In 1960, the National Football League introduced a rating system in order to end the age old argument of "who is the best quarterback". Unfortunately, the formula was poor and the rankings were not in agreement with public consent. As a result, that system was replaced in 1973 with the one that we use today. However, the NFL was not forthcoming with the formula. Several sports-minded mathematicians published articles or books in which they reverse-engineered the formula. They tried to deduce the formula from the published ratings, and what they believed would be the logical numbers to input to the formula. .
The NFL has recently published the exact sequence of steps and computations needed to calculate the exact value of the quarterback rating. In hindsight, the mathematicians who attempted to deduce the formula came pretty close, but they could not determine the computations exactly. This is not surprising due to the fact that the result can range from 0 to 158 1/3. In addition, the formula is so complicated, and is made up of many calculations and steps that are not seen as rational or even necessary. .
The five statistics that are used as raw data when computing the equation are attempts, completions, yards, touchdowns, and interceptions. The first step is to divide the number of completions by the number of attempts, this is the completion percentage. If the completion percentage is less than 30, award zero points; but if it is greater than 77.5, award 2.375. If in between, subtract 30 from the completion percentage and multiply the result by 0.05. The second step is to divide the number of yards by the number of attempts, this is the yards per attempt. If the yards per attempt is less than 3.0, award zero points; but if it is greater than 12.5, award 2.375. If in between, subtract 3 from the yards per attempt and multiply the result by 0.25. The next step is to divide the number of touchdowns by the number of attempts, this is the touchdown percentage.
