i think there is arguably, one score in particular that would be extremely unlikely but certainly possible. yes , i realize that a score of 700 to 140 is unlikely but it is also virtually impossible.
You can see the scores from all 15,000-some games that have been played in NFL history from 1920 until today here. Sorting by the count column, you can see that there are 257 final scores that have only ever been achieved once. The latest one of these, hence the least likely given the data, was a score of 51-16.
Any other possible score not appearing on this list would been even less likely than the scores that have actually been achieved. I think it would be quite impossible to define one single score as the least likely.
Using one example of a simple technique based on the scarcity of combined final scores and individual final scores, 54-44 is the least likely of those that have occurred in the Super Bowl Era.
According to Pro Football Reference, there have been 191 different combinations of final game-scores that have occurred only once in the Super Bowl Era.
To narrow this down, I performed the following analysis:
- Count all instances of each winning-team final score
- Count all instances of each losing-team final score
- Multiply respective frequency values for winning-team and losing-team final scores by the "Occurance" value provided by Pro Football Reference
- If 41-17 is the only instance of a winning team scoring 41 points, but that game result of 41-17 has happened three times, then I record three instances of 41 points
- For each final game-score, sum the winning-team and losing-team results from step 3, creating a Combined Occurrence Frequency
- Filter all final outcomes to those that have occurred only once
- Filter all Combined Occurrence Frequencies from step 4 to the lowest value
Least Likely Result
- This score occurred in week 14 of 1985
- Winning-team score of 54 has occurred five times
- Losing-team score of 44 has occurred two times
- Result is seven combined occurrences of winning- and losing-team scores
Second Least Likely Result
- This score occurred in week 12 of 1966
- Winning-team score of 72 has occurred one time
- Losing-team score of 41 has occurred seven times
- Result is eight combined occurrences of winning- and losing-team scores