Removing the Spread (De‑juicing)

Here we will discuss the backend math of our odd calculations.

Suppose a sportsbook offers Team A at +120 and Team B at −145.

Implied probabilities:

• For +x odds: $p = 100/(x+100)$
• For -y odds: $p = y/(100+y)$

Thus:

• $p^*_A = 100/(120+100) \approx 45.45$%
• $p^*_B = 145/(145+100) \approx 59.18$%
• $p^*_A + p^*_B = 104.63$% → embedded vig

Normalize (de-juice):

• $p_A = p^*_A/(p^*_A+p^*_B) \approx 43.44$%
• $p_B = p^*_B/(p^*_B+p^*_A) \approx 56.56$%

Converted back to American odds, this is roughly +131 and -131.