In the analysis of the best individual players, I chose to examine quarterbacks and runningbacks exclusively because they have the most measured statistics of any positions that were examined in this study. A two-variable t-test was conducted with the null hypothesis that the average wins with the starting player was equal to that of the replacement player. The charts include a pValue to show statistical significance, as well as a 95% confidence interval for the average displacement of wins per player. In other words, if 100 simulations were conducted, approximately 95% of the results would lie within the given parameter.
For quarterbacks, the chart shows that Drew Brees and Tom Brady are the most valuable quarterbacks in the NFL. Although there is not enough data to reject the null hypothesis because neither Brees’ nor Brady’s pValue is below 0.05, it is fair to believe that performing additional simulations for these players would have resulted in a pValue below the threshold, thus rejecting the n
ull hypothesis. Additionally, their 95% confidence intervals show that one can expect to lose as many as six additional games without Brees, and four without Brady. After these two quarterbacks, the results become more unpredictable as can be seen by the high pValue and confidence intervals of Tony Romo, Kirk Cousins, and Cam Newton. For these quarterbacks, the replacement player was equally as capable to generate more wins than the starter as they were to generate fewer wins. It is important to note that generating wins is not synonymous with superior individual performance, however, as the statistics of the replacement player were almost always worse than those of the starter. Key players in the NFL succumb to long-term injuries every year, and it is expected that the players and coaching staff of these teams compensate for the loss and continue to find ways to win games.
A similar test was conducted to determine the top NFL runningbacks according to these simulations, and the results were much more concrete than the quarterbacks. The top two players, Marshawn Lynch and Adrian Peterson, rejected the null hypothesis (h=1) that their average number of wins was equal to their replacement. Their pValues were also extremely low, and their confidence intervals shows that one can expect to lose up to five additional games for both players. The next two runningbacks, Jonathan Stewart and Jamaal Charles, did not quite reject the null hypothesis but it is belie
vable to think that additional simulations for these players would have been enough to reject the null hypothesis. Although the pValue of Le’veon Bell is rather high, it is no secret that he plays for a strong team which probably had equal success throwing the football exclusively. As stated earlier, the ability for teams to compensate without a starting player is crucial as it is very unlikely that a team will go an entire season without losing a starting player due to injury.