A popular competition is the NFL eliminator or survivor pool where you choose a team each week and if they lose you are out but if you win you survive to next week but you cannot choose the same time twice in a season.
I think there is a way to identify which pick is the most "value" in terms of your chances of winning the competition if you know(or can estimate) a) how may contestants have picked each team and b) each team’s chance of winning. The general approach you want to pick a good team with little support and avoid good teams with a lot of support and hope that your team win and the other good team lose elsewhere to reduce the number of opponents.
Mathematically your chance of winning the competition overall is equal to your chance of your pick winning this week divided by the number of contestants left if you do win. Call this your survival factor, the aim is to pick the team with the highest survival factor.
For many eliminator pools (ESPN Yahoo) you can see what percentage of people have picked each team.
To work out each teams survival factor I do the following
a) for each game multiply the chance of the favorite winning by the number of people who have picked them add to this the chance of the underdog winning multiplied by the percentage of people who have picked them. This gives the average number of survivors from this game.
b) Then take each team in turn and divide their winning chance in that game by the number of survivors using the average number of survivors from all other games plus the support for this particular team.
This is a one week at a time approach but I think that as it is impossible to predict future matches several weeks in advance this is probably as good a way as any.
Using the current yahoo survivor pool selections and the moneyline from Football Locks.com Tennessee are way too popular and the Giants are too unpopular so I am going for the Giants.
Saturday, 7 August 2010
How much is a win worth in the MLB
There is much talk about a baseball players wins probability added (WPA) and similar stats. I wanted to take a step back and see how much is adding X number of wins to a team actually worth in terms of a) reaching the playoffs and b)winning in the playoffs.
I looked at each team’s W-L record for the last five seasons (2005-2009) and calculated the effect of adding or subtracting wins to their record in terms of reaching the playoffs.
So if a team was 4 games behind the wildcard team adding 1,2 or 3 games has no effect, and the probability of making the playoffs stays at 0. Adding 4 games would lead to a playoff so the chances of making the playoffs is considered to be 50%. Adding 5 or more games leads to a 100% chance of making the playoffs.
Doing this for all 150 teams-seasons showed that each win increases a team’s chances of making the playoffs by 2.8% the actual line is a sigmoid but it is very linear except at the extremes.
However when we get to the playoffs the situation is quite different. I looked at seven years 2002-2008 where there were 49 playoff series. In three of these both teams had the same regular season record. In the other 46 the team with the best regular season record went 24-22 which is little better than a coin toss.
Even splitting the 46 into the 24 with the smallest regular season record difference (5 games or less) and the 22 with the biggest difference(6 or more games) had no effect with the 22 biggest difference teams only going 12-10, the small difference teams went 12-12.
So maybe Billy Beane shouldn't have been too upset when he complained that his "S*** doesn’t work in the playoffs."
I looked at each team’s W-L record for the last five seasons (2005-2009) and calculated the effect of adding or subtracting wins to their record in terms of reaching the playoffs.
So if a team was 4 games behind the wildcard team adding 1,2 or 3 games has no effect, and the probability of making the playoffs stays at 0. Adding 4 games would lead to a playoff so the chances of making the playoffs is considered to be 50%. Adding 5 or more games leads to a 100% chance of making the playoffs.
Doing this for all 150 teams-seasons showed that each win increases a team’s chances of making the playoffs by 2.8% the actual line is a sigmoid but it is very linear except at the extremes.
However when we get to the playoffs the situation is quite different. I looked at seven years 2002-2008 where there were 49 playoff series. In three of these both teams had the same regular season record. In the other 46 the team with the best regular season record went 24-22 which is little better than a coin toss.
Even splitting the 46 into the 24 with the smallest regular season record difference (5 games or less) and the 22 with the biggest difference(6 or more games) had no effect with the 22 biggest difference teams only going 12-10, the small difference teams went 12-12.
So maybe Billy Beane shouldn't have been too upset when he complained that his "S*** doesn’t work in the playoffs."
Baseball Card game based on Game theory
A few months ago TangoTiger asked if anyone could develop a simple game resembling baseball for use with a standard deck of playing cards.
This was my attempt based on the game theory aspects of the confrontation between pitcher and batter.
http://docs.google.com/document/edit?id=1lj1xCAONqYgQdg7tKjNA4W0M_m0Yt2l33mY-Brj8JXk&hl=en
This was my attempt based on the game theory aspects of the confrontation between pitcher and batter.
http://docs.google.com/document/edit?id=1lj1xCAONqYgQdg7tKjNA4W0M_m0Yt2l33mY-Brj8JXk&hl=en
NoahChain football ranking system
NoahChain
A pair-wise ranking system for college football teams
There are five steps to this method
The brief explanation
1. Count chains of wins and losses between each pair of teams.
For example consider the following chains which link team A and B
A beats B, Primary Win for A
A beats C who beats B, Secondary Win for A
A beats E who beats F who beats B, Third level win for A
B beats G who beats A Secondary Loss for A
2. Convert secondary and third level and higher level wins and losses to the equivalent number of primary wins and losses. This is based on the probability that each chain represents team A being higher ranked than team B. This requires a parameter “H” which is the probability of the winner of a single game is higher ranked than the loser. This parameter “H” is the key to this ranking system. H is usually around 80%
3. Calculate the likelihood of team A being better than team B This is based on the number of equivalent victories and losses between the two teams.
4. Determine the average likelihood that team A is better than a random team. This is simply the average of the likelihood of team A being better than the other teams. Repeat this for all teams and then rank all teams on this basis.
5. Iterate the expected win percentage until it stabilises. Alter the percentage of games higher ranking teams are expected to win (parameter “H”) until the value equals the actual percentage of games won by the higher ranked team in that season.
For a more detailed explanation see this google doc link https://docs.google.com/document/edit?id=1dePOpGFRW6BqZQIHLLf1J_mOvZci1_F1K1hb-C5Li34&hl=en#
I hope to have this accepted onto the Massey ranking websites once the 2010 season starts.
It is called NoahChain because it compares teams two by two and looks at chains of victories and defeats.
A pair-wise ranking system for college football teams
There are five steps to this method
The brief explanation
1. Count chains of wins and losses between each pair of teams.
For example consider the following chains which link team A and B
A beats B, Primary Win for A
A beats C who beats B, Secondary Win for A
A beats E who beats F who beats B, Third level win for A
B beats G who beats A Secondary Loss for A
2. Convert secondary and third level and higher level wins and losses to the equivalent number of primary wins and losses. This is based on the probability that each chain represents team A being higher ranked than team B. This requires a parameter “H” which is the probability of the winner of a single game is higher ranked than the loser. This parameter “H” is the key to this ranking system. H is usually around 80%
3. Calculate the likelihood of team A being better than team B This is based on the number of equivalent victories and losses between the two teams.
4. Determine the average likelihood that team A is better than a random team. This is simply the average of the likelihood of team A being better than the other teams. Repeat this for all teams and then rank all teams on this basis.
5. Iterate the expected win percentage until it stabilises. Alter the percentage of games higher ranking teams are expected to win (parameter “H”) until the value equals the actual percentage of games won by the higher ranked team in that season.
For a more detailed explanation see this google doc link https://docs.google.com/document/edit?id=1dePOpGFRW6BqZQIHLLf1J_mOvZci1_F1K1hb-C5Li34&hl=en#
I hope to have this accepted onto the Massey ranking websites once the 2010 season starts.
It is called NoahChain because it compares teams two by two and looks at chains of victories and defeats.
Wednesday, 4 August 2010
How to stop NFL top seeds from resting starters in the last week
To make sure teams have something to play for after the top seed is secured I think the way the bye for the first round of playoffs should change. Instead of the top two seeds getting byes it should be based on their record in the last 3 weeks. If you win in week 17 you get 4 bye week points if you win in week 16 you get 2 bye points and 1 point for a week 15 win. The two division winners with the most bye week points get the bye. Homefield advantage would stay with the highest seeds. This should solve the problem of number one seeds resting starters.
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