My Example:

Players 1 through n are playing a game and in each round there is one winner and after the winner is determined, one of the non-winners gets randomly taken out of the total players pool (i.e. round 1 = n total players, round 2 = n-1, round 3 = n-2, etc).

I am trying to show that if we look at a large sample of these games, a strong player (potentially the winner) should typically have a higher amount of competition round wins at the end of each game. However, I do not understand how to go about adjusting for the increased probability that a player might win each round when a non-winner is eliminated [i.e. round 1 = $\frac{1}{n}$ % chance of winning that round, round 2 = $\frac{1}{n-1}$, round 3 = $\frac{1}{n-2}$, etc]. This is assuming of course that each player has an equal chance of winning each round, which is obviously another hurdle to get over.

Does anyone know how I might account for this increased probability and possibly how to also take into consideration as the game goes on that a stronger player who has won in the first round (or other future rounds) is given a higher probability than the rest to win the next rounds?

Basically, how do I calculate the strength of a player and add it into a predictive model on how they will do based on past games with other players data.

Thank you for any help in advance.

My Example:

Players 1 through n are playing a game and in each round there is one winner and after the winner is determined, one of the non-winners gets randomly taken out of the total players pool (i.e. round 1 = n total players, round 2 = n-1, round 3 = n-2, etc).

I am trying to show that if we look at a large sample of these games, a strong player (potentially the winner) should typically have a higher amount of competition round wins at the end of each game. However, I do not understand how to go about adjusting for the increased probability that a player might win each round when a non-winner is eliminated [i.e. round 1 = $\frac{1}{n}$ % chance of winning that round, round 2 = $\frac{1}{n-1}$, round 3 = $\frac{1}{n-2}$, etc]. This is assuming of course that each player has an equal chance of winning each round, which is obviously what i'm trying to get around.

Does anyone know how I might account for this increased probability and possibly how to also take into consideration as the game goes on that a stronger player who has won in the first round (or other future rounds) is given a higher probability than the rest to win the next rounds?

Basically, how do I calculate the strength of a player and add it into a predictive model on how they will do based on past games with other players data.

Thank you for any help in advance.

My Example:

Players 1 through n are playing a game and in each round there is one winner and after the winner is determined, one of the non-winners gets randomly taken out of the total players pool (i.e. round 1 = n total players, round 2 = n-1, round 3 = n-2, etc).

I am trying to show that if we look at a large sample of these games, a strong player (potentially the winner) should typically have a higher amount of competition round wins at the end of each game. However, I do not understand how to go about adjusting for the increased probability that a player might win each round when a non-winner is eliminated [i.e. round 1 = 1/n % chance of winning that round, round 2 = 1/(n-1), round 3 = 1/(n-2), etc]. This is assuming of course that each player has an equal chance of winning each round, which is obviously another hurdle to get over.

Does anyone know how I might account for this increased probability and possibly how to also take into consideration as the game goes on that a stronger player who has one in the first round (or other future rounds) is given a higher probability than the rest to win the next rounds?

Basically, how do I calculate the strength of a player and add it into a predictive model on how they will do based on past games with other players data.

Thank you for any help in advance.

My Example:

Players 1 through n are playing a game and in each round there is one winner and after the winner is determined, one of the non-winners gets randomly taken out of the total players pool (i.e. round 1 = n total players, round 2 = n-1, round 3 = n-2, etc).

I am trying to show that if we look at a large sample of these games, a strong player (potentially the winner) should typically have a higher amount of competition round wins at the end of each game. However, I do not understand how to go about adjusting for the increased probability that a player might win each round when a non-winner is eliminated [i.e. round 1 = $\frac{1}{n}$ % chance of winning that round, round 2 = $\frac{1}{n-1}$, round 3 = $\frac{1}{n-2}$, etc]. This is assuming of course that each player has an equal chance of winning each round, which is obviously another hurdle to get over.

Does anyone know how I might account for this increased probability and possibly how to also take into consideration as the game goes on that a stronger player who has won in the first round (or other future rounds) is given a higher probability than the rest to win the next rounds?

Basically, how do I calculate the strength of a player and add it into a predictive model on how they will do based on past games with other players data.

Thank you for any help in advance.