# How to Incorporate prior information on CDF values into the model?

I am working with betting data where the closing odds can be thought of the median result.

I am trying to estimate the latent offensive and defensive strength of each team. Thus, I am using the observed scores and I would also like to use the closing odds to incorporate extra information into my model.

``````  data {
// pbserved scores
vector[30] home_scores;
vector[30] away_scores;

int num_teams;

int home_team_index[30];
int away_team_index[30];

// this is the markets' median value of home team score - away team score
}

parameters{

vector[num_teams] offensive_strength;
vector[num_teams] defensive_strength;

vector[num_teams] off_sigma;

}

model{
int h;
int a;

real home_mu[30];
real away_mu[30];

vector[30] home_sigma;
vector[30] away_sigma;

offensive_strength ~ normal(30,10);
defensive_strength ~ normal(0,10);

for(i in 1:30){
h = home_team_index[i];
a = away_team_index[i];
home_mu[i] = offensive_strength[h] + defensive_strength[a];
away_mu[i] = offensive_strength[a] + defensive_strength[h];
home_sigma[i] = off_sigma[h];
away_sigma[i] = off_sigma[a];

}

home_scores ~ normal(home_mu, home_sigma);
away_scores ~ normal(away_mu, away_sigma);

// here I want to specify that probability_beat_spread should somewhere around .5
// I know I can do something like :