QBR isn’t based on passing stats alone. That’s what makes this a good measure of comparison. It incorporates all of a quarterback's contributions to winning, including how he impacts the game on passes, rushes, turnovers, and penalties. Since QBR is built from the play level, it accounts for a team's level of success or failure on every play to provide the proper context, then allocates credit to the quarterback and his teammates to produce a clearer measure of quarterback efficiency.
As I mentioned above, QBR takes into account the entire performance of the QBs game/series of games. During the games, the plays are rarely the same or in the same order. Defensive sets are rarely the same from play to play. Therefore the process is inherently random. Also, we are looking at a snap shot in time of a players performance through these randomly selected circumstances. All meet the criteria for using CLT.
You can obtain a confidence interval based on that QBR as a ranking in the same way you would with the percentage of highest recorded responses on a survey. With that established, a t-test can be conducted as well, and you can also identify standard error from play to play. As you probably know, standard error of a statistic is the estimated standard deviation of a sampled distribution. That’s as close as you get with incomplete samples.
Three principles at play - CLT, Standard Error and Law of large numbers.
I have been reading these posts for a while but do not comment because I normally do not want to get involved. But I do agree with the previous person that said that these statistics do not mean what you think they mean. I like Mccaffrey just as much as the next person, but CLT/SE/LLN aside, you cannot make the claims you are making from this sample. I am currently getting my PhD in statistics, do not feel like I have to prove that to you so you can believe it or not. I do not care what types of statistical summaries and tests you would like to conduct on this data. I hate arbitrary cutoffs for things like sample size, so whether or not you think this data meets the CLT criterion whatever. But, you can't just go using this data to make claims like what you did before..."Based on inferential statistical analysis, Luke won By a landslide this year (5% error allowed). " No, I don't believe it, and no one should for that matter.
No matter what you believe, this was not a random and representative sample. Sure, its "random" in that they have different plays in different orders blah blah blah, but that is not what is meant by random sample. Was the sample of games that Mccaffrey played representative of all the times he could have been put into play... no, probably not. And this is all observational data anyways, so you cannot make large sweeping overarching claims about the comparison between the two quarterbacks, as much as we would like.
So while sure, his numbers might be better based on some type of specific statistical test. However, you cannot use these tests to make these types of conclusions about the data.
2020 Quarterback Competition
in Husker Football
Posted
I have been reading these posts for a while but do not comment because I normally do not want to get involved. But I do agree with the previous person that said that these statistics do not mean what you think they mean. I like Mccaffrey just as much as the next person, but CLT/SE/LLN aside, you cannot make the claims you are making from this sample. I am currently getting my PhD in statistics, do not feel like I have to prove that to you so you can believe it or not. I do not care what types of statistical summaries and tests you would like to conduct on this data. I hate arbitrary cutoffs for things like sample size, so whether or not you think this data meets the CLT criterion whatever. But, you can't just go using this data to make claims like what you did before..."Based on inferential statistical analysis, Luke won By a landslide this year (5% error allowed). " No, I don't believe it, and no one should for that matter.
No matter what you believe, this was not a random and representative sample. Sure, its "random" in that they have different plays in different orders blah blah blah, but that is not what is meant by random sample. Was the sample of games that Mccaffrey played representative of all the times he could have been put into play... no, probably not. And this is all observational data anyways, so you cannot make large sweeping overarching claims about the comparison between the two quarterbacks, as much as we would like.
So while sure, his numbers might be better based on some type of specific statistical test. However, you cannot use these tests to make these types of conclusions about the data.