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Real cases

The idea you practise, in a real situation. Choose, see what actually happens, then reflect.

A case · you decide

Priya and the three perfect votes

Priya — the prior, as a teen explains a board-game leaderboard

The idea in play: every game starts at 5.5 before any real vote.

A new game has three ratings, all 10s. A classic has 2,000 ratings averaging 8.1. A friend says the new game should rank first.

The leaderboard uses a Bayesian average: it adds a block of dummy votes at the prior, 5.5, before counting real votes. Say the block is 100 dummy votes.

New game: (100 × 5.5 + 3 × 10) ÷ 103. Classic: (100 × 5.5 + 2,000 × 8.1) ÷ 2,100.

Which game ranks higher, and why?

Adjust the prior →

A case · you decide

Vera and Dunna: can fans force it?

Vera & Dunna — the volume rule, working with the dummy-count

The idea in play: it is VOLUME, not a loud few, that overcomes the prior.

Twenty devoted fans each give the new game a 10. Dunna runs the numbers with the same 100 dummy votes at 5.5.

(100 × 5.5 + 20 × 10) ÷ 120 = 6.25. Twenty perfect scores lift it less than a point.

The classic, with its 2,000 ratings, sits at about 7.98.

What does this say about the leaderboard?

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A case · you decide

Bayard and Sol do the arithmetic

Bayard & Sol — a 16-year-old building a game-rating site for a board-game club

The idea in play: the Bayesian average blends a prior with the real votes, weighted by how many of each there are.

Tomas's site gives every new game 10 dummy votes at 5.5. A new game has 10 real votes, and they average 9.0. Sol asks what rating the site will show.

Bayard's formula: add up the dummy votes and the real votes, and divide by how many there are in total.

Here that is (10 × 5.5 + 10 × 9.0) ÷ 20.

What rating does the game show?

Adjust the prior →