Saturday, December 18, 2010

PR after Week 14

The system did decently last week. It went 11-5, which isn't too impressive considering that I am only picking winners.
BAL over HOU (835) Hit
ATL over CAR (781) Hit
CLE over BUF (754) Hit
PIT over CIN (624) Hit
GB over DET (535) Miss
PHI over DAL (467) Hit
KC over SD (409) Miss
TB over WSH (267) Hit
NYJ over MIA (238) Miss
NYG over MIN (222) Hit
NE over CHI (129) Hit
DEN over ARI (124) Miss
IND over TEN (123) Hit
JAC over OAK (009) Hit

For whatever reason, I mistakenly left out 2 games from last week. This is the result
SF over SEA (306) Hit
NO over STL (133) Hit

Here are the new Power Rankings:

32 CAR 0.009
31 BUF 0.064
30 ARI 0.091
29 HOU 0.099
28 DEN 0.145
27 CIN 0.147
26 SEA 0.168
25 MIN 0.211
24 DAL 0.249
23 TB 0.259
22 WSH 0.319
21 DET 0.330
20 JAC 0.409
19 TEN 0.432
18 SF 0.437
17 CHI 0.533
16 OAK 0.542
15 MIA 0.549
14 SD 0.565
13 NYJ 0.589
12 NYG 0.639
11 IND 0.705
10 STL 0.751
9 CLE 0.764
8 ATL 0.775
7 KC 0.776
6 PIT 0.854
5 PHI 0.884
4 NE 0.927
3 BAL 0.948
2 GB 0.949
1 NO 0.955

Green Bay's run at 1st ended for the first time so far. Interesting. Let's see the spreadsheet's picks for next week, as always, from highest confidence to lowest:

ATL over SEA (793)
CLE over CIN (608)
OAK over DEN (559)
MIA over BUF (361)
PIT over NYJ (342)
CHI over MIN (262)
PHI over NYG (213)
DAL over WSH (201)
ARI over CAR (129)
TEN over HOU (102)
KC over STL (88)
NE over GB (85)
JAC over IND (59)
DET over TB (26)
BAL over NO (10)
SD over SF (1)

You may have noticed since last week that the spreadsheet isn't just simply picking the team with the higher rating to win the game. What I have done is skew the teams performance numbers more heavily in it's recent games, but only for the picks, not for the power rankings. So, power rankings are determined by the whole years performance, every single game being of equal importance. But the picks view the more recent games as more important. Let's see how it goes this week. We know we are at least 1 - 0 so far. The system picked SD in the Thursday night game with probably the lowest confidence ever (1!), but it worked out.

New States

I've always been interested in redrawing maps. I don't really have the resources to do it well, but here is an attempt at an idea I have had for a while.

First, I just pretended that Hawaii and Alaska don't exist, it just made this a lot easier and nice looking. I took all 48 contiguous states and asked "Could you redraw the state lines to create 48 new states where each state had an equal population?" So this is a result of that. Wherever I could, I tried to make the new state lines either geographically and/or culturally relevant. Also, I tried to make the shapes as regular as possible and not all funky looking. It was hard sometimes when dealing with parts of the country that I was unfamiliar with, but I tried my best. This is obviously only one of many different possible solutions. I also didn't label the map since I felt it cramped it up too much.

I split down to the counties, and redrew the borders around different counties. I used the 2000 Census as my source, where I found county by county populations (or county equivalents according to the Census).

It was kind of hard around the big cities. NY had to be broken in a sort of weird way. One state, which I will call "New York" consists of Bronx, Kings (Brooklyn), New York (Manhattan), and Richmond (Staten Island) counties, so basically all of New York City excluding Queens. Then, for the other state which I will call "Long Island", I included Nassau, Suffolk, Queens counties (All the counties on Long Island excluding Kings) and Westchester. I don't know if this one makes geographical or cultural sense, but there was really not many other ways to do it.

Los Angeles was difficult too, particularly because LA county has a greater population than the average for my new states (9.5 Million, whereas my new states needed to average around 5.8 million). Consequently, LA county was the only county that had to be split itself. I needed to take about 3.5 million out of LA county and donate it to the neighboring new state "Ventura". I did a little quick research on different parts of the county, and finally decided that the San Fernando Valley, Santa Clarita Valley, the Antelope Valley and the "Westside" (as defined by the LA times), would constitute around 3.5 million, and these areas were moved into the new state of "Ventura". The rest of LA county became the new state of "Los Angeles".

The new state of "Chicago" consists of Cook and Lake counties. It doesn't really include the whole metro area, and it was split somewhat arbitrarily. The rest of the metro area were sort of divvied up between the new states of "Illinois" "Michigan", "Indiana" and "Wisconsin".

The Philadelphia metro area was also split between the new states of "Penn" and "Delaware", although most of it went to "Delaware" which included no parts of the original state of Delaware but was named after the Delaware River and Bay. The District of Columbia was included on the Virginia Side, not the Maryland Side. The state of Washington was the only one that remained unchanged. It had a population ~5.8 million in 2000, and that was also the average for the 48 contiguous states.

Average population: 5,836, 483
Standard Deviation: 239, 484

And here is the table in case anyone is interested:

New State Population Largest City
Alabama 6,175,885 Birmingham
Arizona 5,210,556 Phoenix
Bay 5,320,818 San Jose
Chicago 6,021,097 Chicago
Michigan 5,791,047 Toledo
Conn 5,904,389 Worcester
S Carolina 6,015,507 Charlotte
Cascades 5,960,310 Portland
Huron 6,003,160 Detroit
Penn 6,045,205 Allentown
Erie 5,947,651 Buffalo
E Texas 5,972,339 Houston
Piedmont 5,799,216 Atlanta
Illinois 6,005,298 Aurora
Imperial 5,802,483 San Diego
Indiana 5,818,156 Indianapolis
Kentucky 6,002,588 Louisville
Los Angeles 5,949,586 Los Angeles
Long Island 5,906,751 Queens
Delta 5,682,122 New Orleans
Mass 5,831,486 Boston
Maryland 6,026,708 Baltimore
Coral 6,064,038 Tampa
Gold Coast 5,952,077 Miami
Mojave 5,458,623 Las Vegas
Minn 5,725,839 Minneapolis
Missowa 5,998,069 St. Louis
Hi Line 5,798,237 Omaha
N Carolina 6,016,261 Virginia Beach
New England 5,807,561 Syracuse
Georgia 5,958,274 Jacksonville
New Jersey 5,822,286 Newark
N Texas 5,985,492 Dallas
New York 5,778,899 Brooklyn
Ohio 6,054,570 Columbus
Oklansas 5,870,816 Oklahoma City
Delaware 5,380,732 Philadelphia
Plains 5,318,721 Colorado Springs
Alleghany 5,802,187 Pittsburgh
Rockies 5,721,812 Denver
Sierra 5,343,609 Fresno
S Texas 5,737,919 San Antonio
Tenn 5,889,616 Memphis
Virginia 6,430,459 Washington DC
Ventura 5,630,622 San Fernando Valley
Wisconsin 6,010,727 Milwaukee
Washington 5,894,121 Seattle
W Texas 5,507,282 El Paso

Friday, December 10, 2010

PR after Week 13

Before I start, all of everything is done with the database having no knowledge of what happened on Thursday nights. It's just too short of a turn around for me to get it up before Thursday.

The calculations had a pretty good week 13. Here are the results from what was predicted.

STL over ARI (778) HIT
NO over  CIN (732) HIT
PHI over HOU (683) HIT
GB over SF (604) HIT
KC over DEN (583) HIT
IND over DAL (536) MISS
ATL over TB (444) HIT
CHI over DET (390) HIT
CLE over MIA (359) HIT
TEN over JAC (341) MISS
SEA over CAR (222) HIT
SD over OAK (182) MISS
MIN over BUF (101) HIT
NYG over WSH (85) HIT
NE over NYJ (37) HIT
PIT over BAL (17) HIT

I don't know why this thing loves Tennessee so much, it's two weeks now that it's picked Tennessee as the better team. This will need some investigation.

Here are the power rankings after Week 12:
 32 CAR 0.013 
 31 BUF 0.039 
 30 ARI 0.051 
 29 CIN 0.139 
 28 HOU 0.142 
 27 DEN 0.177 
 26 SEA 0.232 
 25 MIN 0.236 
 24 DAL 0.267 
 23 WSH 0.271 
 22 TB 0.278 
 21 SF 0.322 
 20 DET 0.333 
 19 JAC 0.427 
 18 MIA 0.443 
 17 SD 0.453 
 16 OAK 0.519 
 15 TEN 0.529 
 14 NYG 0.593 
 13 IND 0.627 
 12 CHI 0.645 
 11 ATL 0.691 
 10 NYJ 0.698 
 9 CLE 0.816 
 8 STL 0.846 
 7 PIT 0.861 
 6 KC 0.865 
 5 PHI 0.881 
 4 NE 0.898 
 3 BAL 0.925 
 2 NO 0.936 
 1 GB 0.958 

I changed the prediction algorithm just a little bit, let's see if it works any better. Again from most confident to least:

BAL over HOU (835)
ATL over CAR (781)
CLE over BUF (754)
PIT over CIN (624)
GB over DET (535)
PHI over DAL (467)
KC over SD (409)
TB over WSH (267)
NYJ over MIA (238)
NYG over MIN (222)
NE over CHI (129)
DEN over ARI (124)
IND over TEN (123)
JAC over OAK (009)

A couple things to note: The system doesn't seem as confident in its picks as it has been in the previous two weeks. Secondly, it is picking a lot of road winners. And since it has no knowledge of Home/Away, I suspect it will do pretty badly this week. Let's see.

Saturday, December 4, 2010

Map of Music LA

I've been recently seeing maps like this and this lately. I saw another one with band/solo artists too, but I can't find it now. I know I found it on reddit, but I can't seem to hit the right key words in the title of the submission. Well, just imagine that it would be a similar thing with different musical artist.

Everywhere in the thread there were discussions about which artists should be assigned to a certain state. California, being the most populous state, obviously had a lot of contenders. I got the idea that you could probably do one for the whole of California, maybe by county. In my mind, I tried to decide who would go into LA County and I was struck by the same sort of gridlock.

So I brought it down even a further level and thought that you can just do one for LA and try to map where the famous bands of LA originated. Some of these were hard to place and I had to do some reading about the history of the bands to assign them some sort of location. There was also sometimes some ambiguity as to whether I should include them or not. For example, 2pac was born in NY, raised in Baltimore, moved to the Bay Area, but eventually settled in LA, where he reached celebrity. He also boasts of his ties to LA more than any of those other cities. I just tried to include what was fair. I also didn't want to include individual members of bands that were already represented either. So NWA counts for Ice Cube, Dr. Dre and Eazy E. And it's not all super accurate as to "where they originated" but I tried to do the best I could and not just cram everybody into Hollywood. I also tried to have as broad of a variety of genres as I could.

The map includes most of LA County (save the Antelope Valley and farther north. I would have loved to include Frank Zappa, but he would just be an island up there by himself in Lancaster) and about the northwestern half of Orange County.

In case you can't figure it out: GnR = Guns N Roses, SOAD = System of a Down, RATM = Rage Against the Machine, RHCP = Red Hot Chili Peppers. If you don't know what NWA stands for, I'll just let you look that one up yourself.

Friday, December 3, 2010

PR After Week 12

First let's take a look at this week's prediction results. I instantly noticed that my 1 and 2 both lost without looking at the numbers. I was a bit disappointed, but did find some diamonds in the rough.

I will order Week 12 games by the discrepancy of their Power Ranking Score (PRS). This would reflect the confidence that my system has in it's pick. The pick is just assumed to be the team with the higher score.

PIT at BUF (Confidence = 802)
The system has PIT as a winner. This pick almost went awry, as you would have noticed if you heard about Buffalo's comeback heroics. PIT was still a winner so this was a CORRECT pick.

CAR at CLE (782)
The system picked CLE as a winner. Despite the close game, again, the system picked the CORRECT winner.

TEN at HOU (657)
The system picked TEN as a winner, but they were shut out, so this was a terribly INCORRECT pick.

NO at DAL (638)
The system picked New Orleans CORRECTLY.

STL at DEN (577)

NE at DET (576)
New England wins, CORRECT pick.

CIN at NYJ (538)
Another CORRECT pick.

TB at BAL (533)
Baltimore wins, CORRECT pick.

KC at SEA (452)
Kansas City, CORRECTLY picked.

PHI at CHI (332)
Chicago wins convincingly, the system picked PHI, its second favorite team, but it was the INCORRECT winner. You may also notice the dramatic drop in confidence. The system is getting to its more uncertain games.

GB at ATL (319)
The system's favorite team was beaten, meaning both its top 2 teams went down. Atlanta wins, making this an INCORRECT pick.

SD at IND (316)
The system picked Indianapolis, which lost. Yet another INCORRECT pick.

JAC at NYG (309)
The system CORRECTLY picked New York as the winner

MIN at WSH (309)
The system picked Washington to win INCORRECTLY.

SF at ARI (149)

The system was not very confident in its San Francisco win, but they won convincingly, making this a CORRECT pick.

MIA at OAK (51)
The system had the least confidence when picking Oakland to win, and they lost. Making this an INCORRECT pick.

You may have noticed that as the confidence rating dropped, so did the success of the system. The overall performance was 10-6.

For this week at least, the important cut off seemed to have been at 0.400 confidence. The system had a +400 confidence in 9 games, of which it picked correctly 8 times.

So without further ado, here are the updated power rankings (excluding HOU v PHI on Thursday)

32 CAR 0.010
31 ARI 0.054
30 BUF 0.058
29 MIN 0.159
28 HOU 0.173
27 DAL 0.180
26 CIN 0.183
25 SEA 0.232
24 DEN 0.237
23 TB 0.264
22 DET 0.295
21 JAC 0.313
20 SF 0.352
19 WSH 0.383
18 OAK 0.390
17 MIA 0.458
16 NYG 0.468
15 SD 0.573
14 TEN 0.653
13 CHI 0.686
12 ATL 0.708
11 IND 0.716
10 NYJ 0.800
9 CLE 0.816
8 KC 0.820
7 STL 0.831
6 NE 0.838
5 PHI 0.856
4 BAL 0.896
3 PIT 0.912
2 NO 0.915
1 GB 0.956

And here are the Picks for Week 13 and confidence values, from most confident to least:

STL over ARI (778)
NO over  CIN (732)
PHI over HOU (683)
GB over SF (604)
KC over DEN (583)
IND over DAL (536)
ATL over TB (444)
CHI over DET (390)
CLE over MIA (359)
TEN over JAC (341)
SEA over CAR (222)
SD over OAK (182)
MIN over BUF (101)
NYG over WSH (85)
NE over NYJ (37)
PIT over BAL (17)

Saturday, November 27, 2010

College Football Playoffs

Here is my proposal for a playoff in college football.

First let me discuss some of the issues that prevent a playoff from happening:

1) It would prolong the season too much. Some people propose 32 team playoffs or say they want something similar to March Madness without realizing how impossible it would be in football. Particularly because you can't play back to back football games. A 32 team playoff would take longer than a month to run, if each round is held a week apart. It is just not realistic.

2) It would lessen the importance of the regular season. I believe that this is really an empty argument. Every other sport with a playoff still has important regular seasons. If teams are playing for a playoff spot, those games are still important because their playoff hopes are on the line. A game between two crappy teams would be unaffected. It is not important now, and it would still be unimportant. The difference is that more teams would be in a playoff hunt, whereas in the current system, only the top few teams have truly NC-meaningful games.

3) The bowl system as they are set up make too much money for the bowls. This is true and probably the biggest reason against a playoff system, there is too much money to lose. The big boys don't want to give up a good system for one with unknown implications for their wallets. From their point of view, it isn't broken, so it shouldn't be "fixed".

4) The importance of certain bowl games will be lost. For example, the Pac10 and Big10 have historically been against anything new which changes the set up of the Rose Bowl. It is understandable because the tradition of the Rose Bowl is a good one, and I do like the whole Big10-Pac10 thing. I do think that these traditions are important. Eventually though, they have caved in little with the +1 system, which does not guarantee a Pac10-Big10 match-up (for example, this year, you will most likely not see the Pac10 in the Rose Bowl, because Oregon will be playing in the NC game instead). All the other minor bowls may lose their "importance" as well, although I am not sure how "important" the Bowl or the Humanitarian Bowl are right now. In any case, there is no reason not to continue their current practices in an NIT-sort-of-way.

I will try to address all of these issues throughout my proposal.

Essentially, my proposal is for an 8-team playoff tied to conference champions. Another issue is that the AQ conferences will not want to lose their guaranteed tie-ins, but my proposal would maintain them. At this point, I really do believe that the MWC deserves AQ much more than the Big East, but it is how it is, and you have to convince the big boys that they will improve their lot, not degrade it.

So if the AQ conferences keep their AQ, that will guarantee 6 teams in the playoff, with 2 spots remaining. It will be up to each AQ conference to have system to determine their champions. Just to refresh, AQ conferences are ACC, Big 10, Big 12, Big East, Pac 10, and SEC.

The 2 remaining spots will be determined as such: all schools in all of FBS will be considered. Any 0 loss team will be taken before any 1 loss team, any 1 loss team will be taken before any 2 loss team, and so on. Tie breakers between same-loss teams will be determined by any BCS-type system. Last rule, both wild cards cannot come from the same conference.

Next, the 4 main bowls will be the sites of all playoff games (Fiesta, Orange, Rose, and Sugar). The tie-ins will be maintained as well as possible. The quarterfinals will play very similarly to how the main 4 bowls currently play:

Fiesta Bowl - Big 12 Champ versus Wild Card

Orange Bowl - ACC Champ versus Big East Champ

Sugar Bowl - SEC Champion versus Wild Card

Rose Bowl - Pac 10 Champ versus Big 10 Champ

Which wild card plays in Orange/Sugar will be determined as such. Firstly, the SEC champ cannot play an SEC-nonchamp, and the Big 12 cannot play a Big 12-nonchamp. Secondly, travel distance to the bowl site should be minimized for the 2 teams.

The Semi-finals and Championship games will rotate between the same 4 sites in such a way that each year, one site will host the NC-game, two sites will host the 2 semi-finals games, and 1 site will host only the quarterfinal game. For a 4 year cycle the system would work as such:

Year 1:
1) Rose Bowl Champ versus Fiesta Bowl Champ plays Rose-Semifinal
2) Sugar Bowl Champ versus Orange Bowl Champ plays Sugar-Semifinal
3) Rose-Semi Champ plays Sugar-Semi Champ in Fiesta-NC game
4) Orange Bowl hosts no additional games

Year 2:
1) Rose Bowl Champ versus Fiesta Bowl Champ plays Fiesta-Semifinal
2) Sugar Bowl Champ versus Orange Bowl Champ plays Orange-Semifinal
3) Fiesta-Semi Champ versus Orange-Semi Champ plays Sugar-NC game
4) Rose Bowl hosts no additional games

Year 3:
1) Rose Bowl Champ versus Fiesta Bowl Champ plays Rose-Semifinal
2) Sugar Bowl Champ versus Orange Bowl Champ plays Sugar-Semifinal
3) Rose-Semi Champ plays Sugar-Semi Champ in Orange-NC game
4) Fiesta Bowl hosts no additional games

Year 4:
1) Rose Bowl Champ versus Fiesta Bowl Champ plays Fiesta-Semifinal
2) Sugar Bowl Champ versus Orange Bowl Champ plays Orange-Semifinal
3) Fiesta-Semi Champ versus Orange-Semi Champ in Rose-NC game
4) Sugar Bowl hosts no additional games.

Here are some issues with my system that may be problematic:

In the current system, each of these sites hosts an additional game once every four years. I am hoping that hosting an additional game 3 times every 4 years will not be too much of a strain.

Teams must play additional games and it may be a strain to players who are actually college students. This is a given with any playoff system, with an 8 team playoff, you minimize the additional games. Each year, 2 teams will play 2 additional games, and 2 teams will play a single additional games. This is out of 120 schools, so indeed, I think the strain of additional games is minimized.

Teams may potentially have to travel between 3 locations on their playoff run. This really can't be helped in any way that I can imagine. The situation with March Madness is even worse, so I hope that it is reasonable to ask a single team to travel from Pasadena, to Glendale, AZ to New Orleans, for example. The Semis are set up to host the winner of its bowl game particularly to limit travel. The Rose Bowl and Fiesta Bowl are always kept on the same side of the bracket to minimize travel, and the same goes for the Sugar and Orange Bowls. The conference tie-ins and wild-card rules are also maintained to limit travel.

Notre Dame loses its preferential treatment. I don't care. You still have a shot just like Boise St. does. Deal with it.

For 2008-2009 the match-ups would have been such:
Fiesta Bowl: Oklahoma (Big 12 Champ) plays Utah (Wild Card, 0 losses)
Orange Bowl: Virginia Tech (ACC Champ) plays Cincinnati (Big East Champ)
Rose Bowl: USC (Pac 10 Champ) plays Penn St. (Big 10 Champ)
Sugar Bowl: Florida (SEC Champ) plays Texas (Highest ranked 1 loss team, cannot play Oklahoma in Fiesta)

Fiesta Bowl: Texas (Big 12 Champ) plays Boise St. (Wild Card, 0 losses)
Orange Bowl: Cincinatti (Big East Champ) plays Georgia Tech (ACC Champ)
Rose Bowl: Oregon (Pac 10 Champ) plays Ohio St. (Big 10 Champ)
Sugar Bowl: Alabama (SEC Champ) plays TCU (Wild Card, 0 losses)

Fiesta Bowl: Oklahoma (B12 Champ) plays Stanford (Wild Card, highest 1 loss team)
Orange Bowl: UConn (BE Champ) plays Virginia Tech (ACC Champ)
Rose Bowl: Oregon (P10 Champ) plays Wisconsin (B10 Champ)
Sugar Bowl: Auburn (SEC Champ) plays TCU (Wild Card, 0 losses)

Power Rankings

I wanted to try my hand at creating a power rankings system. Here is what became of some ideas. The system only takes two things into account, who you played, and what were the scoring patterns of that game. Wins and losses or nothing else of the kind is factored in. Most importantly, my own biases are not factored in. I just ran the data through the machine. It took a pretty long time to enter all the data in by hand, and I am not too sure I will be continuing these rankings.

I was mostly motivated by the fact that wins and losses do not truly reflect how well a team has played. I wanted to build some sort of measure that would tell me how competitive a team has been, regardless of wins and losses. I feel that beating a shitty team by 1 point should not be so much more valuable than losing to a great team by 1 point. When you only look at wins and losses, all that nuance is lost. So intentionally, I have left out wins and losses from the formulation. Instead here is my list of the most competitive teams in the NFL. So for all games up to week 11 (not including Thanksgiving Thursday games), here is how it came out.

The number you see next to the ranking and team name is a sort of "adjusted winning percentage, which is my final measure by which I have ordered these teams.

CAR 0.009

BUF 0.079

ARI 0.083

HOU 0.101

MIN 0.117

CIN 0.220

SF 0.233

JAC 0.238

DAL 0.244

DEN 0.249

DET 0.280

SEA 0.305

TB 0.330

MIA 0.393

WSH 0.426

OAK 0.444

SD 0.484

NYG 0.547

CHI 0.589

ATL 0.657

KC 0.757

NYJ 0.758

TEN 0.758

CLE 0.792

IND 0.800

STL 0.826

NE 0.856

BAL 0.863

NO 0.881

PIT 0.882

PHI 0.921

GB 0.977

I will try to explain how the calculations worked.

I wanted to know how competitive a game was without just looking at the final score, instead looking at the duration of the game. Since the point difference only changes when there is a score, you only need to record each score and the time of the score. With that, you can see each lead throughout the game. By looking at the time difference between scores, you can know how long that lead/deficit was maintained. So for each game, a team was given a score based on its "cumulative lead", which I would define as the sum of its lead at each minute of the game (with seconds as fractions).

However, I also scaled the leads logarithmically, which means that as the lead increases, it's relative value decreases. Try to imagine it like this. The difference between a 8 point lead and a 9 point lead is much bigger than the difference between a 58 point lead and a 59 point lead. Although they are actually both different by only a point, the difference between 8 and 9 is actually valued a lot higher. I did this to actually reflect the value of a score in a football game, and consequently reduce the power of "blowouts". So that additional touchdown late in the 4th to push the lead to 35 is not actually as valuable as the late touchdown which gives you the lead.

So in this way, for each game, each team was given a "raw" score.

Secondly, I wanted to introduce a strength of schedule factor, where the "raw" score was adjusted based on the performance of the opponent in all other games. Admittedly, this could have been much more rigid, but I am not absolutely sure how to go about doing it. The trouble is that "the performance of the opponent in all other games" is also skewed by the opponents' strength of schedule, and you get into this weird web of recursion that I was unsure of how to tackle. I chose only to go one level deep, but seemingly you can just keep going deeper and deeper into strength of schedule, where you have to look at the previous opponents of the previous opponents of the previous opponents of the opponents. And so on.

Additionally, I encountered the problem of how heavily to weigh in the strength of schedule. I tried different percentages and eventually settled for a 10 percent skew, such that the "raw" score was multiplied by the "SOS factor" (90% - 100%) to give the "adjusted" score (losses had to be multiplied in a similar but different way). Changing the percentages (for example having the SOS factor run from 50% - 100%), gave slightly different results.

Finally, I wanted a final score that ran from 0 - 1, so I treated the "adjusted" scores as a normal distribution and returned the percentile of each team's score.

I don't think there were many surprises in the Thursday games this week, but I will keep track of how things pan out with my rankings.

#6 NE beat #22 DET
#4 NO beat #24 DAL
#11 NYJ beat #27 CIN

Anybody would have called those though. Let's see how the Sunday games turn out. If I had a better understanding of how to do these things, I would want to eventually create a system that would somehow return a probability distribution for future match-up, ie 5 percent chance of Team A winning by 10, 4% chance winning by 9, and etc. etc. I have no idea how to do that though.