As Chase notes on Twitter:
Since for some reason these always fascinate me, I found myself wondering just how often a unique score occurs. Obviously by definition, the number of them should decrease over the years as there are fewer unique scores to have, and the chart of scores per year (including the NFL, AAFC, and AFL since 1920) mostly bears that out (the blue line is the number of unique scores per year, the red line is the percentage of games resulting in a unique score in a given year):
1920 is the first year of the NFL so of course it has the highest number of unique scores at 46 (out of 90 total games played). There are spikes at 1946 and 1960 correlating to the starts of the AAFC and AFL, respectively, owing mostly to the much larger number of games. That spike you see after 1980 is the introduction of the two-point conversion in 1994, making possible a lot of scores that weren't seen previously. For example, there have been 167 times since 1940 that a game has ended with one team scoring 15 points.. and 101 of those have come since 1994.
What missing game scores are we unlikely to see any time soon? Well, according to our summary of all scores, we've only seen a team score 4 points one time ever, so it seems that it'll be a while before we remove any more X-4 scores from the list. Even a final score of 5 has been achieved a whopping 13 times since 1940, including this very unlikely 8-5 final score. Still, at nearly 15,000 games and counting, it's pretty impressive that every week brings the possibility of seeing something unique.