How TSG can qualify for the Europa League

The scenario:

With one round of matches remaining, TSG Hoffenheim sit in eighth place with 51 points, one adrift of seventh-placed VfL Wolfsburg. As the two DFB Cup finalists, RB Leipzig and Bayern Munich, have both already qualified for the Champions League, the team that finishes the season in seventh place will go into the Europa League qualifying rounds. The club that comes sixth, meanwhile, will go straight into the group stages. This position is currently occupied by Eintracht Frankfurt, who are three points ahead of TSG. Another club still in with a fighting chance of securing themselves European football is Werder Bremen. Having beaten TSG 1-0 on Saturday, coach Florian Kohfeldt's team sit in ninth place with 50 points on the board.

As none of these European candidates will face each other on the final day of the season, TSG no longer have their fate in their own hands. At least one of their rivals will need to slip up if Hoffenheim are to play European football next term.

However, one advantage for TSG is their goal difference of +20. All of their direct rivals for the Europa League places have a worse goal difference.

The candidates and their remaining fixtures:

6. Eintracht Frankfurt 54 points, 59:43 goals (+16): Bayern Munich (A)

7. VfL Wolfsburg 52 points, 54:49 goals (+5): FC Augsburg (H)

8. TSG Hoffenheim 51 points, 68:48 goals (+20): FSV Mainz 05 (A)

9. Werder Bremen 50 points, 56:48 goals (+8): RB Leipzig (H)

TSG will finish sixth if…

…Hoffenheim win, Frankfurt lose and Wolfsburg don't win.

TSG will finish seventh if…

…Hoffenheim win, Frankfurt lose and Wolfsburg win.

…Hoffenheim win, Wolfsburg don't win and Frankfurt don't lose.

…Hoffenheim draw, Wolfsburg lose and Bremen don't win.