Charles Robinson: Sean Payton should be atop our radar

Well, clearly Holmgren is not even close to being the usual case. His 10 years really skews the data. There may be nothing different about it, other than the fact that he lasted about 2.5 times longer than the average of the others. He is most definitely an outlier.

Another way if thinking about it...is it more likely that you will have a coach last 10 years, or a coach last 3.5? Pretty clearly, the numbers show that you're now much more likely to have 3.5. No one else has come chose to replicating the success of Holmgren.

 

Further, I remember in school, when doing basic stats, looking at say, class grades, you'd throw out extreme grades from either side, when figuring out a curve. Why? Because the outliers unfairly skew the data for the majority of the class.

Same idea here.

 

resnor, that's a sample size of 9. You can get all kinds of weird results with small samples like that.

Regardless of sample size, there's no way to tell whether 10 is an outlier or not until you specify the distribution it came from. If you know the distribution it came from (of course we don't because that's what we're trying to figure out) then you can calculate the probability of having a "10" (or greater) in a sample size of 9 and then say that the probability is "too low" if you want (after specifying some threshold). Even then, it's not good practice to throw away data if it's pretty clear it's real data obtained under the same conditions as the other data.

What people do in (basic) stats classes I don't know, but you don't need to throw out outliers to figure out a grade curve. You just need to fit a reasonable function like a logistic function, which is known to model a huge number of distributions of human ability or task difficulty well (incidentally it's used in educational testing to measure the abilities of test takers):
https://en.wikipedia.org/wiki/Logistic_function

 

Maybe it wasn't a curve, but to find the median. I don't remember. It was like 25 years ago. LOL. I remember, though, if we had a list a grades, like 43, 67, 69, 71, 73, 72, 77, 64, 61, 71, 99, we would discard the 43 and the 99, as both of those skewed our data. If you're looking for the average grade, those two grades are unimportant, and unfairly skew the data. If you're looking at the average tenure of a SB winning coach on a second team, Holmgren is so far unlike any other coaches tenure to render it meaningless, imo. The average coaching length is really not longer than the average NFL coach for almost 90% of these second team coaches.

 

Median isn't affected at all by outliers so some prefer it because of that. The technical reason why the mean is more often used is because "fitting" a line or a curve or a function to data is usually done to minimize error, where error is measured by something called "least squares". That is, you calculate (D-M)^2 where D is a single data point and M is the mean, take the difference and square it, for each data point and sum them up.

This way of calculating error seems weird right? Why not just calculate D-M, or absolute value of (D-M) as the error (where M could be the median or mean), and try minimizing that? It's because subsequent analysis is hard to do when you do that (when you use methods from calculus). Least squares error is easy to work with using all kinds of other tools of analysis, so that's become the default.

Anyway, regarding this particular sample.. ask yourself whether you would think "10" is an outlier if you had a sample size of 9000 (instead of 9) with the exact same proportion of numbers. That is, you had 1000 10's in that sample. I bet you wouldn't say 10 is an outlier!! Point is.. there's no way to tell whether 10 is indicative of something real or not without knowing the distribution (which we don't know), and that's the intuitive reason why there is no principled method of determining whether something is an outlier or not.

 

Uh, I would still argue that 90% of coaches have a second team tenure right in line with the average time of an average NFL coach. By including Holmgren, you're arguing that these coaches actually have an average that is slightly longer than the average coach, but that isn't really accurate. About 90% of the Super Bowl coaches can expect to have a second team tenure right in line with the average non winning SB coach.

So discard the outlier or not, the fact is, winning a SB doesn't seen to garner these coaches a longer leash with their second team.

 

No the analysis must be done on all the data, and when you do that, winning a SB gives these coaches on average a longer leash.

What you're trying to do is also doubly unjustifiable. You're saying remove outliers from the sample, but not from the population from which the mean was calculated. You think that "10" skews things for the sample? Yeah.. well guys like Don Shula (26 years Dolphins coach) and Belichick (16 years so far) skew the population mean, so you need to at least compare to the population mean when you get rid of all "outliers" in the population (by some unspecified method I guess..)

 

Yeah, that makes sense. The overall NFL average is probably lower, so a lower number for these guys is probably still a tad longer.

 

Mike Shula deserves an interview.. Cam is on his way to the best season hes ever had and its because of Mike.

 

Well, I never thought I would see "(D-M)^2" anywhere again since I traded my MBA course work for M.Div. course work. But, here it is! WOW!