Sec. 4.2 



THE NORMAL FREQUENCY DISTRIBUTION 



93 



be poorer one season than another. Hence an average of .350 during 

 a season with a lively ball and generally mediocre pitching might not 

 represent a better batting performance than an average of .320 at- 

 tained with a less lively ball and more effective pitching. 



These matters should be reflected in the general level of batting 

 averages and in the consistency with which players' averages grouped 

 about the general average. That is, the mean and the standard 

 deviation of the batting averages should be taken into account. This 

 is precisely what is done when standard normal units are employed. 



Figure 4.24. Graph of the standard normal frequency distribution whose for- 

 mula is given by equation (4.23). 



There also seems to be evidence indicating that batting averages 

 can be assumed to be reasonably normal in their distribution. 



Batting averages for some of the better batters from the National 

 and American leagues (undifferentiated here but kept separate when 

 the standard normal units were computed) are presented in an 

 ordered array in Table 4.23, first as they usually appear and then in 

 terms of standard normal units. • 



Some interesting conclusions can be drawn from Table 4.23, al- 

 though they might be disputed upon the basis of other evidence and 

 other points of view. For example: (a) The best batter listed for 

 1940 (Deb Garms) ranks fifteenth in standard normal units, con- 

 sidering all 4 years together. (6) The batter with the best average 

 of all (Ty Cobb) — when the level and dispersion of batting averages 

 within a league and year are taken into account — had an actual 

 average of .385, which was bettered by five other batters unless 



