NFL playoff picture after Week 4: the three unbeaten teams can afford a loss, Buffalo no longer can, and 11 teams can clinch by winning out

Kansas City, Minnesota and San Francisco can each lose a game and still clinch a playoff place without help. All three are 4-0, and all three have a clinch number of 12 with 13 games left. Minnesota's and San Francisco's are the first numbers of that kind the NFC has had this season. Buffalo, the only club that could afford a loss after Week 3, has used it: the Bills lost 26-29 at home to New England, and their clinch number stayed on 13, which is now their whole remaining schedule. Eleven clubs can now clinch by winning out, up from six after Week 3, and the table splits cleanly at one line. Every club at 3-1 or better has a clinch number and no tragic number, and every club at 2-2 or worse has a tragic number and no clinch number.

Every figure here is from the table at the end of Week 4, which closed with Atlanta's 45-24 win in New Orleans on Monday night. All 32 clubs have played four games and all 32 have 13 left. The league has split three at 4-0, eight at 3-1, twelve at 2-2, four at 1-3 and five at 0-4, and there has still been no tie. No Week 5 game is in these numbers. The worst case behind a clinch number has every rival win every game it has left, without checking whether those rivals are scheduled to meet each other, and a level finish is always scored against the club being asked about.

The three 12s come from one count. Only six AFC clubs can still finish 16-1 or better, Kansas City and the five 3-1 clubs, and only five NFC clubs can, Minnesota, San Francisco, the Giants, Chicago and Seattle. That makes 16-1 enough for any of them. At 16-1 Kansas City could lose the West to a 16-1 Las Vegas on the tie, but the only other club ahead of it in the wild-card queue would be the North's runner-up at 16-1. At 15-2 the AFC's five 2-2 clubs could draw level and take the ties, and the Chiefs would be out. Minnesota at 16-1 could lose the North to Chicago and still go in as a wild card behind Seattle, and at 15-2 the NFC's seven 2-2 clubs could draw level. San Francisco's case is the same with Seattle and Chicago changing places. All three division numbers are 13, the whole schedule, because Las Vegas, Chicago and Seattle can each reach 16-1 and win the tie. Minnesota's and San Francisco's numbers arrived before they kicked off. When the Rams won 24-20 in Philadelphia in Sunday's early games, the Eagles fell to 2-2 and the NFC clubs that could reach 16-1 went from seven to six. From then on both unbeaten clubs had 13 with 14 games left, whatever else finished in that window. Their own wins, 15-10 over Miami and 24-14 over Denver, took them to 12 with 13 left.

Every 3-1 club needs all 13, for the same reason: 16-1 is safe, and 15-2 is not, because the 2-2 clubs can catch it there. Buffalo shows how. At 15-2 New England, 2-2 after winning in Orchard Park, could take the East on the tie, and Baltimore and Las Vegas at 16-1 would take two of the three wild cards, with four more 2-2 clubs level with the Bills for the last one. Buffalo's division number is 13 as well. The loss moved neither number; it used up the game Buffalo had to spare. Jacksonville won 22-17 in Cincinnati and still needs all 13 for both of its numbers, because Indianapolis beat Washington 30-13 in London and can still reach 15-2, where it would take the South on the tie. Five clubs picked up a clinch number of 13 this week: Cleveland, which beat Pittsburgh 27-24 on Thursday night, Baltimore, 24-18 winners over Tennessee, and in the NFC the Giants, who beat Arizona 36-24, Chicago, 23-12 over the Jets, and Seattle, 30-23 over the Chargers. Las Vegas lost 27-30 to Kansas City and kept its clinch number, 13, its whole schedule. The Giants also took a division number of 13, because Philadelphia lost. Cleveland and Baltimore have none: both are 3-1, and at 16-1 either could be matched by the other and lose the tie.

If the season ended today, the AFC's division leaders would be Kansas City, Jacksonville, Buffalo and Cleveland, seeded in that order, with Baltimore, Las Vegas and New England as the wild cards and Denver first out. Kansas City would have the bye, and the wild-card round would be Jacksonville against New England, Buffalo against Las Vegas and Cleveland against Baltimore. The NFC's would be Minnesota, San Francisco, the Giants and Carolina, with Chicago, Seattle and the Rams as the wild cards and Atlanta first out; Minnesota would have the bye, and the games would be San Francisco against the Rams, the Giants against Seattle and Carolina against Chicago. Equal records in these lists are ordered by ESPN's seeding, which applies the league's tiebreakers; we do not compute the tiebreakers ourselves. That is how Cleveland leads the North over Baltimore although its point margin is minus 14 and Baltimore's is plus 20, and how New England and the Rams hold the seventh places ahead of four other AFC 2-2 clubs and five other NFC 2-2 clubs. It is also how Carolina, 32-26 winners over Detroit on Sunday night, leads the South over Atlanta at 2-2 and holds the fourth seed. That makes the Panthers the only division leader in the league without a clinch number; they carry a tragic number of 13, like every 2-2 club.

At the other end, every club at 2-2 or worse is now in the same position, whatever its division: once it reaches 15 losses it is finished even if it wins every other game and every rival loses out, and at 14 it is still alive. That makes 13 for the twelve 2-2 clubs, 12 for the four 1-3 clubs, the Jets, Washington, New Orleans and Arizona, and 11 for the five 0-4 clubs, Miami, the Chargers, Houston, Tennessee and Tampa Bay. The NFC South's extra game is gone. After Week 3 no South club had won twice, so a South club could still take the division at 2-15, and the South's clubs carried one more than everyone else with their records. Carolina and Atlanta have two wins each now. Point margin enters none of this: Miami's minus 55 is the worst in football and carries the same 11 as Houston's minus 25.

Week 5 cannot put a zero anywhere either. No clinch number can fall below 10 and no tragic number below 9, so nobody clinches and nobody is eliminated. Kansas City and Carolina have the bye. Every line below was checked against all 19,683 ways the nine games touching each conference can end, ties included, and a tie counts as not winning. The AFC turns on one count: how many of its five 2-2 clubs win. New England is home to Las Vegas, Denver goes to the Chargers, Cincinnati goes to Miami, and Indianapolis plays at Pittsburgh, so at most four can. Kansas City's clinch number goes to 11 during its bye if no more than one of them wins, and stays 12 if two or more do; its division number goes to 12 unless Las Vegas wins in New England. Cleveland at the Jets, Baltimore at Atlanta and Las Vegas share one rule. A win takes the clinch number to 11 if no more than one 2-2 club wins and to 12 if two or more do. A loss leaves 12 if no more than one wins and takes the number away if two or more do. Buffalo, at the Rams on Monday night, and Jacksonville, which meets Philadelphia at Tottenham Hotspur Stadium in London on Sunday, October 11, follow the same rule unless their own 2-2 division rival, New England or Indianapolis, fails to win. Then a win brings a clinch number and a division number of 11, and a loss leaves both on 12, whatever the other 2-2 clubs do. If the rival does win, a win leaves a division number of 12 and a loss takes it away. In the North, Cleveland or Baltimore picks up a division number of 12 by winning while the other does not, or by tying while the other loses. A 2-2 club that wins picks up a clinch number of 12, its whole remaining schedule, only if it is the only one of the five to win.

The NFC turns on the same count, with six 2-2 clubs in action: the Rams, home to Buffalo, Atlanta, home to Baltimore, Detroit at Arizona, Green Bay, home to Chicago, Philadelphia in London, and Dallas, home to Tampa Bay in Thursday night's opener. None of them plays another, so all six can win. Minnesota, at New Orleans, and San Francisco, at Seattle, go to 10 with a win if no more than one of the six wins and to 11 if two or more do, and to 11 or 12 the same way with a loss. A San Francisco win also brings a division number of 11, and a loss takes the 49ers' division number away. Minnesota's division number goes to 11 with a win, or 12 if Chicago wins in Green Bay; with a loss it is 12, or gone if Chicago wins. The Giants, at Washington, Chicago and Seattle follow the AFC's 3-1 rule: with no more than one 2-2 winner, 11 with a win and 12 with a loss; with two or more, 12 with a win and no clinch number with a loss. The Giants have Buffalo's exception with two rivals. If neither Philadelphia nor Dallas wins, a win brings 11 and a division number of 11 and a loss leaves 12 and 12; if either wins, a win leaves a division number of 12 and a loss takes it away. Carolina's numbers can move while it rests. If Atlanta does not beat Baltimore, the Panthers pick up a clinch number and a division number of 13, their whole remaining schedule, and keep their tragic number of 13. If Atlanta wins, Carolina gets no division number; it gets the clinch number of 13 only if Atlanta is the only one of the six to win, and otherwise its tragic number falls to 12. As in the AFC, a 2-2 club that wins picks up a clinch number of 12 only if it is the only one of the six to win. The Week 5 fixtures are on the schedule page, and the what-if page lets you pick results for upcoming games within each conference and watch the record order move.

How to read these numbers. A clinch number, also called a magic number, is the fewest further wins that guarantee a place even if every rival wins every game it has left. A tragic number is the further losses after which a place is impossible even if the club wins everything else and every rival loses. Zero means it is done, and a blank means the arithmetic cannot settle it yet. A level finish is scored against the club being asked about in both directions, so a clinch here can come later than the league's own announcement and an elimination can be declared on a tie alone. The official tiebreakers and the question of who plays whom are not part of the calculation. Every club's numbers are on the magic numbers page, the seeding and tiebreaker order on the playoff page, the conference tables on the standings page, and the working on the methodology page. The three unbeaten clubs this week's arithmetic turns on have their own pages: Kansas City, Minnesota and San Francisco.