Since 1980, when Bill James introduced his statistical methods of evaluation and projection, a legion of supporters have followed and expanded on his work. One particular area of work concerned an estimation of a team’s winning percentage based solely on the number of runs a team scores and the number of runs a team allows. This estimation became known as the Pythagorean algorithm of baseball and is expressed algebraically as:
Win % = RS2/(RS2 + RA2), where RS = Runs Scored and RA = Runs Allowed. Other ways of expressing this are :Win % = 1/[1 + (RA/RS)2] or (RA2 + RS2) Win % = RS2 (note: there are other recent, somewhat more accurate, ways of estimating Win %, but the Geochecker does not take kindly to those who use these other methods)
Puzzle
The season was at All-Star break, mid July, and with the trading deadline on August 1st, The GM(General Manager) was considering what, if any changes should be made to his team. His first consideration, of many, was an analysis of how his team had performed relative to his opponents. The GM was a great proponent of Pythagorean analysis, so started his evaluation using it. His team had played 91 games at the All-Star break and his team had scored 460 runs, and given up 320 runs. The Pythagorean analysis had correctly, with rounding, predicted the team’s winning %.
The GM was also evaluating his two main competitors, Northern Lights and Western Sunsets, using the same analysis.
At the break, Northern Lights, a great offensive team, had allowed 473 runs. They led the GM’s team by ½ a game, having played 3 more games. They also outperformed their expected wins by 2.
Meanwhile, Western Sunsets, the leading defensive club, trailed Northern Lights by 2 games, having played 2 fewer games, underperformed their expected wins by 1, and had scored 199 runs.
N 42 43.(RSNorthern Lights) W 071 18.(RAWestern Sunsets)
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