Poll: The Greatest Coach in NFL History Not Named Shula

I got it, thanks.

However, being the type of game that football is, how much worth can we put into "probability" when it comes to wins? Injuries, weather, deflated footballs (lol) all affect the game. If the Dolphins had to play 8 games in monsoon like conditions due to some freak of nature, how much would that affect the outcomes of games?

What I'm saying is, you can definitely use math to determine certain parts of the game, but the overall outcome would seem (at least to me) impossible to even come close to in regards to predicting. And because the Pats have been determined, twice, to be cheaters, and have had many more accusations, and have shown that they are able to do things that no other team in the history of the game has done, makes me think they are still cheaters.

 

All depends on how predictable the conditions are, which can be tested by looking at how stable the stats are over time.

For example, home win% has remained very stable in the NFL at 57% with about 12% standard deviation for a "normal" distribution. What that means is around 68% of all home win% will be within 1 standard deviation, or 57-12=45% and 57+12=69%. It also means 95% of the home win% will be within 2 standard deviations, or 57+24=81% and 57-24=33%. And generally that's what you see. NE has been at around 83%, but when you factor in there being 32 teams, that's 44% likely.

btw.. that's only for regular season. Average divisional game home win% is way higher at around 73% (since 1990). Problem using this stat is you have too few divisional round games per year, so it's not that useful for predicting results on a single year basis (small sample size = large variation = not useful for prediction).

Or check the league standings on a year-by-year basis. Average number of wins is about 8 (obviously) but the standard deviation is very stable at around 3. So 68% of all W/L records in a single year should be between 8-3=5 wins and 8+3=11 wins. 68% of 32 is 21.76, so we're saying 21-23 teams per year should have 5-11 wins. It's very stable.

Or what about rushing yard distributions. Check this out:
https://i.imgsafe.org/6b23d89437.png

That's the distribution of runs in 2005 vs. 2015. Almost identical! So when you have something that predictable, you can easily test how likely or not something was. And btw the fumbling stats from which I calculated the probability of NE having that absurdly low probability from 2007 was also very stable.

Of course, if the conditions change too much (e.g. your example of playing 8 games in monsoon-like conditions) you can't use these stats and would have to start gathering stats in those conditions, but the win% calculations I'm basing stuff on are pretty stable over time.


Oh, and IF a stat is not stable over time, like say completion percentage:
https://i.imgsafe.org/6b351a79d0.png

you can adjust for it either by directly adjusting each year (divide by that year's mean and multiply by current year's mean) or you fit a line through the data and extrapolate, meaning the WAY the stats change is stable.

 

Great work and very interesting, but I still find it hard to believe that there can be any true way of quantifying wins in this game. Think of flipping a coin. I can flip a coin 100 times and the first 99 can be all heads. Now, some people will think, based off of those 99 flips, that the chance of getting another heads would be statistically impossible. However, and I'm sure you know this, that 100th flip still has a 50% chance of landing on either heads or tails. Maybe I'm thinking about this all wrong, but like I mentioned earlier, injuries, bad calls, turnovers, weather and any other number of unknowable things can change the outcome of the game. Cheating, whether it be insuring that you keep your TO's low or that you are more likely than not going to call the right play (both things the Pats have been proven to do), takes away a lot of those unknowable's. To me, that's a huge advantage and the reason the Pats can win with below average players.

 

BTW, I haven't done all the math that you have, but I'm going by the following when I talk about their fumbling rate.

http://www.sharpfootballanalysis.co...ts-prevention-of-fumbles-is-nearly-impossible

 

Your coin flip example is a case where we a priori know the coin is fair (that's the assumption there), meaning that the probability of heads or tails is 50% irrespective of 99 heads in a row being observed.

In most situations, including football, we do not a priori know the bias of that coin so to say. That is, we have to use data to estimate whether the coin is biased or not. There are really two approaches for doing so, and which you use depends on the question you want to answer. You can either use something called Bayesian inference, or you use something called hypothesis testing.

For Bayesian inference, you list a set of hypotheses. For example, you could say hypothesis 1 = coin designed to be fair (50% probability of heads), hypothesis 2 = coin is biased to 75% heads, hypothesis 3 = coin is biased to 99% heads, etc... Bayesian inference is just the correct math for showing how to take each additional observation (each observed coin flip) and calculate what are called the likelihoods of different hypotheses being correct. Likelihoods are probabilities, but they are called likelihoods instead of probabilities because we want to distinguish between the probability of an event occurring vs. the likelihood of a hypothesis being true (events vs. theories so to say should be distinguished).

So for each additional data point, the likelihoods of all your stated hypotheses will change. If you observe 99 consecutive heads, the likelihood of hypothesis 3 will be way greater than 2 which will be greater than 1, but none will ever go to zero. Point is, you use the data to infer what the most likely bias of the coin is.


The other approach, hypothesis testing, only tests ONE hypothesis called the null hypothesis, which in the case of your coin example is that the coin is fair. In the case of making the playoffs in the NFL it would be that you have a 12/32 chance of making the playoffs because 12 teams out of 32 make the playoffs each year. Basically you need to know what the expected distribution of events (heads or tails) looks like. If you have data for a population you use that. The run distribution data in my previous post is an example.

The goal is now to take one sample, say the actual number of times NE made the playoffs with Brady starting all 16 games in a season, or the number of consecutive times the Bills failed to make the playoffs, then use the distribution you have to calculate the probability that sample came FROM that distribution. That is, you're asking what the probability is that the data you think is weird would have come from the population data you have if you just randomly sampled. Those are the probabilities I've been listing.

Of course, we need the distributions of fumbling rates to do the calculation for the fumbling data, which brings me to your second post:

Sharp started the ball rolling, but there were so many (valid) critiques against the first version that came out you're best off not referring to his data. Basically, the critiques were: 1) cherry picking data to not include indoor teams, 2) data depicting just fumbles lost instead of all fumbles, 3) including special teams fumbles, and 4) assuming the distribution is normal in calculating statistical significance for plays per fumble instead of fumbles per play (it holds for the latter, not the former).

Anyway, I think the best source after the back-and-forth debates on which stats to use are:
http://www.advancedfootballanalytic...ral/224-the-patriots-have-great-ball-security

Basically, NE is a major outlier among outdoor teams, but Atlanta and New Orleans are better than NE in ball security overall. Thing is, indoor vs. outdoor is real, so as long as you're willing to make the argument just for outdoor teams (and I'm fine with that), then what NE did is extremely unlikely to be explained by chance alone. I don't have the calculation I did from long ago, but the conclusion was similar to Brian Burke in that link.

 

Awesome post.

But if those things I mentioned (injuries, weather etc) do affect the outcome of games how do you adjust your probabilities without knowing how much those things affect the outcome? If injuries, for example, were somehow measured and showed that the Pats win at an abnormal rate with injuries to key players when compared to the rest of the league, would that determine anything? What if weather, injuries, turnovers, rookies, or even how players that do OK on other teams and play lights out when they come to the Pats (and vice verse) could be measured? If many of these things were to show that the Pats have been able to not only overcome them, but overcome them by statistically impossible rates, would that mean anything?


Thanks for the link. After reading it, however, I came away even more convinced that their TO rate was made possible by tampering with footballs.lol

 

You can adjust for anything once you have the data. My current stance is based only on the data available so if anyone has the kind of data you're talking about (preferably in easy-to-download format) I'd love to do a more discerning analysis. In the meantime, all I can say is we don't know what the analysis would look like if we had that data.

 

You mean you aren't going to take my hint and figure all that out?

Damn...

 

Hate to admit it but the Hoody is the best of the bunch even with the cheating. If the NFL can't control him why should he change?Also he gets the most out his roster bar none.

 

I'd tend to agree, but just how much is he being helped by past/current cheating? No one can really say. And because of that, I can't give him the nod as GOAT.

 

bill is guilty of multiple crimes, including fraud. I would vote for him spending time in jail before I would vote him into the Hall Of Fame.