De-vig a two-way tennis market

Question

A tennis match (no draws possible) is quoted at decimal odds: Player A 1.55, Player B 2.55. What are the fair win probabilities after removing the bookmaker's margin, and how big is that margin?

Accepted Answer

Step 1: raw implied probabilities (1/	ext{odds}): \frac{1}{1.55} = 0.6452, \qquad \frac{1}{2.55} = 0.3922. Step 2: the overround. Sum them: S = 0.6452 + 0.3922 = 1.0374. They exceed 1 by 3.74\%, which is the bookmaker's built-in margin on this two-way book. Step 3: de-vig by normalizing. Divide each raw probability by S so they sum to 1 (the proportional method): PA = \frac{0.6452}{1.0374} = 0.622, \qquad PB = \frac{0.3922}{1.0374} = 0.378. Check: 0.622 + 0.378 = 1.000. Fair probabilities: about 62.2\% for A and 37.8\% for B. The fair odds implied are 1/0.622 = 1.61 for A and 1/0.378 = 2.65 …

De-vig a two-way tennis market

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