How will NFL Teams will fair in 2006? (1 Viewer)

[nerangers]

The article I entered for the FGB contest dealt with the Pythagorean Win Theorem. Figured I would supply the data here. I thought the results were interesting.

The Pythagorean Win Theorem was originally used to calculate win-loss records for baseball, but was adapted for football. In a nutshell, a team’s Win-Loss record could be roughly estimated by using points scored on offense divide by the points allowed on defense, then raising the ratio by an exponent of 2.37. Once you have the projected number of wins, you compare it to the actual number of wins the team had that season. Teams that win one or more games over the projected number of wins tend to regress the following year. Likewise, teams that lose one or more games under the projected number of wins tend to improve the following year.

Here are the results going into 2006:

Cincinnati Bengals, 11-5, 9.72, Regress

Indianapolis Colts, 14-2, 12.74, Regress

Jacksonville Jaguars, 12-4, 10.68, Regress

Houston Texans, 2- 14, 3.71, Improve

Denver Broncos, 13-3, 11.73, Regress

San Diego Chargers, 9-7, 10.67, Improve

Oakland Raiders, 4-12, 5.45, Improve

Minnesota Vikings, 9-7, 6.90, Regress

Green Bay Packers, 4-12, 6.65, Improve

Tampa Bay Buccaneers 11-5, 8.86, Regress

I was curious how accurate it has been.

NERangers Pythagorean Win Theorem Data

Calculating Pythagorean Win Theorem Data

Last year, 12 out of 15 were predicted correctly. Other years were not as accurate, but still interesting to see the results.

Now if I could only find a good use for it!

 

[KnowledgeReignsSupreme]

I've always been a big fan of PWT

 

[SSOG]

The article I entered for the FGB contest dealt with the Pythagorean Win Theorem. Figured I would supply the data here. I thought the results were interesting.

The Pythagorean Win Theorem was originally used to calculate win-loss records for baseball, but was adapted for football. In a nutshell, a team’s Win-Loss record could be roughly estimated by using points scored on offense divide by the points allowed on defense, then raising the ratio by an exponent of 2.37. Once you have the projected number of wins, you compare it to the actual number of wins the team had that season. Teams that win one or more games over the projected number of wins tend to regress the following year. Likewise, teams that lose one or more games under the projected number of wins tend to improve the following year.

Here are the results going into 2006:

Cincinnati Bengals, 11-5, 9.72, Regress

Indianapolis Colts, 14-2, 12.74, Regress

Jacksonville Jaguars, 12-4, 10.68, Regress

Houston Texans, 2- 14, 3.71, Improve

Denver Broncos, 13-3, 11.73, Regress

San Diego Chargers, 9-7, 10.67, Improve

Oakland Raiders, 4-12, 5.45, Improve

Minnesota Vikings, 9-7, 6.90, Regress

Green Bay Packers, 4-12, 6.65, Improve

Tampa Bay Buccaneers 11-5, 8.86, Regress

I was curious how accurate it has been.

NERangers Pythagorean Win Theorem Data

Calculating Pythagorean Win Theorem Data

Last year, 12 out of 15 were predicted correctly. Other years were not as accurate, but still interesting to see the results.

Now if I could only find a good use for it!

The problem I have with predicting future performance based on Pythagorean Wins is that teams with good records almost universally outperformed their PWT and teams with bad records almost univerally underperform their PWT. That's just the nature of the NFL and the small sample size (only 16 games). Each game is 6.25% of the year. That's the equivalent of over 11 baseball games. As a result, it's hard to tell if PWT is really predicting a decline, or if we're just observing simple regression to the mean.

 

[Chase Stuart]

The problem I have with predicting future performance based on Pythagorean Wins is that teams with good records almost universally outperformed their PWT and teams with bad records almost univerally underperform their PWT.

That's not a problem.

 

[SSOG]

The problem I have with predicting future performance based on Pythagorean Wins is that teams with good records almost universally outperformed their PWT and teams with bad records almost univerally underperform their PWT.

That's not a problem.

Well, it is, because then when the team regresses, is it because it outperformed its PWT, or is it because of simple regression to the mean? If a team gets 11 wins and underperforms its PWT, is it less likely to regress to the mean the following year?

 

[KnowledgeReignsSupreme]

The problem I have with predicting future performance based on Pythagorean Wins is that teams with good records almost universally outperformed their PWT and teams with bad records almost univerally underperform their PWT.

27/32 teams finished within 1.5 wins of their predicted PWT totals. That's not a drastic difference IMO. Only 3/32 were more than 2 wins away from the predicted totals.A team that finished with 8.9 predicted wins and 8 actual wins isn't a team you look at to regress in year N+1.

 

[Chase Stuart]

The problem I have with predicting future performance based on Pythagorean Wins is that teams with good records almost universally outperformed their PWT and teams with bad records almost univerally underperform their PWT.

That's not a problem.

Well, it is, because then when the team regresses, is it because it outperformed its PWT, or is it because of simple regression to the mean? If a team gets 11 wins and underperforms its PWT, is it less likely to regress to the mean the following year?

Now I'm getting a bit confused here. A team never regresses because it outperformd its PWT from the previous year.

 

[Chase Stuart]

Taking a quick look at the PWT here, and it looks like its different than the one I'm used to seeing. Isn't the normal PW% (PF^2.37)/(PF^2.37 + PA^2.37)?

 

[SSOG]

The problem I have with predicting future performance based on Pythagorean Wins is that teams with good records almost universally outperformed their PWT and teams with bad records almost univerally underperform their PWT.

27/32 teams finished within 1.5 wins of their predicted PWT totals. That's not a drastic difference IMO. Only 3/32 were more than 2 wins away from the predicted totals.A team that finished with 8.9 predicted wins and 8 actual wins isn't a team you look at to regress in year N+1.

Well, if he was looking at a 2-win difference, that'd be one thing... but he's talking about a 1-win difference. With a 1-win difference, I feel a lot of it is just random chance

 

[SSOG]

The problem I have with predicting future performance based on Pythagorean Wins is that teams with good records almost universally outperformed their PWT and teams with bad records almost univerally underperform their PWT.

That's not a problem.

Well, it is, because then when the team regresses, is it because it outperformed its PWT, or is it because of simple regression to the mean? If a team gets 11 wins and underperforms its PWT, is it less likely to regress to the mean the following year?

Now I'm getting a bit confused here. A team never regresses because it outperformd its PWT from the previous year.

That's the whole premise of this thread: if a team outperforms its PWT, it's likely to regress. I was just saying that I think this is a case of lurking variables. Teams with lots of wins are more likely to outperform their PWT. Teams with lots of wins are likely to regress. Therefore, there will be a strong correlation between outperforming PWT and regressing in year N+1; however, as we all should know, correlation does not necessarily imply causation.

Taking a quick look at the PWT here, and it looks like its different than the one I'm used to seeing. Isn't the normal PW% (PF^2.37)/(PF^2.37 + PA^2.37)?

Is 2.37 the exponant used for baseball PWT? I know that Football Outsiders, at least, uses a different exponant in their PWT calculations (they calculated what exponant produced results that correlated best with real-world data, and it differed from the Baseball exponant). As a result, you'll see PWT from several different sources, but a lot of times they'll use different exponants (again, as opposed to Baseball, where the concept originated and the exponant is standard and fixed).I just said the word exponant a lot.

 

[nerangers]

Taking a quick look at the PWT here, and it looks like its different than the one I'm used to seeing. Isn't the normal PW% (PF^2.37)/(PF^2.37 + PA^2.37)?

This was the article I read that gave me the idea to play around with it: Pythagoras on the GridironI am pretty sure I did the calculations right....if not, let me know. I am not a stats person and was trying to re-engineer the results.

 

[nerangers]

Is 2.37 the exponant used for baseball PWT?

I am pretty sure it is 1.82 based on the article I read SSOG

 

[Chase Stuart]

The problem I have with predicting future performance based on Pythagorean Wins is that teams with good records almost universally outperformed their PWT and teams with bad records almost univerally underperform their PWT.

That's not a problem.

Well, it is, because then when the team regresses, is it because it outperformed its PWT, or is it because of simple regression to the mean? If a team gets 11 wins and underperforms its PWT, is it less likely to regress to the mean the following year?

Now I'm getting a bit confused here. A team never regresses because it outperformd its PWT from the previous year.

That's the whole premise of this thread: if a team outperforms its PWT, it's likely to regress.

I was just saying that I think this is a case of lurking variables. Teams with lots of wins are more likely to outperform their PWT. Teams with lots of wins are likely to regress. Therefore, there will be a strong correlation between outperforming PWT and regressing in year N+1; however, as we all should know, correlation does not necessarily imply causation.

1) Which one is the premise?

Scenario A: Team A scores 350 points and allows 350 points. Team A goes 10-6. Team A "should" have gone 8-8. Team A next year will be likely to win 8 games.

OR

Scenario B: Team B scores 350 points and allows 350 points. Team B goes 10-6. Team B "should" have gone 8-8. Team B will next year win two fewer games than they should.

I'm hoping it's scenario A, because the premise in scenario B is clearly flawed. But in scenario A, you've got a few things jumping out:

1) A team doesn't regress because it won more games than it should have last year; there's no causation at all going on.

2) A team with 8 wins and a team with 10 wins should be projected with pretty similar win totals for next year anway

3) Most importantly, if you project a team off its PWT, then you're really predicting any regression at all. You're just projecting them to play like they should.

Taking a quick look at the PWT here, and it looks like its different than the one I'm used to seeing. Isn't the normal PW% (PF^2.37)/(PF^2.37 + PA^2.37)?

Is 2.37 the exponant used for baseball PWT? I know that Football Outsiders, at least, uses a different exponant in their PWT calculations (they calculated what exponant produced results that correlated best with real-world data, and it differed from the Baseball exponant). As a result, you'll see PWT from several different sources, but a lot of times they'll use different exponants (again, as opposed to Baseball, where the concept originated and the exponant is standard and fixed).

I just said the word exponant a lot.

The exponent is different for baseball. But in my quick look the entire formula used here was different.

 

[SSOG]

Is 2.37 the exponant used for baseball PWT?

I am pretty sure it is 1.82 based on the article I read SSOG

Gotcha. I knew that Baseball used one exponant and Football Outsiders used another, but I wasn't sure which you were using.