Of course, more unequal batting averages makes it easier for opposing teams to pitch around a team’s best hitters.
The most common measure of dispersion in random variables, such as batting averages, is the standard deviation. A team with a high standard deviation in individual batting averages has less consistent hitting up and down the lineup. A team with a low standard deviation in individual batting averages has consistent hitting throughout the lineup. A second measure of dispersion is the coefficient of variation, which in the case of team batting averages would be the ratio of the standard deviation to the mean batting average.
The following table lists the mean batting average, the standard deviation and the coefficient of variation for the 8 hitters on each National League team with the most at bats so far this year. Teams are ranked by the standard deviation of their team’s batting average. Philadelphia and Los Angeles have the smallest standard deviation in team batting. New York and Atlanta have the least consistent team batting, with standard deviations more than three times higher than in Philadelphia.
The next table lists the mean on-base percentage, the standard deviation and the coefficient of variation for the 8 hitters on each National League team with the most plate appearances so far this year. Teams are ranked by the standard deviation of their team’s on-base percentage. Philadelphia and Los Angeles have the smallest standard deviation in on-base percentage. Colorado and Cincinnati have the least consistent team on-base percentage, with standard deviations more than five times higher than in Philadelphia.
Of course a low standard deviation in either batting average or on-base percentage is only valuable if averages are high. Uniformly poor hitting is also undesirable. Each team’s starting hitters can be evaluated by both the mean and standard deviation in their hitting statistics. In this sense team hitting statistics can be displayed in the same type of graph that financial economists use to show risk and return. Teams prefer both a higher mean and a lower standard deviation in hitting statistics.
The following graph shows the batting average risk-return graph for National League teams. Philadelphia and St. Louis are on the “frontier”. Philadelphia has the lowest risk. Among the higher batting average teams, St. Louis has the lowest standard deviation.
Whether hitting is measured in terms of a batting average or on-base percentage, the Philadelphia Phillies have the most consistent hitting and lowest dispersion across players. The St. Louis team batting average is 14 points higher than the Phillies and the risk-return tradeoff means that the Cardinals’ higher average was obtained by nearly tripling the dispersion in averages across players.
Regardless of how hitting is measured, Miami, Chicago and the New York Mets are the worst hitting teams. The Mets, for example, have more dispersion in batting averages across players than the Cardinals but have a team average that is 47 points lower than St. Louis. The inconsistent hitting in the Mets lineup makes it much easier for opposing teams to pitch around their best hitter David Wright (who is hitting .306).