After finishing all simulations, two forms of regression analysis were used to correlate the displacement of wins between starter and replacement for each position. In the first table, “PWAR” denotes the values calculated in the study by Hughes et. al., whereas “MWAR” are the numerical estimates that have been calculated from this research. The “pValue” for the MWAR estimates denotes the level of statistical significance for each positional value; a pValue lower than 0.05 suggests there is overwhelming statistical evidence to support the corresponding MWAR value. In this table, runningbacks, left tackles, and cornerbacks have a pValue < 0.05, which helps to justify that these values are accurate. For the quarterback and linebackers, however, the high pValue suggests that there is too much variation in the data to make any concrete conclusions about the results.
The R² values at the bottom of the chart numerically estimate how much the positional values account for the variation of all of the data data. Although PWAR accounts for approximately 40% of the data variation, it is key to note that a large portion of their estimates were based off the Vegas Line Odds, one of the most well known and accurate sports betting lines in the country. Hughes et. Al. based their data from real NFL games and statistics by compiling the Vegas Odds and results from previous games within the past five years where a starting player was either injured or suspended. If they had conducted their formula without using the Vegas Odds as a starting point, it can be speculated that their R2 value would be significantly lower.
Although MWAR only accounts for 8% of the data variation, the formula for compiling this data was created entirely from scratch. In a perfect world, one would like their R² value to be at or near 100% to justify that their data accounts for all the variations that can occur during these simulations, though this is never the case. Perhaps conducting more simulations may have increased the R² value, it is impossible to definitively predict the behaviors of this value and increased simulations could have ultimately lowered it as well.
The chart in the second table depicts the average displacement of wins when the difference in rating between the starter and replacement is taken into consideration. For quarterbacks and linebackers, the replacement player performs better than the starting player in this aspect, which suggests that these positions are not heavily influenced by physical attributes. Runningbacks, left tack
les, and cornerbacks, on the other hand, show that physical ability is much more significant factor in determining one’s success at that position.
It can be seen that these three positions also show statistical significance with a pValue >0.05. Quarterbacks also begin to show traces of statistical significance with a pValue of 0.051. The ‘Rating Difference Coefficient’ at the bottom of the chart depicts the win displacement for each point of rating difference between starter and replacement for all the positions. The pValue for this rating is 0.025, which shows that this average is statistically significant. The average difference in rating between starting and replacement player was approximately 24.09 points; when multiplied by the rating difference coefficient (-0.0787), it can be estimated that the average win displacement with respect to the difference in player rating is approximately 1.90 games.