# AutoTippers

The competition ladder consists of some player aliases having the full name "AutoTipper". These players are actually automated computer players; their tips are determined by various honest algorithms.

## HomeTeam

Always chooses the home team (ie. team X in an X-vs-Y game). The theory is that if a team is playing at their home ground they will have a playing advantage. The home ground advantage appears to be most beneficial for interstate teams.

Parameter Formula
Winner The home team
Margin [average of all past winning margins?]
Std. Dev. 40
Probability (num_home_wins+1) / (num_matches_played+2)

## LadderRank

Chooses the team which currently occupies the higher position on the AFL ladder. The theory is that they have won more games in the past so they would probably do better in this match. Does not take home ground advantages into account.

Parameter Formula
Winner [the team with the current highest AFL ladder position]
Margin [details]
Std. Dev. 40
Probability (winners_points + 4) / (winners_points + losers_points + 8)

## BookieOdds

The Bookie's payout figures are normalized and used to compute what they think the probabilities of each team winning are.

Parameter Formula
Winner Team with higher Probability
Margin [details]
Std. Dev. 40
Probability [normalized Bookie's odds]

## FenceSitter

For the probabilistic competition this is the "null" tipper which tips p=0.5 for every match. It's score will always be zero. For the Gaussian competition it always picks a margin of 0 and a standard deviation of 40 (which most human players seem to use). There is no way to "sit on the fence" in the normal competition.

Parameter Formula
Winner N/A
Margin 0
Std. Dev. 40
Probability 0.5

## EloHomeAway

A system which ranks teams based on their "Elo" scores, similar to that used in professional chess. Incorporates a HGA (home ground advantage) parameter.

Parameter Formula
Winner (implied by Probability)
Margin N/A
Std. Dev. N/A
Probability [algorithm based on the team's Elo scores]

## BlendElo

Performs an "optimal" posterior weighting of 3 sub-tippers: EloHomeAway, Bookie's Odds, and the "null" tipper (which picks p=0.5 for everything).

Parameter Formula
Winner (implied by Probability)
Margin N/A
Std. Dev. N/A
Probability [algorithm based on blending the 3 sub-tippers]

## Weighted

Performs a posterior weighting of every other player's tips after they have entered them. The weights are based on the bit scores of each player so far in the season. Note that this tipper has access to other player's tips so it is "cheating" slightly.

Parameter Formula
Winner (implied by Probability)
Margin N/A
Std. Dev. N/A
Probability [algorithm based on blending other player's tips]

## Converting probabilities to margins

An algorithm which only predicts probability p can be used to predict a margin m (assuming a standard deviation s) by choosing m such that the integral from (-Infinity..0) of the distribution ~N(m,s2) is equal to p. Note that this is not the only way in which this could be done.