How to Calculate Odds to Win a Series

We know how to calculate a team’s odds to win one game. How on earth do we figure out a team’s odds to win a series?

Learning how to calculate series odds will make finding value a breeze whether you are betting the MLB season or playoffs, college baseball, the NBA or NHL playoffs, or just a backyard pickup best-of-7.

Figuring out series odds is not impossible, it just takes a bit of grunt work. The task can appear daunting at first look because there are so many different possible combinations when talking series. There are 8 different ways that a 3-game series can unfold but up to 70 different ways that a best-of-7 series can play out.

If Team A is playing Team B in a best-of-7 series and Team A wins the series, they could have won in either 4, 5, 6 or 7 games. Team A could have won games 1, 3, 4, and 5. Team A could also have won games 2, 5, 6, and 7. Team A could even have won games 1, 2, 5, and 6. You get the point. There are tons of possibilities.

We can combine and figure out all of these odds fairly easily by using a branch of math called conditional probability. The process of calculating a team’s odds of winning a series is the same whether they play 2 games, 7 games, 100 games, or any number of games.

I will give an example of this process using a potential 2019 NBA Finals matchup between the Houston Rockets and Philadelphia 76ers.

The NBA Finals is a best-of-7 series and has a 2-2-1-1-1 format. The team with the better regular season record gets the home court advantage. Houston would be the higher seed in this case, so we begin our series in Houston.

Imagine we did some handicapping based on season statistics and now want to figure out the chances the 76ers have of winning this series.

Here is what we determined from our handicapping. Remember, this is all hypothetical:

• The 76ers have a great home court advantage and own a 60% chance of winning at home
• The Rockets have a 55% chance of winning at home for all games except Game 7
• Harden will go off if it gets to Game 7 – Houston has a 70% chance of winning Game 7

Let’s figure out the 76ers’ chances to win the series given that our handicapping is spot on. To do this, we need to figure out the chances that Philly wins in 4 games, 5 games, 6 games, and 7 games respectively and then add those percentages together.

Let’s dive in!

Game 1 in Houston

This first one is pretty simple. There are only 2 possible outcomes after Game 1, right? Either the Sixers are up 1-0 or down 1-0.

Since the game is in Houston, we determine that the Rockets have a 55% chance of winning while Philly has only a 45% chance.

After 1 game, there is a 55% chance that Houston is up 1-0 and a 45% chance that Philly is up 1-0. The only way we can get to 1-0 is by being 0-0 first, hence the “Previous W-L column”. Hopefully everyone is still with me. Let’s move on.

Game 2 in Houston

Game 2 is also in Houston. The Rockets again have a 55% chance of winning while the 76ers have a 45% chance.

After 2 games there are 3 possible win-loss records for the series. Either team could be up 2-0 or it could be a 1-1 split.

The only way to get to 2-0 is to be 1-0 first and then win again. This is very easy to calculate. It is simple multiplication.

There are 2 ways to get to a 1-1 series, however. Houston could win the first and then Philly comes back, or vice versa.

Here are those calculations in table form. I’ll explain a bit more below the table.

The odds Philadelphia wins 2 straight road games is simply 45% times 45% or 20.25%. The math is identical for Houston (55% * 55%).

To figure out the odds of a 1-1 split after 2 games, I took the odds that Philly wins the first and Houston the second (45% times 55%) and added that to the odds that Houston wins the first and Philly the second (55% times 45%) to get 49.5%.

A 1-1 split is the most likely 2-game outcome. Houston going up 2-0 is the next most likely. Philly gaining a 2-0 advantage is the least likely scenario, which makes sense because they are on the road for the first 2 games.

Let’s move on.

Game 3 in Philadelphia

Back in Philly for Game 3, the Sixers have a 60% chance of winning while the Rockets now have just a 40% chance.

There are 3 possible series records that we enter this game with: 2-0 PHI, 2-0 HOU, or tied 1-1. In the Game 2 section, we calculated the odds of each of these outcomes occurring.

After 3 games, the series record could be 3-0 PHI, 3-0 HOU, 2-1 PHI, or 2-1 HOU. Let’s figure out how we can get to each of those outcomes and do the math.

After 3 games, the most likely outcome is 2-1 Houston, but 2-1 Philly is virtually as likely. Interestingly enough, it is actually more probable that the Sixers go up 3-0 than the Rockets do.

Game 4 in Philadelphia

Game 4 requires the most calculations of any game in the series. After Game 4, we begin eliminating possible combinations because some of them (i.e. 4-0 or 0-4) result in the series being over.

Yaye, our first endgame scenario! We do not really care about the odds that Houston sweeps. We are interested in the odds that Philly sweeps, though, because that is who we are thinking about betting on.

The odds that the Sixers sweep the Rockets are 7.29%. Let’s remember this so we can add it to the other outcomes later.

Game 5 in Houston

Back in H-Town, the Rockets now have a 55% chance of winning Game 5 while Philly has just a 45% chance.

Here is how the math pans out for this pivotal game.

If the series makes it to 5 games, it will most likely be a 3-2 series. We have another endgame scenario here for Philly, however. There is a 12.39% chance that the 76ers win the series in exactly 5 games.

If we add this 12.39% chance to the 7.29% chance that Philly sweeps, we determine there is a 19.68% chance that Philly wins the series in 5 games or less.

Game 6 in Philadelphia

The last game in Philly – the Sixers once again have a 60% chance of getting the W while the Beard and his crew have only a 40% chance.

If the series makes it to Game 6, the record must be 3-2. That is the only way a series can get to 6 games. Here are the possibilities.

Our third endgame scenario – Philly in 6.

The odds that the Sixers win the series 4-2 are 19.32%. Adding this to the odds they sweep and the odds they win in 5 gives us a 39% chance that Philly wins in 6 games or less.

Onto Game 7 where we determined that the Rockets have a major advantage.

Game 7 in Houston

We predict that if the series reaches this point, James Harden will take control and dominate – giving his Rockets a 70% chance of winning while Philadelphia holds only a 30% chance.

There is only one way to get to Game 7. The series must be tied 3-3 after 6 games. Here are those odds.

Thanks to Harden’s anticipated heroics, the Sixers only have a 9.43% chance of winning the series in exactly 7 games.

Here are the 4 endgame scenarios that we determined.

Series W-L	Chances of Occurring
PHI 4-0	7.29%
PHI 4-1	12.39%
PHI 4-2	19.32%
PHI 4-3	9.43%
Total	48.43%

Adding these up tells us that Philadelphia has a 48.43% chance to win the series. It is most likely that they will win in 6 games. A 4-1 win is the next most likely scenario.

If this were a real series, you could simply check the series odds on Philly and bet them if they provide value.

Using this pattern, you can calculate the odds of a baseball team winning a best-of-3, a hockey team winning a best-of-7, or two chess players in a best-of-30.

Use this newfound power to your advantage. See you on top!