Conditional probability of several events? (sports-related)

In summary, the speaker is working on determining the probability of a team in a given sport, specifically football, reaching a certain level in a season. They plan to use a cumulative distribution function to assign a final number to each team based on their number of wins and playoff performance. However, they are struggling with how to connect the two factors and are considering breaking it down into three events: playoff progress, making it into the playoffs, and winning a certain number of games. They are seeking help and clarification on how to approach this problem.
  • #1
hb1547
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I'm casually working on determining the probability of a team in a given sport (let's say football) reaching at least a certain level in a season.

There are two main parts to this: How many games they won in the season, and how far they got in the playoffs. I'd like to assign one final number to each team that designates how well they did in the season, using a cumulative distribution function (eg, a team that wins every game and the championship would have a 1, a team that lost all games would have 0).

There are two parts to this that I can see:
- The probability of getting at least n wins during the season. This is easy using a binomial distribution.
- The probability of making it at least so far in the playoffs. This is also easy.

What I'm having a hard time figuring out is how to connect them properly. My guess would be that this is a P(B | A) event, where B is making it that far, and A is winning that many.

I'm having a hard time thinking through how to express B though, since winning playoff games is independent of how many you win in the season, except that season games get you into the playoffs.

So is it better to think of this as 3 events?
C - Playoff progress
B - Getting into the playoffs
A - Winning x games

And so this is P(C | (B | A))?

I always think myself into circles with probability formulae. Any hints, help, insight would be great.
 
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  • #2
hb1547 said:
There are two parts to this that I can see:
- The probability of getting at least n wins during the season. This is easy using a binomial distribution.

That doesn't make sense unless two teams that play each other can both win the game.
 

1. What is conditional probability in the context of sports?

Conditional probability in the context of sports refers to the likelihood of an event occurring given that another event has already occurred. For example, what is the probability of a team winning a game given that they are playing on their home field?

2. How is conditional probability calculated in sports?

Conditional probability is calculated by dividing the probability of the two events occurring together by the probability of the initial event occurring. In the sports context, this would be the probability of a team winning a game on their home field divided by the probability of them winning a game overall.

3. Why is conditional probability important in sports?

Conditional probability is important in sports because it can help predict the outcome of a game or event based on previous events. It can also be used to analyze and make decisions related to strategies and player performance.

4. What are some limitations of using conditional probability in sports analysis?

One limitation of using conditional probability in sports analysis is that it assumes that events are independent of each other, when in reality, there may be other factors at play. Additionally, it is important to use a large sample size of data to accurately calculate conditional probabilities.

5. Can conditional probability be used in sports betting?

Yes, conditional probability can be used in sports betting to calculate the likelihood of certain outcomes and make more informed bets. However, it should be noted that there are still many other factors that can affect the outcome of a game and nothing is guaranteed in sports betting.

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