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**Evenly Matched Teams**

If the two teams are evenly matched, then we say the probability that Team A wins each game is 0.50. The probability that Team B wins each game is also 0.50, and the sum of these two probabilities is 1.0 as expected.

The question here is, what is the likelihood of each possible playoff outcome:

- 4-0 Team A wins
- 4-1 Team A wins
- 4-2 Team A wins
- 4-3 Team A wins and

- 4-0 Team B wins
- 4-1 Team B wins
- 4-2 Team B wins
- 4-3 Team B wins

**Team A is Stronger**

If the two teams are not evenly matched, then let’s say the probability that Team A wins each game is P. The probability that Team B wins each game is now therefore Q = 1 – P, and the sum of the probabilities P + Q = 1.0 as expected.

For example, if the probability that Team A wins each game is P = 0.81, then the probability that Team B wins each game is Q = 1 – P = 0.19.

Again, the question is, what is the likelihood of each possible playoff outcome:

- 4-0 Team A wins,
- 4-1 Team A wins,
- 4-2 Team A wins,
- 4-3 Team A wins, and

- 4-0 Team B wins,
- 4-1 Team B wins,
- 4-2 Team B wins,
- 4-3 Team B wins?

**Discussion**

This answer to this problem is relatively easy to discuss yet somewhat complex to calculate, Fortunately, it can be broken down into several similar parts.

**Series Goes 4-0 or 0-4**

An easy start: if Team A wins in 4 straight, then the probability is simply

And similarly: if Team B wins in 4 straight, then the probability is simply

*in this example very unlikely*.

**Series Goes 4-1 or 1-4**

Now, if Team A is to win the series 4-1, then after 4 games, they must be up 3-1 just before the 5th game in the series. That means there is one loss in the 4 games played and there are only 4 ways that can happen.

Therefore the probability is

Explanation:

- is the
probability of Team A winning 4 games and Team B winning one game.**one-time** - is the number of combinations in which one team wins 3 games and the other wins only one game.

Click for explanation of combinations

Similarly, if Team B is to win the series 4-1, then after 4 games, they must be up 3-1 just before the 5th game in the series. Therefore the probability is

**Series Goes 4-2 or 2-4**

If Team A is to win the series 4-2, then after 5 games, they must be up 3-2 just before the 6th game in the series. That means there are 2 losses in the 5 games played and there are only 10 ways that can happen.

So we have established the pattern, if Team A is to win the series , the probability is

Likewise, if Team B is to win the series , the probability is

**Observation**

Notice that compared to a single game, a seven game series increases the probability that the strong team wins the series. For example, with P = 0.81, as shown above, the probability that Team A wins the series is calculated at 0.972. Note further that the probability that Team B wins the series decreases from 0.19 to only 0.028.

Using Odds:

The single game had odds of 81:19 or about 4:1 whereas the series has odds of 972:28 or about 35:1.

**Plots**

See the plots of all possible outcomes for all probabilities:

Example probabilities are given for the specific case where .

**Live Plot**

Click for Best of Seven Live Chart

*Using PLOTLY live plots*

Each chart series can be toggled off and on

by clicking its legend entry.

On a desktop device, reset the chart to full scale

by reloading the web page.

On a mobile device, reset the chart to full scale

by double tapping.

The live chart looks best on a laptop or desktop screen. If viewing on a mobile device select ‘Request Desktop Website’ and use landscape orientation of the device.

**Static Plots**

**Reference**

Best of Seven Outcome Probability Dec 2020

**One game played**

If Team A is to win the series , the probability is

**Two games played (imagine the 2024 Celtics in such a situation)**

If Team A is to win the series , the probability is

**Closed form solution**

Now what is the probability of each series arrangement?

If Team A is to win the series , the probability is

If Team B is to win the series , the probability is