Barring Acts of Dumbledore, does the House Cup always go to the Quidditch Cup Winners?

Question

We all know that Dumbledore tends to cheat in Harry's favor, giving him loads of points towards the end of the year. We also know that Quidditch scores DO, in some way, factor into the House Point system (though it may not be a simple score = house point scale).

Given that the team who wins the Quidditch Cup tends to win a lot of their games, does it stand to reason that they have a better shot at the cup?

The scores we tend to see for the House Points are in the 300-400 range, and each team can earn at least 150 points from Quidditch games (from the linked score, we can determine they got at least ~50 points from the game Harry won).

This means that fully half of the House Points could come from a single student catching a shiny thing.

Are there canon examples of Houses winning the House Cup but not winning the Quidditch Cup, excepting those where Dumbledore handed out a gagillion points just before the House Cup was awarded?

Answer 1

No; I have a counterexample.

Consider the academic year 1985–6. We have the following information:

• Gryffindor won the Quidditch Cup.

  In a pep talk to the team in Harry’s third year, Oliver Wood says:

  “This is our last chance — my last chance — to win the Quidditch Cup,” he told them, striding up and down in front of them. “I’ll be leaving at the end of this year. I’ll never get another shot at it.

  “Gryffindor hasn’t won for seven years now.”

  — Prisoner of Azkaban, chapter 8 (Flight of the Fat Lady)

  The events of Prisoner of Azkaban take place in the 1993–94 academic year. Working backwards, this means the last Gryffindor Quidditch victory is 1985–6.

• Slytherin won the House Cup.

  At the final feast of Harry’s first year, we learn they’re on a successful streak:

  It was decked out in the Slytherin colours of green and silver to celebrate Slytherin’s winning the House Cup for the seventh year in a row.

  — Philosopher’s Stone, chapter 17 (The Man with Two Faces)

  Harry’s first year ends in 1992; this means that Slytherin have won the House Cup for every academic year since 1985–6.

There’s nothing to suggest this was a particularly unusual year (in particular, that Dumbledore did any fiddling with the points), and so I think this provides a counterexample.