The NFL season is upon us and nothing makes me more excited for week 1 than betting team over-unders. For me I think it's both the thrill of predicting the right outcome and the idea that math could matter. Let's start with simple math. Less than or equal to 8. That will be the average amount of wins this year in the league (less than because of possible ties). Did you know the average line this year is 8.2 wins? When I saw this it was actually what I was expecting, most average bettors ride overs. But what I wasn't expecting was that the average vig on the over (or the cost to bet the over) was significantly higher than the under. On average this cost was 3 times higher. These two things don't add up. It means there are some inefficiencies with several of these odds makers' lines.

The goal of this post will be to calculate the most likely probability of each team winning greater or less than the odds makers’ over-under and correctly betting the outcomes with the greatest expected value. To do this correctly, we first need to figure out what each team’s week-by-week probabilities are of winning.

The goal of this post will be to calculate the most likely probability of each team winning greater or less than the odds makers’ over-under and correctly betting the outcomes with the greatest expected value. To do this correctly, we first need to figure out what each team’s week-by-week probabilities are of winning.

## Ranking System

I have developed a ranking system over the past 5 years. The concept, which isn't rocket science, is that in general a teams total wins at the end of the season is the best statistic to determine how good or bad a team is. Of course a lot goes into winning a football game and over the course of a season multiple factors contribute to the success of a team, like injuries and strength of schedule to name a few, but in the long run (over 30 years of data) these abnormalities smooth themselves out.

So I went through 30 years of data and labeled each team with a ranking of 1 to 5 driven entirely by the amount of wins the team had during the season (1: 0 - 3 wins, 2: 4 -6 wins, 3: 7 - 9 wins, 4: 10 - 12 wins, 5: 13 - 16 wins). Now if you can imagine, 7,680 games of data, each labeled with a Home Team Ranking versus a Away Team Ranking. For example, we know that during the course of the past 30 years a team ranked 3 has played another team ranked 3 (3H_3) 767 times. During these match-ups the home team won 58% of the time with a median margin of 3 points. Heres another one, a home team 4 has played an away team 3 (4H_3) 647 times. During these match-ups the home team won 77% of the time with a median margin of 7 points.

As you can see in the exhibit above, I have given each team a ranking for this season. Its important to note that when ranking teams you need to remove the strength of schedule factor and rank teams based on how good they are. You will also notice I give each team a sub ranking. In my analysis below and in the future I weigh my outcomes (60% base and 40% sub). So for example if the Seahawks (4 , 3) are playing the Dolphins (3 , 2) I will actually calculate the probability in each scenario (4H_3, 4H_2, 3H_3, 3H_2). Weighing the probabilities gives us a little more of a diversified approach.

Now that you know how the ranking system works we can calculate the expected probability of each team winning each week. As you can see below:

So I went through 30 years of data and labeled each team with a ranking of 1 to 5 driven entirely by the amount of wins the team had during the season (1: 0 - 3 wins, 2: 4 -6 wins, 3: 7 - 9 wins, 4: 10 - 12 wins, 5: 13 - 16 wins). Now if you can imagine, 7,680 games of data, each labeled with a Home Team Ranking versus a Away Team Ranking. For example, we know that during the course of the past 30 years a team ranked 3 has played another team ranked 3 (3H_3) 767 times. During these match-ups the home team won 58% of the time with a median margin of 3 points. Heres another one, a home team 4 has played an away team 3 (4H_3) 647 times. During these match-ups the home team won 77% of the time with a median margin of 7 points.

As you can see in the exhibit above, I have given each team a ranking for this season. Its important to note that when ranking teams you need to remove the strength of schedule factor and rank teams based on how good they are. You will also notice I give each team a sub ranking. In my analysis below and in the future I weigh my outcomes (60% base and 40% sub). So for example if the Seahawks (4 , 3) are playing the Dolphins (3 , 2) I will actually calculate the probability in each scenario (4H_3, 4H_2, 3H_3, 3H_2). Weighing the probabilities gives us a little more of a diversified approach.

Now that you know how the ranking system works we can calculate the expected probability of each team winning each week. As you can see below:

The next step is to take this data and create a random generator. The reason we generate different scenarios versus just adding up the probabilities to get an average is because a football game is binary, a team wins or loses. So to just add up .85 + .65 really doesn't tell us anything besides the average amount of games the team will win is 1.5.

After running 5,000 iterations for each team the following data was concluded below:

After running 5,000 iterations for each team the following data was concluded below:

As you can see above we have determined several things. The most important being the median amount of games each team is expected to win and the probabilities of each team going over and under the odds makers' line.

A couple of things to point out on the far right columns of the exhibit above. As you can see both the Over and Under columns have columns labeled value and risk. If you frequent this site in the coming months its important to understand what these mean. Value is the expected value of a $100 wager. We will always be focusing on those bets with the highest expected value and ignore those with negative value. Risk is the amount of your bankroll you should wager and should be used to compare and size more than one bet.

My season bets below:

A couple of things to point out on the far right columns of the exhibit above. As you can see both the Over and Under columns have columns labeled value and risk. If you frequent this site in the coming months its important to understand what these mean. Value is the expected value of a $100 wager. We will always be focusing on those bets with the highest expected value and ignore those with negative value. Risk is the amount of your bankroll you should wager and should be used to compare and size more than one bet.

My season bets below: