Bundesliga after matchday 5: Leverkusen get a top-four clinch line, Dortmund's title line is gone, nothing is clinched

Bayer Leverkusen now carry a top-four clinch line. Before this round no total they could reach guaranteed a top-four finish. After a 4-3 win at Mainz on October 10 the line is 87 points from their remaining 29 matches, and 87 is all 29 won: do that and the top four is certain whatever anyone else does. Their ceiling did not move, 97 before the round and 97 now. The bar came down to meet it, from 98 to 97, because the four clubs that sat level with them on 7 points all dropped points.

Everything here is as of the October 12 update, which covers 45 of the season's 306 matches. All 18 clubs have played five and have 29 left. The round ran from October 10 to October 12, Korean time, home side first: Mainz 3-4 Leverkusen, Paderborn 0-2 Stuttgart, Union Berlin 1-0 Elversberg, Dortmund 2-2 Werder Bremen, Augsburg 2-2 Bayern Munich and Hoffenheim 2-3 Hamburg on the 10th, Köln 2-1 Mönchengladbach and Leipzig 6-0 Frankfurt on the 11th, Freiburg 2-1 Schalke on the 12th. The next round starts on October 17.

A top-four line clears the fourth-highest ceiling among a club's rivals, and a rival who can only finish level still counts as a threat. Before the round Augsburg, Mainz, Elversberg and Bremen could each reach 97, the same as Leverkusen, so the bar was 98 and Leverkusen's cell was empty. This round Augsburg and Bremen drew, which leaves them on 8 points with a ceiling of 95, and Mainz and Elversberg lost, which leaves them on 7 and 94. Leipzig beat Frankfurt 6-0 and now have the highest ceiling outside the top four, 96. One above that is 97, exactly what Leverkusen can still reach. Every one of those results counted. Change any single one of them, a draw at Mainz, an Augsburg win over Bayern, a Bremen win at Dortmund or an Elversberg win at Union Berlin, keep the other eight as they were, and the engine returns an empty cell for Leverkusen again. Our September 20 piece on Leverkusen was about that one missing point.

Our September 20 piece on this round said Augsburg vs Bayern and Freiburg vs Schalke would decide whether the top-four column showed three numbers, two or one. It shows four. None of the three lines it was watching was erased, and the piece counted only lines that could disappear, not one that could appear. Bayern's 88 allowed one draw and no defeat; they drew 2-2 at Augsburg and the line is 86. Freiburg's 88 could end only on a defeat; they beat Schalke 2-1 and the line is 84. Dortmund's 86 was the one no single result could take, and it is 84 after the draw with Bremen. All four lines now add to the same total, 97: Freiburg and Dortmund 13 plus 84, Bayern 11 plus 86, Leverkusen 10 plus 87.

The title column lost its only number. The piece said anything short of a home win over Bremen would end Dortmund's title line of 89, and Dortmund drew 2-2. No club now carries a title clinch number. Freiburg and Dortmund are level on 13 points with the same ceiling of 100, Freiburg listed first on goals, 14 scored and 4 conceded against 11 and 4. For either of them to be certain of first, the total has to clear the other's 100, which means 101, and 13 plus everything 29 matches can produce is 100. In the other direction those two are the only clubs without a title tragic number. Bayern and Leverkusen read 29, and the lowest is Mönchengladbach's 25.

At the bottom the piece said Hoffenheim vs Hamburg would take at least one of two 89s, and both on a draw. Hamburg won 3-2 away. Hoffenheim's line did not shrink, it went: Hoffenheim, on 3 points, now have no safety line at all and carry a relegation tragic number of 29, every match they have left. Hamburg's 89 is 85. Paderborn vs Stuttgart was to take exactly one of 88 and 89, with a Stuttgart win ending Paderborn's 88. Stuttgart won 2-0, Paderborn's 88 is gone, since 29 matches top out at 87, and Stuttgart's 89 is 85. Paderborn's row is not blank, though. It reads 87, because the total every safety line points at fell from 92 to 91 in the same round. That total is one above the second-lowest ceiling in the league, and the two lowest are now Mönchengladbach's 87 and Hoffenheim's 90, where before the round they were Mönchengladbach's 90 and Union Berlin's 91. What pulled it down is that Hoffenheim vs Hamburg had a winner, which left the losing side on a ceiling of 90. A Hoffenheim win would have done the same, leaving the total at 91 and Paderborn's 87 in place. Had that match been drawn, with the other eight results unchanged, Paderborn would have no safety line, and neither would Hamburg or Union Berlin.

Union Berlin are the other half of the same move. They had no safety line before the round because they could not get past 91 and the total was 92, and their relegation tragic number was 30. They beat Elversberg 1-0, their ceiling is still 91, and the total came down to it: the line is 87 and the tragic number is gone. Like Paderborn's 87 and Leverkusen's 87 at the other end, it means winning every match left. Mönchengladbach lost 2-1 at Köln, have no points after five matches, and are now joined by Hoffenheim as the only two clubs without a safety line. Their relegation tragic number went from 30 to 28. Köln's 88, which only a Gladbach win could have pushed out of reach, is 84.

The three fixtures the piece said could not erase anything did not. Mainz's 85 is 84 and Leverkusen's is 81. Elversberg's 85 is 84. Leipzig's 86 is 82 and Frankfurt's 87 is 86. Schalke's 87, which the piece said a defeat would not touch, is 86 after the 2-1 loss at Freiburg. Sixteen clubs carry a safety line and every one of them adds to 91, from Freiburg and Dortmund's 78 to Paderborn and Union Berlin's 87.

Nothing is settled at either end. No club has a zero in any of the six columns, and every club's reachable range still runs from first to eighteenth. Fourteen clubs carry a top-four tragic number, up from ten: 29 for Leipzig, Augsburg, Bremen, Mainz, Elversberg and Köln, 28 for Stuttgart, Hamburg, Schalke, Frankfurt, Paderborn and Union Berlin, 27 for Hoffenheim and 26 for Mönchengladbach. The four clubs inside the top four have none, because losing every remaining match still leaves fewer than four clubs certain to finish strictly above them. The next round cannot change any of that. Run all 19,683 combinations of its nine results through the engine and no clinch number reaches zero, no tragic number reaches zero, and every reachable range still reads first to eighteenth.

The next round runs from October 17 to 19, Korean time. Leverkusen host Freiburg on the 18th with a line that needs every remaining match won. A win keeps the 87 whatever happens elsewhere. A draw keeps it only if all three of these hold: Leipzig fail to win at Bayern, Augsburg fail to win at Elversberg, and Bremen fail to beat Paderborn. A defeat keeps it only if Bayern beat Leipzig, Elversberg and Augsburg draw, Paderborn avoid defeat at Bremen, Schalke avoid defeat at home to Mainz and Frankfurt avoid defeat at home to Köln. Bayern's 86 survives a win or a draw against Leipzig in every combination; a defeat leaves it only if Freiburg win at Leverkusen, Augsburg fail to win at Elversberg and Bremen fail to beat Paderborn. Paderborn at Bremen and Union Berlin at home to Dortmund, both on the 17th, are the two 87s at the bottom. For either club a win keeps the line, and a defeat keeps it only if Mönchengladbach beat Hoffenheim on the 19th, the last match of the round. A draw keeps it unless Hoffenheim win at Mönchengladbach and the other of the two avoids defeat.

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. 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, and every line in this piece moves with other clubs' results as well as the club's own. The table is at, the remaining fixtures at, the qualification and relegation rules at, every club's clinch and tragic numbers at, the method at, and a single club's lines on its own page, such as Leverkusen's or Paderborn's. To run next weekend's results through yourself, use.