Calculating Score

Estimating the accuracy of a prediction

Suppose that a player makes a Bitcoin (BTC) price prediction with an initial price at the start of the week for 1 BTC is 100,000 USD. We will consider a hypothetical pool containing 1 BTC and 100,000 USD. The total value of the pool is 200,000 USD, with 50% of the value in BTC and 50% in USD. We define the state of the pool as a vector whose components represent the percentage of the value of the assets in the pool. In this example, the initial state of the (BTC, USD) pool is (50.00, 50.00).

Suppose that the closing price at the end of the week for 1 BTC is 150,000 USD. Here, although the pool remains fixed with 1 BTC and 100,000 USD, the state has changed. The total value of the pool has increased to 250,000 USD. Accordingly, BTC takes up 60% (= 150,000 / 250,000) of the pool’s value while it is 40% (= 100,000 / 250,000) for USD. Consequently, the closing state of the pool is (60.00, 40.00).

Forecasting Bitcoin price is equivalent to predicting the closing state of this pool. For instance, a player wants to predict that BTC will increase by 20%, bringing the value of 1 BTC to 120,000 USD. Following the same calculation as above:

• The total value of the pool is 220,000 USD;

• BTC takes up 120,000 / 220,000 = 54.45% value of the pool;

• USD takes up 100,000 / 220,000 = 45.45% value of the pool.

Hence, the submission of this user is represented as (54.55, 45.45).

In summary, the two vectors for the submission and the actual result are as follows.

To determine the accuracy of a prediction, we choose a scoring formula based on the angle θ between these two vectors. The angle can be easily calculated as:

Then, the raw score is determined by:

The closer the two vectors are, the smaller the angle and the higher the score. The raw score will be assigned on a range of 0–1000 points, with 0 being the lowest and 1000 being the greatest.

Bonus points

Players also receive bonus points for making early predictions. Forecasting the price of Sunday-BTC on Monday is far more difficult than forecasting it on Thursday. Thus, bonus points help to ensure that participants are treated fairly when they make predictions on different days of the week.

We offer the following bonus levels:

• 100 points on Monday;

• 60 points on Tuesday;

• 30 points on Wednesday;

• None on Thursday.

Therefore, the maximum score a player can achieve is 1100 points.

One quarter after the official mainnet event, this scale will be adjusted by players who have the governance right (see more in Tokenomics).