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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ii/paper-4/13j/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 4 / 13J / a / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-03

No intercept should be included unless the ordering of the two teams has an external meaning such as home advantage. If

η_{ij, k ℓ} = β_{i} + β_{j} + β_{{i, j}} - β_{k} - β_{ℓ} - β_{{k, ℓ}},

(1)

then reversing the teams gives

η_{k ℓ, ij} = - η_{ij, k ℓ}

, so the logistic model automatically gives

P ({k, ℓ} wins against {i, j}) = 1 - P ({i, j} wins against {k, ℓ}) .

(2)

An intercept would not change sign when the teams are swapped and would violate this required symmetry. Thus an intercept does not make sense in the stated model.

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