I wonder how frequentist and bayesian calculate the winning probability for Tottenham versus Arsnel, Saturday.
For frequentists, the following is how I understand:
- Imagine a population made of all the historical games between Tottenham versus Liverpool[Do not consider the specific day of the week because of the assumption that all games are played with the same condition.]. Here I don't exactly know what the population could be made of. I don't know if I can assume the population is made of all the historical data but, to me, the historical data seem to be just a sample to measure for the frequency.
- Repeatedly draw samples.
- Record frequencies of Tottenham that won the game versus Liverpool.
I don't know if the way I think about the frequentists' way is correct.
For Bayesians, I don't know yet. However, for the sake of simplicity, I can think of two factors of players to win the game over the opponent:
- the number of goals each player scores
- the number of attack assists
How can I think of the prior distribution for the two factors of players?
- This is the the way I think about the prior distribution. I do not need two different prior distributions because the prior distribution is all about the probability distribution of winning the games. So I just need one prior distribution. If I am not correct, please feel free to correct me.
What could be the data to apply to the likelihood?
I also hope to know what issues that bayesians would say frequentists may run into for this probability calculation.