The Effect of Each Square Foot of Foul Area on Strikeouts

 Previous recent posts here have shown that:

1)       AF has decreased from 1954 to 2000 ( ).

2)        The relationship of SO/ sq. ft. to SO has been generally parallel over the years, but changed when AF changed most dramatically in the 90’s  ( ).

3)       There is strong evidence of an inverse relationship between SO by hitters and foul area (AF). Rank-ordering stadiums/teams according to AF, and analyzing and comparing teams/stadiums by yearly SO average over multiple periods from 1954-1968 in both the NL and AL.  

( )

( )

It would be reasonable to believe that if a relationship between SO and AF exists on the basis of rank-order analysis of yearly average SO, analysis of each square  foot AF on SO for each team/stadium might also cast a new light on, or further confirm, the inverse  relationship.   This  analysis and data is submitted here to stimulate  further discussion and analysis of the impact of AF on SO.

AF in AL ballparks in use for 2 or more years 1954-2000 have been measured and early SOwere downloaded as previosuly reported, and yearly averages derived.  When yearly SO were divided by stadium sq. ft., a yearly SO/ sq. ft. figure could be derived for each stadium team, or league-wide. The average SO/ Sq. Ft.  for AL over the entire 46-year period was 0.028, with an average AL AF of 30,500 sq. ft., and 859 average AL yearly SO.   

 The data for years 1964-1968 were first analyzed to gain insight into the effect of sq. ft. AF on SO for Cleveland Stadium, which was had largest AF in modern AL history, and are displayed in graph form (Fig.  1). As previously, stadiums/ teams were ranked according to their total square foot area (x-axis) , and their average yearly SO / sq. ft. AF derived and displayed (y-axis).  An inverse relationship between rank order and average yearly SO previously displayed for the AL ’64-68 is again evident: a virtual straight-line relationship of increased SO/sq. ft. for decrease in AF.  The saw-tooth curve of rank-order analyses of stadiums vs. yearly  average SO seen in the previous postings is dramatically smoothed when each sq. ft., not thousand-foot gradations, are included in the analysis.  The deceptive position of Boston and New York at the far right tail end of the Yearly Average SO analysis ( ) , even below trendline and barely above teams with greater AF, is now potentially seen as a distortion of the extremely low foul area. Their SO/ sq. ft. is in line with the rest of the AL.

A statistically significant relationship of the mean SO/ sq. ft. of the 6 teams with lowest AF compared to the 6 with the highest was calculated (p= 0.001) using the means test, a stronger relationship than shown for previous rank-order vs average SO analysis.  However, this is driven by the large differences in foul area vs. small differences in SO.  The curve exaggerates the appearance of effect; the exact magnitude of effect is not yet indicated.

Fig. 1: Teams/stadiums are listed L to R (X-axis) from largest AF to smallest.  SO / sq. ft. (average yearly SO divided by AF in sq. ft)   for each team/stadium are charted on y-axis.  A linear inverse relationship is defined: the smaller the AF, the greater the SO

When data for the 19 stadiums/teams from 1969-2000 were analyzed in similar fashion, the anticipated, intuitive inverse relationship was again uncovered (Fig. 2).


 Fig. 2. Teams/Stadiums of 1969-2000 are listed on x-axis with largest AF to the left, smallest to the right.  SO / Sq. Ft. are on the y-axis.  The upward trendline is superimposed on a curve that is not constantly upward in direction, with 6 downward steps along its course.  A number of factors may contribute to the latter departure, most notably the large numbers of years and pitching/batting philosophies included in the analysis.

Different stadiums are known to have different effects on runs scored, batting statistics, and pitching statistics, and the effects are globally described as a ballpark factor.  Park factors (F) have been defined for SO as well (FK).  The recent posts at this site certainly suggest an opportunity may be at hand to create a unique FK for each park based on AF.  Whereas the data is derived from hitters' SO, pitchers' SO might also be similarly compared. This would allow comparison of the effect of  AF on each pitcher or group of pitchers  in an individual park, and allow for creation of a measure by which to compare the SO records of different staffs, or individual pitchers,  in stadiums of vastly different AF, even over different periods.  A future post will analyze this possibility more closely.


[1]   STRIKE THREE! My Years in the ‘Pen.  Tomsick T.A., Cincinnati Book Publishers, Cincinnati, OH, pp. 177-9, 2010

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