Odds Formats Converted

Conversions start with identifying the quote. An American line always starts with a plus + or minus - sign. Decimals are always a positive number higher than 1.00.

Say a sportsbook posts a baseball odds line in American as follows:

• Favored team:
• Underdog team: +150

That's math talking: a payout of 1.5 times the stake if the underdog wins, or a required stake to cover the favorite. To convert a plus-150 American line into a decimal line, calculate 1 + (150/100) = 2.50. Decimals express the quoted price. Finally, converting decimal 2.50 into a fractional line comes out as 3/2.

One number, three formats, all pointing to the same payout. The price baked in by the sportsbook tells the implied probability: 40%.

Reading American odds:

• Positive American odds: 100 / (odds + 100)
• Negative American odds: |odds| / (|odds| + 100)

Reading decimal odds: 1 / decimal odds Reading fractional odds: b / a+b x 100 The root task of odds is converting to implied probability, not the other way around. Take a decimal odds line of 1.67:

• Convert to probability: 1 ÷ 1.67 = 0.60
• Convert to percentage: 0.60 × 100 = 60.0%

The implied probability suggests the sportsbook is quoting 60% on that line. Similarly, a fractional odds line of 3/5:

• Convert to probability: 3 ÷ (3+5) = 0.375
• Convert to percentage: 0.375 × 100 = 37.5%

So American, decimal, and fractional odds are a notation issue, not a quote issue. All tiers of implied probability have which team is which built in, but sign and format do not:

• Memorise positive American to meaning: 100 / (odds + 100)
• Memorise negative American to meaning: |odds| / (|odds| + 100)
• Memorise decimal to effect: 1 / decimal odds
• Memorise fractional to proportion: b / a+b x 100

Sportsbook odds describe different payouts tied to different outcomes. But converting among lines doesn't really change the description.