Implied Probability

Implied probability converts betting odds into a percentage, revealing what the odds suggest about an outcome's likelihood. It's the fundamental concept connecting odds to probability. Every bet you place has an implied probability—understand it, and you understand whether you're getting value or paying too much for a chance to win.

Understanding Implied Probability
Calculation Formulas
The Margin Factor
Using Implied Probability
Finding Value Bets
Common Calculations

Understanding Implied Probability {#understanding}

Betting odds tell you two things:

How much you win if correct
What probability the market assigns to that outcome

The Break-Even Concept

Implied probability answers: How often must this outcome happen for the bet to break even?

Example: Odds of 2.00 (even money)

Win $100 on a$ 100 bet
Break even at 50% win rate
Implied probability: 50%

Example: Odds of 4.00 (3/1)

Win $300 on a$ 100 bet
Break even at 25% win rate
Implied probability: 25%

Why This Matters

Your Assessment	Implied Probability	Action
60% likely	50% implied	Value bet (bet)
50% likely	50% implied	Fair odds (skip)
40% likely	50% implied	Bad value (avoid)

If your probability estimate exceeds implied probability, you have an edge.

Calculation Formulas {#formulas}

Decimal Odds to Implied Probability

The simplest formula:

\text{Implied Probability} = \frac{1}{\text{Decimal Odds}} \times 100

Examples:

Decimal Odds	Calculation	Implied Probability
1.50	1/1.50	66.7%
2.00	1/2.00	50.0%
2.50	1/2.50	40.0%
3.00	1/3.00	33.3%
5.00	1/5.00	20.0%
10.00	1/10.00	10.0%

American Odds to Implied Probability

Negative American odds (favorites):

\text{Implied Probability} = \frac{|\text{American Odds}|}{|\text{American Odds}| + 100} \times 100

Example: -150 odds

\text{IP} = \frac{150}{150 + 100} \times 100 = \frac{150}{250} \times 100 = 60\%

Positive American odds (underdogs):

\text{Implied Probability} = \frac{100}{\text{American Odds} + 100} \times 100

Example: +200 odds

\text{IP} = \frac{100}{200 + 100} \times 100 = \frac{100}{300} \times 100 = 33.3\%

Fractional Odds to Implied Probability

\text{Implied Probability} = \frac{\text{Denominator}}{\text{Numerator} + \text{Denominator}} \times 100

Example: 3/1 odds

\text{IP} = \frac{1}{3 + 1} \times 100 = \frac{1}{4} \times 100 = 25\%

Quick Reference Table

Decimal	American	Fractional	Implied Prob
1.25	-400	1/4	80.0%
1.50	-200	1/2	66.7%
1.80	-125	4/5	55.6%
1.91	-110	10/11	52.4%
2.00	+100	1/1	50.0%
2.10	+110	11/10	47.6%
2.50	+150	3/2	40.0%
3.00	+200	2/1	33.3%
4.00	+300	3/1	25.0%
5.00	+400	4/1	20.0%
10.00	+900	9/1	10.0%

The Margin Factor {#margin}

Why Probabilities Exceed 100%

In a fair market, implied probabilities sum to 100%. In betting markets, they exceed 100%—the excess is the bookmaker's margin.

Example: Tennis match

Player A: 1.65 → 60.6% implied
Player B: 2.30 → 43.5% implied
Total: 104.1%

The 4.1% is the margin (overround).

Calculating Margin

\text{Margin} = \left(\sum \frac{1}{\text{Odds}_i}\right) - 1

Or in percentage terms:

\text{Margin \%} = \left(\sum \text{Implied Probabilities}\right) - 100\%

Removing The Margin

To find true probabilities, normalize:

\text{True Probability} = \frac{\text{Implied Probability}}{\text{Total Implied}} \times 100

Example:

Player A implied: 60.6%
Player B implied: 43.5%
Total: 104.1%

True probabilities:

Player A: 60.6% / 104.1% = 58.2%
Player B: 43.5% / 104.1% = 41.8%

Now they sum to 100%.

Margin by Market Type

Market	Typical Margin	Implied Total
Sharp books (main)	2-3%	102-103%
Recreational books	4-6%	104-106%
Props/Specials	6-10%	106-110%
Exotic bets	10-20%	110-120%

Lower margin = better value for bettors.

Using Implied Probability {#using}

Reading Market Sentiment

Implied probability reveals market consensus:

Implied Prob	Market View
80%+	Heavy favorite, expected to win
60-80%	Clear favorite
50-60%	Slight favorite
40-50%	Slight underdog
20-40%	Clear underdog
Under 20%	Long shot

Line Movement Analysis

Track how implied probability changes:

Time	Odds	Implied Prob	Movement
Opening	2.20	45.5%	-
Day before	2.00	50.0%	+4.5%
At close	1.85	54.1%	+8.6%

Market moved 8.6% toward this outcome—significant action or news.

Comparing Bookmakers

Use implied probability to find best value:

Bookmaker	Odds	Implied Prob	Value?
Book A	2.10	47.6%	Base
Book B	2.20	45.5%	Better
Book C	2.30	43.5%	Best

Book C asks for lowest break-even rate—best value.

Finding Value Bets {#value}

The Value Formula

Value exists when your probability estimate exceeds implied probability:

\text{Edge} = \text{Your Probability} - \text{Implied Probability}

Example:

Your estimate: Team A wins 55%
Odds: 2.10 (implied 47.6%)
Edge: 55% - 47.6% = 7.4% edge

Expected Value Calculation

\text{EV} = (\text{Your Probability} \times \text{Profit}) - (\text{Loss Probability} \times \text{Stake})

Example: $100 bet at 2.10 odds, 55% estimated probability

\text{EV} = (0.55 \times \$110) - (0.45 \times \$100) = \$60.50 - \$45 = +\$15.50

Positive EV = profitable long-term.

Value Bet Thresholds

Your Edge	Recommendation
0-2%	Marginal, careful
2-5%	Solid value
5-10%	Strong value
10%+	Excellent value (verify estimate)

Converting Edge to Recommended Stake

Use Kelly Criterion with your edge:

\text{Kelly \%} = \frac{\text{Edge}}{\text{Odds} - 1}

Example: 7.4% edge at 2.10 odds

\text{Kelly} = \frac{0.074}{1.10} = 6.7\% \text{ of bankroll}

Common Calculations {#calculations}

Price to Break-Even Probability

Quick mental math:

Odds	Quick Estimate
2.00	50% (easy)
1.50	67% (2/3)
3.00	33% (1/3)
4.00	25% (1/4)
5.00	20% (1/5)

Common Betting Odds Decoded

Odds	Implied Prob	Meaning
1.10	90.9%	"Almost certain"
1.50	66.7%	"2 out of 3"
1.91	52.4%	"Coin flip with vig"
2.00	50.0%	"Coin flip (fair)"
3.00	33.3%	"1 in 3"
10.00	10.0%	"1 in 10"
100.00	1.0%	"1 in 100"

Probability Difference Table

How much implied probability changes with odds movement:

Odds Move	Probability Change
2.00 → 1.90	50% → 52.6% (+2.6%)
2.00 → 2.10	50% → 47.6% (-2.4%)
3.00 → 2.80	33.3% → 35.7% (+2.4%)
3.00 → 3.20	33.3% → 31.3% (-2.0%)

Probability changes more at shorter odds.