Bundesliga fixtures October 10-12 - which of the nine can erase a clinch number, and which cannot

Hoffenheim and Hamburg each need 89 points from their remaining 30 matches to guarantee survival on their own results, and on October 10 they play each other. Eighty-nine is a total that 30 matches cannot produce. It takes 29 wins and two draws, which is 31 matches, so the only way past it is to win all 30 and take 90. At least one of those two lines is gone by the end of that day, and a draw takes both.

Everything here is as of the September 21 update, which covers 36 of the season's 306 matches. All 18 clubs have played four and have 30 left, so no club holds a match in hand. The last round ran from September 19 to September 21, and the next one opens on October 10. Dates in this piece are Korean time (KST), so a match played on a German evening is listed under the next day.

Start with how little is posted. Three clubs carry a top-four clinch number: Dortmund 86 from 30 matches, Bayern 88, Freiburg 88. One title clinch number exists in the entire league, Dortmund's 89. For the other 15 clubs there is no total they can still reach that would guarantee a top-four place, so the column is blank, and a blank cannot be deleted. Sixteen clubs carry a safety number and two do not, Union Berlin and Moenchengladbach. Nothing is settled in the other direction either. Every club's reachable range runs from first to eighteenth, ten clubs carry a top-four tragic number, and the lowest of them is Moenchengladbach's 28, which is 28 more defeats out of 30 remaining matches.

The round is nine fixtures across three days. October 10 KST brings six: Mainz vs Leverkusen, Paderborn vs Stuttgart, Union Berlin vs Elversberg, Dortmund vs Werder Bremen, Augsburg vs Bayern, Hoffenheim vs Hamburg. October 11 KST brings two: Koeln vs Moenchengladbach, Leipzig vs Frankfurt. October 12 KST brings one: Freiburg vs Schalke. In Germany the same nine run from Friday 9 October, when Dortmund host Werder Bremen, through six matches on Saturday 10 October, Leipzig vs Frankfurt among them, to Koeln vs Moenchengladbach and Freiburg vs Schalke on Sunday 11 October. Six of the nine can put a posted number out of reach on one result and three cannot touch one. All 18 clubs play, and the one line a single result can erase outside October 10 and 11 KST belongs to Freiburg, who host Schalke on the 12th. Before any of it, 18 days from September 22 to October 9 KST carry no fixture at all, and a stretch with no results is a stretch in which no number moves.

Three of the nine reach the top of the table. Dortmund host Werder Bremen on 12 points from four wins, with a top-four line of 86 and a title line of 89. The 86 has room in it: 29 wins and a defeat is 87, and 28 wins with two draws is 86, but 28 wins with one draw and one defeat is 85. Dortmund hold that line through one defeat, or through two draws, but not through one of each, which is why no single result against Bremen can take it. The 89 has no room at all, and anything short of a win at home to Bremen ends the only title clinch number in the league. Augsburg host Bayern, whose 88 allows one draw and no defeat, because 29 wins and a draw is 88 while 29 wins and a defeat is 87. If Bayern lose at Augsburg, the 88 has to come out of 29 matches, which top out at 87. Freiburg hold the third of the three top-four lines, also 88, and it ends the same way, on a defeat at home to Schalke on October 12. Schalke's own number is a safety line of 87, and 87 is exactly what 29 matches reach, so a defeat does not touch it. Bremen and Augsburg are both on 7 points with no top-four number of their own, so in those two fixtures only one side has anything to lose in the arithmetic.

Three reach the relegation end. Paderborn host Stuttgart and both sides hold a line that one result can end. Paderborn need 88, and 29 matches top out at 87, so a defeat ends theirs. Stuttgart need 89, which means winning all 30, so anything short of a win ends theirs. Run the three outcomes and exactly one of the two numbers dies in each: a Stuttgart win ends Paderborn's 88, a draw ends Stuttgart's 89, and a Paderborn win ends Stuttgart's 89 as well. Hoffenheim vs Hamburg is the same shape with 89 against 89, except that a draw there takes both at once, which no other fixture in the round can do. Koeln host Moenchengladbach on October 11 with a safety line of 88, and only a Gladbach win pushes it past what 29 matches can hold. Gladbach have 0 points from four and no safety line to lose. They and Union Berlin are the only two clubs carrying a relegation tragic number, and both read 30, the full remaining schedule, which is the weakest form that number can take.

Three of the nine cannot put anything out of reach. Mainz vs Leverkusen puts two clubs on 7 points against each other with safety lines of 85 apiece, and 85 survives a defeat with room to spare. Union Berlin vs Elversberg is the same on one side, Elversberg's 85, and on the other there is nothing to remove, because Union Berlin on 1 point from four have no reachable safety line at all. Leipzig vs Frankfurt on October 11 looks closer and is not: Leipzig's 86 and Frankfurt's 87 both sit inside what 29 matches can still produce, which tops out at 87.

What to watch. On October 10, Hoffenheim vs Hamburg takes at least one 89 off the board and both of them on a draw. Paderborn vs Stuttgart takes exactly one of 88 and 89. Dortmund vs Werder Bremen decides whether the league still has a title clinch line at all. On October 11, Koeln vs Moenchengladbach is the one with a number in it and Leipzig vs Frankfurt is not. Augsburg vs Bayern and then Freiburg vs Schalke on October 12 decide between them whether the top-four column still shows three numbers, two or one, and Dortmund's 86 is the one no single result can take.

Update, October 12: The round was played on the dates this piece gave, and our piece on the results is at. Hamburg won 3-2 at Hoffenheim, which took Hoffenheim's 89 and left Hoffenheim with no safety line at all; Hamburg's is 85. Stuttgart won 2-0 at Paderborn and Paderborn's 88 ended as described, but Paderborn now carry 87, because the safety total itself fell from 92 to 91 in the same round. Had Hoffenheim vs Hamburg been drawn, Paderborn would have no line. Dortmund drew 2-2 with Werder Bremen, and the league no longer has a title clinch line. Bayern drew 2-2 at Augsburg and their 88 is 86, Freiburg beat Schalke 2-1 and their 88 is 84, Köln beat Mönchengladbach 2-1 and their 88 is 84, and the three fixtures this piece said could not erase anything did not. The top-four column shows four numbers, not three, two or one. Leverkusen's 4-3 win at Mainz, together with points dropped by Augsburg, Bremen, Mainz and Elversberg, lowered the top-four bar from 98 to 97 and gave Leverkusen a line of 87. This piece counted only lines that could disappear. Union Berlin gained a safety line of 87 the same way, when the total came down to their ceiling of 91.

How to read these numbers. A clinch number is the minimum a club must still collect for an outcome to be guaranteed even if every rival wins every remaining match, which is why lines in September sit so close to a perfect record. A tragic number is how many more defeats make an outcome impossible even if the club wins everything else. A reachable range is the highest and the lowest finishing place still arithmetically open. On ties, a rival who can only draw level with a club is still counted as a threat to it, so our clinch can trail an official announcement by a day, while in the other direction a rival has to finish clearly above a club to eliminate it and drawing level is not enough. Goal difference, head-to-head fixtures and the official tie-breaking rules are not part of the calculation. The table is on the league page, the remaining fixtures on the schedule page, the qualification and relegation rules on the postseason page, every club's clinch and tragic numbers on the magic number page, the method on the methodology page, and a single club's lines on its own page, such as Hoffenheim's. To run one of these results through and watch a line disappear, use the what-if page.