Brier scores measure the distance between what you forecast and what actually happened. So Brier scores are like golf scores: lower is better. Perfection is 0. A hedged fifty-fifty call, or random guessing in the aggregate, will produce a Brier score of 0.5. A forecast that is wrong to the greatest possible extent—saying there is a 100% chance that something will happen and it doesn’t, every time—scores a disastrous 2.0, as far from The Truth as it is possible to get.
