`bpl`

is a python 3 library for fitting Bayesian versions of the Dixon & Coles (1997) model to data.
It uses the `stan`

library to fit models to data.

```
pip install bpl
```

`bpl`

provides a class `BPLModel`

that can be used to forecast the outcome of football matches.
Data should be provided to the model as a `pandas`

dataframe, with columns `home_team`

, `away_team`

, `home_goals`

and `away_goals`

.
You can also optionally provide a set of numerical covariates for each team (e.g. their ratings on FIFA) and these will be used in the fit.
Example usage:

```
import bpl
import pandas as pd
df_train = pd.read_csv("<path-to-training-data>")
df_X = pd.read_csv("<path-to-team-level-covariates>")
forecaster = bpl.BPLModel(data=df_train, X=df_X)
forecaster.fit(seed=42)
# calculate the probability that team 1 beats team 2 3-0 at home:
forecaster.score_probability("Team 1", "Team 2", 3, 0)
# calculate the probabilities of a home win, an away win and a draw:
forecaster.overall_probabilities("Team 1", "Team 2")
# compute home win, away win and draw probabilities for a collection of matches:
df_test = pd.read_csv("<path-to-test-data>") # must have columns "home_team" and "away_team"
forecaster.predict_future_matches(df_test)
# add a new, previously unseen team to the model by sampling from the prior
X_3 = np.array([0.1, -0.5, 3.0]) # the covariates for the new team
forecaster.add_new_team("Team 3", X=X_3, seed=43)
```

The statistical model behind `bpl`

is a slight variation on the Dixon & Coles approach.
The likelihood is:

where y_h and y_a are the number of goals scored by the home team and the away team, respectively.
a_i is the *attacking aptitude* of team i and b_i is the *defending aptitude* of team j.
gamma_i represents the home advantage for team i, and tau is a correlation term that was introduced by Dixon and Coles to produce more realistic scorelines in low-scoring matches.
The model uses the following bivariate, hierarchical prior for a and b

X_i are a set of (optional) team-level covariates (these could be, for example, the attack and defence ratings of team i on Fifa). beta are coefficient vectors, and mu_b is an offset for the defence parameter. rho encodes the correlation between a and b, since teams that are strong at attacking also tend to be strong at defending as well. The home advantage has a log-normal prior

Finally, the hyper-priors are

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