NFL Ratings after Week 12

NFL Rankings 

Through Week 12: (29 NOV 2016)
(delta calc'd from Week: 11 (22 NOV 2016)

Comments? Leave some below!

NCAAF Ratings after Week 13

NCAA Football Top 25 Rankings

Updated: Week 13, 27 NOV 2016

(Delta Calc'd from Week 12, 20 NOV 2016)

(Click here for a more detailed explanation of my NCAAF rating system)

Some of these rankings my surprise you, but keep in mind that there is no bias towards any team or preconceived notions, and the only thing considered is what each team has accomplished so far.

(For those viewing from a phone, tap the rankings and rotate to enlarge)

A quick note about my ratings: I implemented an improvement between Weeks 12 and 13. I believe it was important enough to incorporate mid-season. For those interested: you can read the details here!

Notes:

• #2 Ohio State defeats #4 Michigan to cement itself as the #2 team in my ratings. This is significant because I do not project any future conference champion (e.g. Clemson, Washington, Wisconsin, Penn St, etc..) jumping the Buckeyes after the conference championship games next week. OSU gained 7.46 points after beating Michigan (keep in mind, other factors affect that increase, such as all of OSU's opponents change in ratings, etc.). Clemson will not get nearly that after defeating #23 Virginia Tech, and they are the closest team to OSU, sitting at #3 nearly 12 points behind. #5 Washington has a tougher opponent in #7 Colorado. However, they are even further behind (~15 points).
• Michigan lost so little points due the loss to #2 Ohio State that the positive affects of Michigan's opponents ratings on its own were greater than the penalty for losing to OSU and actually gained 0.27 points.
• This is not a real reward by any means, considering all the teams around Michigan gained at least 2.5 points.
• With the rest contenders closing the gap on #4 Michigan, I do not project that Michigan will be in the Top 4 after next week's games.
• Washington's win over #22 Washington State bumped them to #5, jumping Penn State.
• Undefeated Western Michigan finally ends their skid in my rankings (despite not losing!) by beating their second Top 60 team (#55 Toledo), jumping to #15.
• Florida State cracks my Top 10 after defeating #12 Florida.
• #13 Oklahoma is the only Big 12 team ranked in the Top 25
• The Big Ten still occupies 4 of the Top 6 rankings.
• Three AAC (American Athletic Conference) teams are ranked in my Top 25: #14 Navy, #16 South Florida, and #25 Houston
• Here's a look at the four major conference championships next Saturday:
• #6 Penn St vs #8 Wisconsin
• #1 Alabama vs #12 Florida
• #5 Washington vs #7 Colorado
• #3 Clemson vs #23 Virginia Tech
• Top 10 // Top 25  Teams for each conferences:
• ACC: 2 // 5 
• Big Ten: 4 // 5
• Big 12: 0 // 1
• Pac 12: 3 // 5
• SEC: 1 // 5

Poll Comparison

As always, please leave questions/comments below! If you would like to see more than just the Top 25, or any ratings for Div I-AA, Div-II, or Div-III, just let me know!

NCAAF Ratings Improvement

The Issue

It became evident after Week 12 of the 2016 NCAAF regular season that I needed to make an improvement to my ratings. I needed to account for the disparity of talent between the divisions in college football (Div I-A vs Div I-AA vs Div-II, etc).This improvement was nothing I hadn't considered before, rather, I just hadn't quite worked out how to implement it in a completely mathematical and objective way. However, as I mentioned, after Week 12, it was very clear I needed to figure out how to implement it because of the issue it was creating without it.

During Week 12, North Carolina beat The Citadel. The Citadel was a previously undefeated Div I-AA team. After the victory, UNC jumped 9.29 points in the ratings. To put that into perspective, The Ohio State University gained 6.73 points after defeating #4 Michigan. (Note: you will not find that 6.73 value on this blog because that was using the algorithm prior to the implemenation of this improvement. The current algorithm gave OSU a 7.46 increase in the rating for the victory). Now, as I explain in detail in the explanation of my rating system, there are other factors that contribute to a change in a team's rating from week to week other than that team's specific outcome (such as their  rating going into the game, opponent's change in ratings, etc). However, to suggest that UNC's victory over Div I-AA Citadel (which UNC was heavily favored to win) was approximately equal to OSU's victory over Michigan is an indicator that something needed to be addressed.

Why the issue arose

At the beginning of the season, I start all teams with the same rating variables (mu and sigma) equal to each other. I introduce zero bias. However, this means that Div I-A teams are started with the same values as Div I-AA, Div II, and Div III teams. Teams do play inter-division games, and this can help the average of the divisions begin to shift as you would expect: Div I-A being the highest and Div III being the lowest. However, there are so few inter-division games that the average differs very little. The fact is, the vast majority of the games are played within the divisions. This leads to distributions of teams for each division spread around a nearly identical average (see Figure 1, below).

Figure 1: Distributions of teams values using previous algorithm

In Figure 1, the cartoon (not real data, just an example) shows the distribution of teams within Div I-A (red) and Div I-AA (blue) late in the season. The horizontal axis represents rating and the vertical axis represents the number of teams that have a particular rating. Typically, a normal distribution would have a few teams that are very highly rated (to the right of this graph) and a few teams with very low ratings (to the left of this graph), while most of the teams are somewhere in between. Due to the vast majority of the games being played within each division, there is little opportunity to separate these curves from one another. In other words, the teams within each division will fall in a normal distribution around the same average as shown above. What this means is that beating the best team in Div I-AA is equivalent to beating the best team in Div I-A, because the ratings of the best team in each division will be nearly the same. This is obviously not realistic. However, it is a problem the previous version of my algorithm encountered because I did not pre-bias my ratings.

Why wasn't this improvement implemented sooner?

As I mentioned, it's something that has been on my mind. However, it just wasn't obvious to me the issue it was causing for several reasons. First, when I post my ratings, I separate the divisions. Second, it wasn't until this year that I added a new column ("Last Result" column) that makes it very easy to see who they played without having to go to ESPN and check their schedule, or dig into the variables of my code. So this change in my output of my ratings made this issue obvious, thus prompting me to come up with a solution on how to implement the improvement.

The Solution

My overriding rule for the implementation of this improvement was to ABSOLUTELY NOT introduce bias into the ratings. I did NOT just want to say "well, Div I-AA teams should be scaled to 80% of Div I-A," and so on. I would have no justification for that factor, and I could no longer say that my ratings have zero bias.

Therefore, in addition to each teams' individual ratings, I now rate each division overall as well (henceforth, referred to as the "current" method). The overall division ratings are calculated from each inter-divisional match-up. The overall division ratings are then used to scale the average team ratings for each division. Every team in the division is scaled using the same numerical factor (both mu and sigma values are scaled) so that the relative ratings between each team in that division are not compromised. This is extremely important because there are much more games played within the division, so I did not want to change the ratings within each division in any way, or else I would be undoing what my rating system is intended to do in the first place. The current method is within my iterative process, and thus apart of the calculation that gets converged.

The result of using this method creates a non-biased and objective method to distinguish the divisions' average team rating, as shown below in Figure 2. Once again, in the cartoon, the red and blue lines represent Div I-A and Div I-AA distributions, respectively. However, note that the highest rated team in Div I-AA is not nearly equivalent to the highest rated team in Div I-A. In fact, a decent number of teams in Div I-A are rated higher than Div I-AA. Remember, this is just an illustration and where that best team in Div I-AA actually falls relative to the Div I-A teams is a function of the outcome of the inter-division games.

Figure 2: Distributions of teams values using current algorithm

The current method uses nothing but the results of games played in order to determine the factors, and will fluctuate week to week as more inter-division games are played, as well as team's that play in those inter-division games experience rating changes from week to week. In addition, the factors will vary from season to season. For example, perhaps in 2017 Div I-AA is closer in talent to Div I-A relative to 2016. My rating system will reflect that, and therefore the averages from each division will be closer.

NFL Ratings after Week 11

NFL Rankings 

Through Week 11: (22 NOV 2016)
(delta calc'd from Week: 10 (15 NOV 2016)

Comments? Leave some below!

NCAAF Ratings after Week 12

NCAA Football Top 25 Rankings

Updated: Week 12, 20 NOV 2016

(Delta Calc'd from Week 11, 13 NOV 2016)

(Click here for a more detailed explanation of my NCAAF rating system)

Some of these rankings my surprise you, but keep in mind that there is no bias towards any team or preconceived notions, and the only thing considered is what each team has accomplished so far.

(For those viewing from a phone, tap the rankings and rotate to enlarge)

Notes:

• The top 6 teams remain unchanged from last week.
• Undefeated Western Michigan continues to drop, but not because of a loss... rather everyone else is simply playing higher quality opponents and "passing" Western Michigan up.
• Florida climbs 16 spots to #15 after defeating LSU.
• Oklahoma is the only Big 12 team ranked in the Top 25
• The Big Ten still occupies 4 of the Top 6 rankings.
• Three AAC (American Athletic Conference) teams are ranked in my Top 25: #22 Houston, #23 Navy, and #24 South Florida
• These rankings have set up amazing rivalry week:
• #2 Ohio State vs #4 Michigan
• #1 Alabama vs #14 Auburn
• #7 Washington vs #19 Washington State
• Top 10 // Top 25  Teams for each conferences:
• ACC: 2 // 5 
• Big Ten: 4 // 5
• Big 12: 0 // 1
• Pac 12: 3 // 5
• SEC: 1 // 4

Poll Comparison

As always, please leave questions/comments below! If you would like to see more than just the Top 25, or any ratings for Div I-AA, Div-II, or Div-III, just let me know!

NFL Ratings after Week 10

NFL Rankings 

Through Week 10: (16 NOV 2016)
(delta calc'd from Week: 9 (9 NOV 2016)

Comments? Leave some below!

NCAAF Ratings after Week 11

NCAA Football Top 25 Rankings

Updated: Week 11, 13 NOV 2016

(Delta Calc'd from Week 10, 6 NOV 2016)

(Click here for a more detailed explanation of my NCAAF rating system)

Some of these rankings my surprise you, but keep in mind that there is no bias towards any team or preconceived notions, and the only thing considered is what each team has accomplished so far.

(For those viewing from a phone, tap the rankings and rotate to enlarge)

Notes:

• Ohio State moves to #2 after Clemson (now #3) and Michigan (now #4) lose.
• Undefeated Western Michigan continues to drop, but not because of a loss... rather everyone else is simply playing higher quality opponents and "passing" Western Michigan up.
• The Buckeyes climb another spot, into my Top 4 with a win against #22 Nebraska.
• Washington falls 3 spots to #8 after losing to #10 USC, who gained 11 spots with the win.
• These rankings are setting up would could be an amazing rivalry week in two weeks (if these ranks hold)
• #2 Ohio State vs #4 Michigan
• #1 Alabama vs #14 Auburn
• #8 Washington vs #9 Washington State
• The Big Ten occupies 4 of the Top 6 rankings.
• Top 10 // Top 25  Teams for each conferences:
• ACC: 2 // 4 
• Big Ten: 4 // 5
• Big 12: 0 // 2
• Pac 12: 3 // 6
• SEC: 1 // 5

Poll Comparison

As always, please leave questions/comments below! If you would like to see more than just the Top 25, or any ratings for Div I-AA, Div-II, or Div-III, just let me know!

NFL Ratings after Week 09

NFL Rankings 

Through Week 9: (9 NOV 2016)
(delta calc'd from Week: 8 (2 NOV 2016)

Comments? Leave some below!

NCAAF Ratings after Week 10

NCAA Football Top 25 Rankings

Updated: Week 10, 7 NOV 2016

(Delta Calc'd from Week 9, 31 OCT 2016)

(Click here for a more detailed explanation of my NCAAF rating system)

Some of these rankings my surprise you, but keep in mind that there is no bias towards any team or preconceived notions, and the only thing considered is what each team has accomplished so far.

(For those viewing from a phone, tap the rankings and rotate to enlarge)

Notes:

• Western Michigan drops out of my Top 10, but not because of a loss... rather everyone else is simply playing higher quality opponents and "passing" Western Michigan up.
• The Buckeyes climb another spot, into my Top 4 with a win against #22 Nebraska.
• Undefeated Washington is at #5. OSU is the only team with a loss ranked above the Huskies. Why is that? For starters, Strength of schedule. Again, I will emphasize that SoS is an output of my ratings, not an input... but it does give a clue as to why the ratings ended up as they did. The Buckeyes have the #16 SoS, while Washington's ranks #86. Despite the loss, Ohio State has accomplished more this season than Washington.
• .UNC cracks my Top 10 for the first time this season, boasting wins over #13 FSU, #40 Pitt, #43 Miami
• Appalachian State is up to #37... look out michigan!
• Top 10 // Top 25  Teams for each conferences:
• ACC: 2// 5
• Big Ten: 4// 5
• Big 12: 0// 2
• Pac 12: 1// 5
• SEC: 3// 6

Poll Comparison

• ((Updated to include the College Football Playoff Rankings, which aren't released until Tuesday))
• The AP and Coaches polls are trying really hard for the Big 12... ranking Oklahoma and West Virginia in the top 10.
• According to my ratings, West Virgina is 18th (most notable win against #45 BYU) and Oklahoma is 25th (most notable win against #52 TCU)
• Also, Penn St climbs higher in my ratings (7th) and see a big jump from ~20th in the AP and Coaches poll to 12th and 14th, respectively
• Another difference is that I still have Louisville just outside my Top 10 at #11, while the AP and Coaches polls have UL at #5 and #6. Both the AP and the Coaches have undefeated Washington ahead of the Buckeyes. However, my ratings put the Buckeyes at #4.

As always, please leave questions/comments below! If you would like to see more than just the Top 25, or any ratings for Div I-AA, Div-II, or Div-III, just let me know!

NFL Ratings after Week 8

NFL Rankings 

Through Week 8: (2 NOV 2016)
(delta calc'd from Week 7: (25 OCT 2016)

Comments? Leave some below!