Pricing 2-Leg SGPs with Conditional Probability

When you have paired game history for both legs of an SGP, conditional probability is the most transparent and accurate way to price it. This lesson teaches you the method.

Step Zero: Odds to Probabilities

Before pricing any SGP, you need probabilities, not odds.

Converting American Odds to Implied Probability

Negative Odds to Probability

Implied P = |odds| / (|odds| + 100)

Excel: =ABS(A1)/(ABS(A1)+100)

Positive Odds to Probability

Implied P = 100 / (odds + 100)

Excel: =100/(A1+100)

Examples

Odds	Calculation	Implied Probability
-110	110/(110+100)	52.38%
-150	150/(150+100)	60.00%
+109	100/(109+100)	47.85%
+190	100/(190+100)	34.48%

De-Vigging: Removing the House Edge

When both sides of a prop are available (Over and Under), you should de-vig to get fair probabilities.

De-Vigged Probability (Over)

Fair P(Over) = q_over / (q_over + q_under)

Excel: =A1/(A1+B1)

Why De-Vig Matters

Step	Without De-Vig	With De-Vig
Over implied	52.38%	50.00%
Under implied	52.38%	50.00%
Total	104.76%	100.00%

Key Insight

Always de-vig the inputs when you can. Comparing vigged singles to a vigged SGP can hide or exaggerate your edge.

The Conditional Probability Method

If you have paired game logs for both legs, this is the most transparent way to price a 2-leg SGP:

Joint Probability (Conditional)

P(A ∩ B) = P(A) × P(B | A)

Excel: =(count_A/total) * (count_both/count_A)

Where:

P(A) = Probability that Leg A hits
P(B | A) = Probability that Leg B hits, given that Leg A already hit

You estimate each term directly from game logs.

Tip

Conditional probability is the cleanest way to price a 2-leg SGP when you have paired history because it estimates the joint probability directly.

Worked Example: Williams + Loveland SGP

Let's price the Bears-Rams SGP from the chapter introduction using actual game data.

The Setup

DraftKings is offering:

Leg A: Williams Over 1.5 passing TDs (+109)
Leg B: Loveland Over 0.5 receiving TDs (+190)
SGP: +305

Step 1: Gather Game Log Data

Game #	Williams Pass TDs	Loveland Rec TDs	A Hits (2+)?	B Hits (1+)?
1	1	0	No	No
2	2	0	Yes	No
3	4	0	Yes	No
4	1	0	No	No
5	0	0	No	No
6	0	0	No	No
7	3	2	Yes	Yes
8	1	0	No	No
9	0	0	No	No
10	3	1	Yes	Yes
11	1	0	No	No
12	2	1	Yes	Yes
13	2	0	Yes	No
14	2	0	Yes	No
15	2	1	Yes	Yes
16	2	1	Yes	Yes
17	2	0	Yes	No

Step 2: Count the Outcomes

From 17 games:

A hits (Williams 2+ TDs): 10 games
B hits (Loveland 1+ TD): 5 games
Both A and B hit: 5 games

Step 3: Calculate Conditional Probability

P(A) = 10/17 = 0.588 (58.8%)

P(B | A) = 5/10 = 0.50 (50.0%)

Among the 10 games where Williams hit 2+ TDs, Loveland scored in 5 of them

P(A ∩ B) = 0.588 × 0.50 = 0.294 (29.4%)

Step 4: Convert to Fair Odds

Probability to American Odds

If P > 0.5: Odds = -100 × P/(1-P); If P < 0.5: Odds = 100 × (1-P)/P

Excel: =IF(A1>0.5, -100*A1/(1-A1), 100*(1-A1)/A1)

For P = 0.294:

Fair odds = 100 × (1 - 0.294) / 0.294 = +240

Step 5: Compare to Market

Metric	Value
Your fair odds	+240
Market price	+305
Market implied probability	24.7%
Your probability	29.4%

The market price (+305) implies 24.7%, which is lower than the 29.4% frequency in this sample.

Key Insight

In this case, the SGP appears to offer positive expected value. The book is pricing the correlation lower than the historical data suggests.

The Calculation Workflow

Here's the step-by-step process for pricing any 2-leg SGP with conditional probability:

1. Gather paired game logs for both players
2. Define the events (Over/Under thresholds)
3. Count: How many games does A hit?
4. Count: In games where A hits, how many does B also hit?
5. Calculate: P(A) = count_A / total_games
6. Calculate: P(B|A) = count_both / count_A
7. Calculate: P(A ∩ B) = P(A) × P(B|A)
8. Convert to fair odds
9. Compare to market price

When This Method Works Best

The conditional probability method is ideal when:

✅ You have 15+ paired games of data
✅ Both players have been in consistent roles
✅ The sample is recent and representative
✅ You want transparent, explainable pricing

When to Be Cautious

⚠️ Small samples: With fewer than 10 games, one outlier changes everything
⚠️ Role changes: If a player's usage has shifted, old data may not apply
⚠️ Rookies/new additions: Limited paired history
⚠️ Rare events: TD props with few positive outcomes

Warning

Be cautious with estimates based on fewer than 10 observations. One extra hit or miss can change your probability by 10-20 percentage points.

Practice Exercise

📝 Exercise

Instructions

You have 20 games of data for an NBA SGP:

Leg A: Star PG Over 8.5 assists

Hits in 14 of 20 games

Leg B: Teammate C Over 1.5 blocks

In games where A hits, B also hits in 8 of those 14 games

Market SGP price: +180

Calculate:

P(A) — probability Leg A hits
P(B|A) — probability Leg B hits given A hits
P(A ∩ B) — joint probability
Fair American odds
Is the SGP +EV or -EV?

Key Takeaways

De-vig first — always remove the house edge before calculating
Conditional probability = P(A) × P(B|A) — the cleanest method with paired data
Need 15+ games for reliable estimates
Compare fair odds to market to determine if SGP is +EV or -EV
Watch for role changes that invalidate historical data

Note

Coming Up Next: What if you don't have enough paired game history? We'll learn the r-adjustment method for pricing SGPs with limited data.

Game #	Williams Pass TDs	Loveland Rec TDs	A Hits (2+)?	B Hits (1+)?
1	1	0	No	No
2	2	0	Yes	No
3	4	0	Yes	No
4	1	0	No	No
5	0	0	No	No
6	0	0	No	No
7	3	2	Yes	Yes
8	1	0	No	No
9	0	0	No	No
10	3	1	Yes	Yes
11	1	0	No	No
12	2	1	Yes	Yes
13	2	0	Yes	No
14	2	0	Yes	No
15	2	1	Yes	Yes
16	2	1	Yes	Yes
17	2	0	Yes	No

Game #	Williams Pass TDs	Loveland Rec TDs	A Hits (2+)?	B Hits (1+)?
1	1	0	No	No
2	2	0	Yes	No
3	4	0	Yes	No
4	1	0	No	No
5	0	0	No	No
6	0	0	No	No
7	3	2	Yes	Yes
8	1	0	No	No
9	0	0	No	No
10	3	1	Yes	Yes
11	1	0	No	No
12	2	1	Yes	Yes
13	2	0	Yes	No
14	2	0	Yes	No
15	2	1	Yes	Yes
16	2	1	Yes	Yes
17	2	0	Yes	No

Pricing 2-Leg SGPs: Conditional Probability