Bundesliga table after matchday 4: Dortmund win all four and still need 86 points to clinch a top-four place

Borussia Dortmund have won all four of their matches, scored nine, conceded two and lead the Bundesliga on 12 points. The arithmetic still gives them nothing. To guarantee a top-four place today they would need 86 more points from 30 remaining matches, and 30 matches are worth only 90. All 18 clubs can still finish first, and all 18 can still finish last.

Every number here comes from the September 21 update, with matchday 4 complete. That is 36 of the season's 306 matches, and all 18 clubs have played four with 30 left. The latest results in the data are from September 21, a 3-1 for Paderborn over Hoffenheim and a 0-0 between Schalke and Elversberg. The table is judged against two lines, the four European qualifying places at the top and the two relegation places at the bottom.

Dortmund's fourth win was a 1-0 at Stuttgart on September 20. Bayern Munich and Freiburg sit two points back on 10, both with three wins and a draw. Bayern have scored 14 and conceded 2, Freiburg 12 and 3, which is the only reason Bayern are second and Freiburg third on identical points. Bayern built most of that in one afternoon, a 7-0 against Union Berlin at home on September 19. Goal difference orders clubs level on points and does nothing else here. The margin reaches none of the clinch or tragic numbers, so a 7-0 and a 1-0 are worth the same three points to the calculations.

The top-four lines all point at one total. A place is guaranteed once no more than three rivals can still reach a club's final total, and today that line sits at 98 points. Dortmund need 86 more points to get there, Bayern and Freiburg 88 each. Nobody else has a line at all. Augsburg, Bayer Leverkusen, Mainz, SV Elversberg and Werder Bremen are level on 7 points, and 7 plus a perfect 90 comes to 97. They are not one result short of their line. They are one point short of having one.

The title works the same way, one step up. Only Dortmund carry a title line, and it reads 89 more points, 101 in total, against their own ceiling of 102. Thirty matches pay 90 for a perfect record and 88 for 29 wins and a draw, so there is no way to land on exactly 89. Today a title guarantee means winning all 30. Bayern and Freiburg have no title line, because their ceiling is 100 and Dortmund's is 102, and no run of their own results changes that. The title line is also where the tie rule is easiest to see. Leipzig sit on 6 points, and losing 28 while winning the other 2 leaves them on 12, exactly what Dortmund hold now. Level is not behind, so Leipzig's title tragic number is 29 rather than 28.

The safety lines are tidier still. Sixteen clubs have one, and it is the same total for every one of them, 92 points. Dortmund need 80 more to reach it, Bayern and Freiburg 82, the five clubs on 7 points 85 each, Hoffenheim, Stuttgart and Hamburg 89. That last figure works like Dortmund's title line: 89 is not a total 30 matches can produce, so in practice it means the perfect 90. Union Berlin and Borussia Mönchengladbach have no safety line today. Union have 1 point and a ceiling of 91, Gladbach have 0 and a ceiling of 90, and 92 is above both. Those two are also the only clubs carrying a relegation tragic number, and for both it is 30, every match they have left, so no club can go down before the final matchday.

Elimination from the top four moves just as slowly. Gladbach have lost all four, sit on 0 points with 16 conceded, and their tragic number of 28 is the lowest in the league, meaning 28 more defeats would close that question. Union, Hoffenheim, Stuttgart and Hamburg are on 29, and Leipzig, Frankfurt, Schalke, Paderborn and Köln on 30. The eight clubs from Dortmund down to Bremen have no tragic number at all. They could lose all 30 of their remaining matches and still not be ruled out, because a rival is only guaranteed the points it already holds.

The next fixtures in the data are on October 10. Dortmund host Werder Bremen, and Augsburg host Bayern, fourth against second. Mainz host Leverkusen, Paderborn host Stuttgart, Hoffenheim host Hamburg, and Union Berlin host Elversberg, which is Union's first chance to move off 1 point. October 11 brings Köln against Mönchengladbach, Gladbach's first chance to move off 0, and Leipzig against Frankfurt.

How to read these numbers. A clinch number is the smallest amount a club must still collect for a place to hold even if every rival wins everything it has left. A tragic number is the count of further defeats after which that place is impossible even if the club wins everything else. Ties are read against the club being judged, in both directions: a rival who could pull exactly level counts as a threat, so a clinch here can trail an official announcement by a day, while a rival merely level with a club cannot eliminate it. Goal difference, head to head records and the official tiebreakers stay out of the clinch and tragic numbers, and only order the table itself. The full table is at, the fixtures at, the qualifying and relegation rules at, every club's clinch and tragic number at, the method at and a results tester at. Dortmund's own page is.