Foresight Score

Accurate forecasting is essential, but how do you measure the quality of your predictions? Enter the Foresight Score: a refined tool that improves on the traditional Brier Score by rewarding accurate, confident predictions and penalizing overconfident mistakes more heavily.

Understanding the Brier Score

The Brier Score is a simple yet powerful tool for evaluating the accuracy of probabilistic predictions. At its core, it measures how close your predictions are to the actual outcomes. This metric is widely used in fields like meteorology, machine learning, and sports analytics, as it offers a straightforward way to quantify the quality of probabilistic forecasts. Let’s break down the formula. The Brier Score for a binary outcome (e.g., an event either happens or it doesn’t) is calculated as :

N: Number of predictions
fi: Predicted probability for the ii-th event
oi: Observed outcome for the ii-th event (1 if the event happened, 0 otherwise)

Here, is the forecasted probability of an event occurring, is the actual outcome (1 if the event occurred, 0 if it didn’t), and is the total number of predictions. The score ranges from 0 to 1, where 0 represents perfect predictions and 1 indicates completely inaccurate predictions. To understand this better, let’s look at an example. Imagine a weather app predicting the chance of rain:

Here’s the forecast for rain on any given day. What is the Brier score for the forecast?

Day 1: It predicts a 90% chance of rain, and it does rain.

Day 2: It predicts a 20% chance of rain, and it doesn’t rain.

Day 3: It predicts a 50% chance of rain, and it rains.

Lower scores indicate better predictions. The Brier Score doesn’t just measure whether you got the outcome right or wrong; it also considers how confident you were in your prediction. The Brier Score has some weaknesses, it is useful relative to a prediction’s dificulty, meaning the same Brier Score can have different meaning, depending on how wll other forecasters predict the outcome. The Brier Score also treats overconfidence in incorrect predictions and underconfidence in correct predictions the same way. For example, predicting 90% rain when it doesn’t rain is penalized just as much as predicting 10% rain when it does, bot yield a 0.81 Brier score. Moreover, it doesn’t prioritize impactful errors over minor ones.

Introducing the Foresight Score

To address these issues, let’s introduce the Foresight Score, a more advanced metric designed to encourage sharper and more reliable predictions. The Foresight Score builds on the Brier Score by penalizing overconfidence in wrong predictions more heavily while rewarding high-confidence correct predictions. It’s especially useful for applications where precise, actionable predictions are critical, like decision-making.

The Foresight Score formula is:

Here’s how it works:

Scaling to Intuition: The Foresight Score is inverted and scaled to range from 0 to 1, where 1 represents perfect predictions and 0 represents entirely inaccurate predictions. This makes it more intuitive for users.

Overconfidence Penalty: The weight is calculated as:

The parameter determines how heavily overconfident incorrect predictions are penalized. Larger values of emphasize the cost of overconfidence.

Sharpness Penalty: The sharpness penalty encourages well-calibrated confidence in correct predictions. It is defined as:

Customization: The parameter adjusts the weight of the sharpness penalty relative to the accuracy term, making the score flexible for different contexts.

By combining these elements, the Foresight Score encourages predictions that are both accurate and confident, while penalizing harmful overconfidence. To address these issues, let’s introduce the Foresight Score, a more advanced metric designed to encourage sharper and more reliable predictions. The Foresight Score builds on the Brier Score by penalizing overconfidence in wrong predictions more heavily while rewarding high-confidence correct predictions. It’s especially useful for applications where precise, actionable predictions are critical, like decision-making predicions.

How It Works in Practice

The tentative formula is:

Where: wi: A weight that increases for overconfident incorrect predictions.
This penalizes high-confidence wrong predictions more than low-confidence ones.

Sharpness Penalty: A term encouraging well-calibrated confidence in correct predictions. Defined as:

Why Use the Foresight Score?

The Foresight Score isn’t just about punishing bad predictions—it’s about creating better incentives. Here’s why it matters: Encourages Better Predictions: It penalizes overconfidence in wrong predictions more than underconfidence in right ones, pushing forecasters to calibrate better.

Actionable Feedback: By separating weights and penalties, it provides clear areas for improvement.

Customizable: Parameters like and can be tuned to fit the importance of sharpness or the cost of errors in different contexts.

Holistic Insight: It evaluates prediction quality across individual events, categories, and entire systems, making it a powerful KPI for continuous improvement.

Forecasting is a skill that can be improved with deliberate practice and the right techniques. For those looking to sharpen their prediction abilities, a dedicated section in this guide provides actionable steps and methods to enhance forecasting performance. Whether tracking personal forecasting skill, comparing performance across teams, or evaluating an entire protocol, the Foresight Score helps align incentives towards better decision-making. By adopting this metric, you not only measure performance but actively guide it toward improvement.