In part 2 of our conditional probability for sports betting tutorial, we’ll go over a few detailed examples of applying the formulas you learned in the previous lesson to actual sports betting scenarios.

### Scenario:

You’re interested in creating a parlay bet involving two specific NBA players: Anthony Davis and LeBron James. You want to bet on Anthony Davis scoring over 20 points and LeBron recording over 8 assists in that same game.

### Step 1: Understanding Individual Probabilities

**Anthony Davis’ Points**: Based on past performance data, say we know Davis has a 60% chance (probability of 0.6) of scoring above 20 points in a game.**LeBron James’s Assists**: Similarly, LeBron has been observed to have a 50% chance (probability of 0.5) of recording more than 8 assists in a game.

### Step 2: Identifying The Terms for Conditional Probability Formula

The crucial part is to determine if there’s a dependency between Anthony Davis’ scoring and LeBron’s assists. So we go look at the data and find out that in 40% of the games Anthony Davis and LeBron have played together, both LeBron recorded 8+ assists and Anthony Davis scored 20+ points. That’s called the **joint probability**.

For the purpose of notation, let’s refer to Anthony Davis as “Player A” and LeBron as “Player B”

As we covered in the previous lecture, the formula for conditional probability is P(A|B) = P(A and B) / P(B).

In step 1, we noted that LeBron has a 50% chance of recording 8 assists in a game. So our P(B) is equal to .5. Similarly, we found that the **joint probability**, P(A and B), of Anthony Davis scoring 20+ points and LeBron recording 8 assists in a game is 40 percent. So our numerator, P(A and B) is .4.

### Step 3: Calculating the Conditional Probability

This is the easy part, the actual calculation.

All we need to do is plug in the terms we found to our conditional probability formula, which again is P(A|B) = P(A and B) / P(B).

We get P(A|B) = .4/.5 = .8 = 80%!

That means that if some divine god fortune teller told us that LeBron would DEFINITELY record 8 assists, there would be an 80% chance of Anthony Davis scoring 20+ points! That’s some really serious synergy between the two players.

### Step 4: How to Apply this to Parlays

We haven’t yet covered the interpretation of a bookmakers odds, so we won’t cover this in great detail **yet**. But the general idea comes down to comparing your assessed probability with the implied probability the sportsbook gives you for this two leg parlay. Let the conditional probability formula sink in for now, and later in the course we’ll revisit this exact example and show you how to assess whether to place the bet or not.