When are NFL playoff races decided - the arithmetic says eight more games at the earliest

Fourteen of the NFL's 32 clubs are holding a playoff place as of the September 18 update, and not one of them can be removed from it by arithmetic for another eight games. That is the answer to when NFL races get decided. Not in September, and on these figures not in October either. Buffalo has won two games. Sixteen clubs have won none. Across the whole league, that is the entire spread.

Every figure here comes from the September 18 update, which covers Week 1 in full plus one game of Week 2. Thirty clubs have played once and have 16 games left. Buffalo and Detroit have played twice and have 15. Seventeen games have been played in a season that will play 272. Nothing after September 18 is in these numbers.

Elimination is one piece of subtraction. A club is out when some rival's guaranteed win total passes the highest total the club can still reach. The highest guaranteed total in the league is Buffalo's two wins, because wins cannot be taken back. The lowest reachable ceiling is 16, held by the 16 clubs at 0-1 and by 1-1 Detroit, who has 15 games left. The gap between those two figures is 14. Each further game moves the gap by at most two, one win added to the floor and one loss knocked off the ceiling. Seven games of that only draws the two level at nine and nine. The crossing needs an eighth. So no club in this league can be arithmetically finished with anything until it and its rival have each played eight more games, and bye weeks push the calendar date later still than the game count suggests.

Counting from the last playoff place instead of the best record gives the same answer. The seventh-highest guaranteed total in the AFC is one win, held by seven clubs behind Buffalo. One against a ceiling of 16 is a gap of 15, which also takes eight games to cross, nine wins against eight. Whichever end of the table you start from, the number is eight.

The figures posted today are that subtraction in table form. Exactly one club carries a clinch number, and both of its figures sit at the maximum: Jacksonville's is 16 with 16 games remaining, and its division number is 16 too. Thirty clubs carry a tragic number and every one of them is 16 or 15, so across the thirty that carry one the difference between the most protected and the least is a single game. Jacksonville and Buffalo carry no tragic number. No club is clinched and none is eliminated, so both of those columns are blank for all 32. A number equal to the remaining schedule says win out, which is the instruction every club in the league is already under.

Seventeen clubs have already dropped a game they cannot get back, the 16 at 0-1 plus 1-1 Detroit, and none of it has moved Jacksonville's number. Fifteen clubs still keep a 17-0 ceiling, and the Jaguars have to clear the highest of them. Eight of those 15 are in the AFC, which has seven playoff places, so one unbeaten club in the conference is already surplus to the field on paper and none of them has lost yet. The records themselves take three values and no more: 15 clubs at 1.000, one at .500 and 16 at .000.

That is why the 14 places are filled the way they are. The AFC field is Jacksonville, Kansas City, Baltimore, Buffalo, Las Vegas, the Jets and Cincinnati, with Pittsburgh the one unbeaten club outside it. The NFC field is Chicago, San Francisco, Minnesota, Arizona, the Giants, Philadelphia and Carolina, which means 1-0 Seattle is out and 0-1 Carolina is in. With records taking three values, wins are not what separated those 14 from the other 18, and nothing in that order is protected by arithmetic yet. Eight games is how long it stays unprotected.

What to watch is losses rather than wins. Only losses pull a ceiling down, and that is half the speed at which any gap closes. The first signal is the number of distinct records in the league, which has to grow past three before the figures can move at all. The second is the first crossing, one club's guaranteed total passing a rival's ceiling, which on today's numbers cannot arrive until each of them has played eight more games. The remaining fixtures are listed on the schedule page, and the figures move against them as results land.

How to read these numbers. A clinch number, also called a magic number, is the minimum further wins that guarantee an outcome even if every rival wins every game it has left. A tragic number is the further losses after which the outcome becomes impossible even if the club wins every game it has left. A blank means the arithmetic cannot yet say anything. A number equal to the remaining schedule means it can say only one thing, win out or lose out. A reachable rank range is the highest and lowest final position still available, and ties are counted against the club in question, so a clinch here can trail an official announcement by a day. The conference tables are on the standings page, every club's figures on the magic numbers page, the seeding and tiebreaker order on the playoff page, and the working itself on the methodology page. Each club has its own page, and the league's only clinch number sits on Jacksonville's.