# Tests¶

`melo`

has a standard set of unit tests, whose current CI status is:

The unit tests do not check the physical accuracy of the model which is difficult to verify automatically. Rather, this page shows a number of visual tests which can be used to access the model manually.

## Toy model¶

Consider a fictitious “sports league” of eight teams. Each team samples points from a Poisson distribution \(X_\text{team} \sim \text{Pois}(\lambda_\text{team})\) where \(\lambda_\text{team}\) is one of eight numbers

specifying the team’s mean expected score. I simulate a series of games between the teams by sampling pairs \((\lambda_\text{team1}, \lambda_\text{team2})\) with replacement from the above values. Then, for each game and team, I sample a Poisson number and record the result, producing a tuple

where time is a np.datetime64 object recording the time of the comparison, \(\text{team1}\) and \(\text{team2}\) are strings labeling each team by their \(\lambda\) values, and \(\text{score1}\) and \(\text{score2}\) are random integers. This process is repeated \(\mathcal{O}(10^6)\) times to accumulate a large number of games.

## Point spread validation¶

I then calculate the score difference or \(\text{spread} \equiv \text{score1} - \text{score2}\) for each game to form a list of comparisons \((\text{time}, \text{team1}, \text{team2}, \text{spread})\) and use these comparisons to train the margin-dependent Elo model:

```
lines = np.arange(-49.5, 50.5)
model = Melo(1e-4, lines=lines, commutes=False)
model.fit(times, teams1, teams2, spreads)
```

Now that the model is trained, I can predict the probability that various matchups cover each value of the line, i.e. \(P(\text{spread} > \text{line})\). Since the underlying distributions are known, I can validate these predictions using their analytic results.