Updated Playoff Picture

[cdcox]

In the AFC the Steelers, Chargers, Raiders and Colts are all looking like probable playoff teams. Since Oakland or San Diego will probably take one of the wild cards, that leaves 7 or 8 teams fighting for the last wild card spot in the AFC.

Last week I called the NFC east playoff teams to be (with 75% certainty) the Eagles, Packers, Bucs, Saints, Falcons, and 49ers. Things only solidified more over the weekend with the odds of these six increasing to 97% even with 4 weeks left to play. So much for parity in the NFC. In fact, I rate the NFC significantly stronger than the AFC, with the top 4 teams and 6 of the top 7. I’m starting to like the NFC’s chances in the Super Bowl.

The first number represents the chance of winning the division, the second number represents the chance of making the playoffs as either a division winner or a wildcard, and the third number represents the power rating that my program calculated based on performance so far and used to predict the outcomes of the remaining games.

"NYJ" .081,.111, 18
"MIA" .437,.578, 12
"BUF" .049,.059, 19
"NEP" .433,.509, 13

"PIT" .878,.901, 8
"CIN" 0,0, 32
"CLE" .043,.136, 17
"BAL" .079,.18, 15

"HOU" 0,0, 28
"IND” .651,.847, 10
"JAX" .002,.006, 23
"TEN" .347,.526, 14

"KCC" .02,.094, 16
"OAK" .342,.774, 5
"DEN" .083,.428, 11
"SDC" .555,.851, 9

"WAS" 0,0, 21
"DAL" .001,.001, 25
"NYG" .01,.019, 20
"PHI" .989,.991, 3

"DET" 0,0, 30
"MIN" 0,0, 31
"GBP" 1,1, 6
"CHI" 0,0, 29

"TBB" .514,.992, 1
"NOS" .215,.998, 2
“ATL" .271,.998, 4
"CAR" 0,0, 24

"SFF" .99,.99, 7
"STL” .01,.011, 22
"ARZ" 0,0, 26
"SEA" 0,0, 27

 

[Guest]

...I rate the NFC significantly stronger than the AFC, with the top 4 teams and 6 of the top 7. I’m starting to like the NFC’s chances in the Super Bowl.

"TBB" .514,.992, 1
"NOS" .215,.998, 2
"PHI" .989,.991, 3
“ATL" .271,.998, 4
"OAK" .342,.774, 5
"GBP" 1,1, 6
"SFF" .99,.99, 7
"PIT" .878,.901, 8
"SDC" .555,.851, 9
"IND” .651,.847, 10
"DEN" .083,.428, 11
"MIA" .437,.578, 12
"NEP" .433,.509, 13
"TEN" .347,.526, 14
"BAL" .079,.18, 15
"KCC" .02,.094, 16
"CLE" .043,.136, 17
"NYJ" .081,.111, 18
"BUF" .049,.059, 19
"NYG" .01,.019, 20
"WAS" 0,0, 21
"STL” .01,.011, 22 (NoRespect says: "Ouch!")
"JAX" .002,.006, 23
"CAR" 0,0, 24
"DAL" .001,.001, 25
"ARZ" 0,0, 26
"SEA" 0,0, 27
"HOU" 0,0, 28
"CHI" 0,0, 29
"DET" 0,0, 30
"MIN" 0,0, 31
"CIN" 0,0, 32

I have taken the liberty of sorting CD's rusults.

The top four teams being in the NFC? 6 of the top 7? That is a bold prediction -- even for a program. Interesting analysis I must say but I would be curious what criteria (and weighting) were used. This looks dangerously like one of those systems that rewards statistics without looking at who they played. The NFC South has had the advantage of playing the AFC North. Either punish the NFC South or reward Cincinnati, you know what I mean? The trick is: How to weigh the Strength of a Schedule before it has been completed?

I have to hand it to you for coming up with this program. The numbers look sound but I am always a little skeptical about any rankings that put Atlanta and the Saints in the top four... I know that it is a historical bias but I can't help it.

I would rate the Jets higher than 18th; and the Packers -- come on, they play in the worst division in football! The Packers are roughly as good a team as the Pats. The Pats lost that game -- in my opinion -- due to poor execution and penalties.

The very fact that I disagree with (some of) the results may be proof that it is right. Good job CD.

 

[cdcox]

NoRespect:

Thanks for the interest in my results. The power rating system definitively considers strength of teams that you win and lose to. I am going to try to explain the Power Rating system without resorting to math. Every team is assigned a power rating based on every NFL game played thus far. So the Patriots’ power rating was affected slightly by the out come of say the 49er vs. Rams game even though the Patriots don’t play either team this season. However, because the Patriots play the AFC West this season, which in turn plays the NFC West, the out come of games in the NFC West affects the Patriots’ power rating. There is enough overlap in schedules to get a relative estimate of the strength of every team in the league. The power ratings are adjusted so that in the games played so far, there are as few “upsets” (as judged by the power ratings of each team) as possible. There is also an adjustment for home field advantage so that a team with a slightly lower power rating would be favored to win a game on their home turf. For teams with equal record, the team with fewer losses to weak teams will ususally be ranked higher. For example, NO is at #2 because all their losses except one (the Detroit debacle) have been against teams that are near the top of the power ratings. They also have several victories against top-rated teams (2 against TB 1, GB 6, Pitt 8, and SF 7) Indy, meanwhile has the same record, but is rated only 10th because they have losses against 3 weaker teams (Miami 12, Tennessee 14, and Washington 21) and only one victory over a stronger team (Philadelphia 3) to offset it. I agree that the system is not perfect, but it is completely unbiased and considers the strength of the opponents in a comprehensive way.

Personally, from the games I have seen, I like TB, Philly and Atlanta from the NFC and only Oakland from the AFC. I’m still waiting for the old farts on the Raiders to crash as the seasons stretches into its last weeks or into the playoffs. If they can avoid that, they could be as tough as anyone to beat.

Thanks again for the interest.

 

[pookie]

Brainiacs!!!!

Great Googily Moogily! You 2 are making my little brain hurt!!

 

[Guest]

NoRespect:

I am going to try to explain the Power Rating system without resorting to math.

Funny. Okay, some of us got top marks in ciphering you know.

Every team is assigned a power rating based on every NFL game played thus far. So the Patriots’ power rating was affected slightly by the out come of say the 49er vs. Rams game even though the Patriots don’t play either team this season. However, because the Patriots play the AFC West this season, which in turn plays the NFC West, the out come of games in the NFC West affects the Patriots’ power rating. There is enough overlap in schedules to get a relative estimate of the strength of every team in the league.

So if I understand correctly, you consider the schedules in a "recursive" fashion? Team A>B, B>C therefore A>C? I always thought that was a logic error. I know it is not predictive.

Let me ask one question. What do you use for input before the first game of the season? Last years data? What is the baseline?

I know you don't want to give out the Colonel's Secret Recipe but I am curious. I have often thought that a program could be written to analyse the relative strengths of each team. It would be be progressively more accurate as the season "progresses" but would be way off base until there is sufficient data.

 

[Phobia]

I can't answer for cdcox, but he rarely posts these things before week 8 of the season. I am assuming he uses only the current season data.

 

[cdcox]

Phobs is right, I never calculate anything until at least 4 games have been played and have zero confidence in the results until about 8 games are played. I may try to incorporate Bayesian statistics into the program next year that would allow me to use preseason “expert opinion” (eg., ESPN columnist predictions, how expert is that?) to make predictions earlier in the season, account for injuries, “hot” teams, etc. But doing this would certainly add more subjectivity to the ratings.

As far as the detailed math, I’m not trying to keep it a secret so much as trying to explain it to a wide audience. Here is a simple description of the mathematics that may give you a basic idea. For each game played so far in the season I calculate a Z-score as follows:

Z = (Strength of Home Team + Home Field Advantage – Strength of Away Team)/ sqrt(2* standard deviation)

Each of the variables in this equation are unknowns that my computer has to solve for (more about that later). The Z-score is related to the probability of the home team winning, expressed as a decimal. I then have an objective function that I try to minimize through adjustment of the team strengths, league-wide home field advantage, and league- wide standard deviation (a total of 34 variables):

Objective function = sum over all games played (outcome – probability of home team winning)^2

The outcome is equal to 0 if the home team actually (meaning on the football field) loses and 1 if the home team wins.

Finding the value of the 34 variables that minimize this non-linear equation is not trivial because there are local minima that you can get sucked into if you just use a gradient-based technique such as Newton-Raphson. I use what is called a Tabeau search. It is similar to a generic algorithm in that new possible sets of variables are generated from combinations of previous variables that were relatively successful. It differs from a genetic algorithm in that certain groups of varialbe values are taken out of the "gene pool" for a certain amount of time to allow more "diversity" than is normally achieved a straight genetic algorithm.

 

[Guest]

I may try to incorporate...preseason “expert opinion” (eg., ESPN columnist predictions, how expert is that?) to make predictions earlier in the season.... But doing this would certainly add more subjectivity to the ratings.

As far as the detailed math, I’m not trying to keep it a secret so much as trying to explain it to a wide audience.

I am going to go out on a limb here and say that you are either an engineer with a fascination for statistics, or a possibly a programmer? Either way your statistical knowledge is impressive.

I think it is safe to say that even if you were trying to keep it a secret, the secret is still safe. That cat is not coming out of the bag. While I can be highly analytical and often have to be, I prefer non-linear thought.

Regarding the introduction of "expert" opinion, that would seem to be somewhat counterproductive now that I see where you are headed. (Not that I was recommending it). After all that careful thought and analysis, why not introduce the variables of bias and misconception.... The absence of readily available expertise is really the reason for the program in the first place is it not? (If there is irony to be had, I will find it.)

Very interesting CD. Are you by any chance a betting man? How have the results been so far?

 

[cdcox]

Good guess on the profession, NR. I'm actually an engineering prof. Much of the math used in this program is self taught. I'm not a programmer, but I do like to program (big difference).

The reason for inserting expert opinion is that sometimes people can see things before they show up in wins and losses that the program can consider. The trade-off is that often the conventional wisdom of people turns out to be wrong. Take for example when McNabb went down. Conventional wisdom, including mine, was that Pilly would be sunk without him. Not so. My computer never knew about this injury, so it went merrily on its way thinking that Pilly was going to be tough to beat, and turned out to be right. Sometimes though the human hunch can prove correct. A couple weeks ago my program had Denver with a 80% chance or so of making the playoffs. I thought they were due for a few losses, and turned out to be right. Bayesian statistics allow the expert opinions to be meshed with the cold hard facts in a statistically consistent way.


Not really much of a gambler. Small ante poker in college is about the extent of it. I like to do these kind of things for the sake of the knowledge. I also have much more confidence that the results are right in mass (1000 simulations of a whole season I can predict percentages of playoff teams) rather than in specific cases (willing to put cold hard cash on the outcome of a single game).

 

[Guest]

I like to do these kind of things for the sake of the knowledge. I also have much more confidence that the results are right in mass (1000 simulations of a whole season I can predict percentages of playoff teams) rather than in specific cases (willing to put cold hard cash on the outcome of a single game).

A noble pursuit. I think the best endeavors are motivated intrinsically and not for gain. I was merely pointing out that If you succeed writing a program that can predict discrete outcomes you will not have to find a market for your services -- the market will find you. Not to mention that a few well placed wagers could finance a considerable number of similar pursuits.

 

[pookie]

A noble pursuit. I think the best endeavors are motivated intrinsically and not for gain. I was merely pointing out that If you succeed writing a program that can predict discrete outcomes you will not have to find a market for your services -- the market will find you. Not to mention that a few well placed wagers could finance a considerable number of similar pursuits.

For the love of God and everything that is good!!! Don't you 2 brainiacs have a convention to attend?

:STFU:

 

[Guest]

For the love of God and everything that is good!!! Don't you 2 brainiacs have a convention to attend?

Pookie...

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</EMBED>

 

[pookie]

Pookie...

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Remembah? AUTOSTART=TRUE..... you silly little braniac!

 

[Guest]

Pookie...

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Listen closely. Don't make me do this again...


(Technology has set communication back 4000 years.)

 

[cdcox]

Here is the latest after last weeks games. Things are looking relatively good for you Pats. Big game this week against the resurgent Titans.

"NYJ" .121,.213, 16
"MIA" .407,.632, 9
"BUF" 0,.002, 20
"NEP" .472,.59, 10

"PIT" .809,.809, 14
"CIN" 0,0, 32
"CLE" .048,.069, 21
"BAL" .143,.157, 17

"HOU" 0,0, 27
"IND” .386,.726, 11
"JAX" .009,.037, 19
"TEN" .605,.796, 13

"KCC" .045,.172, 15
"OAK" .661,.928, 3
"DEN" .067,.165, 12
"SDC" .227,.704, 8

"WAS" 0,0, 23
"DAL" 0,0, 25
"NYG" .003,.025, 18
"PHI" .997,.998, 4

"DET" 0,0, 31
"MIN" 0,0, 30
"GBP" 1,1, 6
"CHI" 0,0, 29

"TBB" .627,.999, 1
"NOS" .355,.998, 2
“ATL" .018,.98, 7
"CAR" 0,0, 24


"SFF" 1,1, 5
"STL” 0,0, 22
"ARZ" 0,0, 26
"SEA" 0,0, 28