The Arithmetic of Life and Death by George Shaffner

Points
          Baker
1,574
703
          Payton
1,571
657
          Schrempf
1,232
591
          Ellis
932
632
          Hawkins
862
436
          Perkins
580
455
          Kersey
234
429
          Anthony
419
540
          Williams
298
518
          McMillan
62
292
          McIlvaine
247
268
          Cotton
24
956
          Wingate
150
361
          Zidek
29
596
          Howard
25
620
           Total
8,239
8,054
     
    In the case of the Supersonics, team point productivity dropped by 185 points, or 2.2 percent, which was even less than the Reign. After equalization, point productivity of the top five players (33.3 percent of the team) was just 44.3 percent of the team total.
    Cecilia then equalized performance for both the Reign and the Supersonics across the same five measurements that she used in her original analyses:
    Equalized Opportunity Model
     

     
    With the early results counted, Cecilia began to feel confident that something like a 50/30 Rule was a far more accurate representation of equal opportunity than 67/30 or 80/20. Further analysis tended to confirm her hypothesis.
    After equalizing the 1997/1998 Mariners baseball team to 239.4 at bats each, Cecilia discovered that the team batting average dropped from .275 to .252 as the number of hits fell to 1,390 from 1,515, an 8.3 percent drop, and home runs fell from 239 to 163 (down 31.8 percent). But total runs scored, which was the most material measurement of team productivity, dropped only 2.9 percent, from 800 to 777. The effects of equalization on top player performance were also similar to her first two analyses, with the top seven (30.4 percent) Mariners producing 38.4 percent of the runs, 36.5 percent of the hits, 59.6 percent of the home runs, and 45.4 percent of the runs batted in.
    Finally, Cecilia equalized opportunity for all of the hockey players on the 1997/1998 Vancouver Canucks to 82.4 shots on goal. As a result, total team goals fell from 193 to 182.7, a drop of 5.3 percent, but assists rose from 286 to 295.9, a 3.4 percent increase. After equalization, the top 30 percent of the team produced 38.2 percent of the goals and 46.8 percent of the assists.
    Cecilia was led to two conclusions. The first was that, despite significant drops in secondary measures such as shots blocked and home runs, equalization of player opportunity had had a smaller negative effect on primary productivity measures than she had expected:
               Team
Measurement
Productivity Drop
          Reign
Points
3.3%
          Supersonics
Points
2.2%
          Mariners
Runs
2.9%
          Canucks
Goals
5.3%
           AVERAGE PRODUCTIVITY
         LOSS
3.4%
     
    Cecilia’s second conclusion was that, by equalizing opportunity, the 67/30 Rule had collapsed to a figure nearer to 47/30:
    EQUALIZED OPPORTUNITY MODEL
     

     
    Before presenting her results to the managing partner and collecting her second consecutive dollar, Cecilia ran the equal opportunity numbers through her “cotton picking” model one last time:
Once again, ten cotton pickers picked 100 bales of cotton;
But, according to the 47/30 Rule, the top three pickers picked forty-seven bales of cotton; and
The bottom seven pickers picked fifty-three bales of cotton.
So the top three pickers produced an average of 15.667 bales each; but
The bottom seven pickers produced an average of 7.571 bales each;
So the top three pickers were still more than twice as productive (2.06 times) as the bottom seven pickers (15.667 ÷ 7.571)!
    Later that evening, after a stimulating debate with the managing partner, an enriched but exhausted Cecilia had time to reflect on the previous few days. Although she suspected that years of additional analysis would lead her to the same controversial conclusions, she