Frequency

Frequency, more precisely relative frequency, is the proportion of times a result has appeared over a series of actual trials. It is an observed, after-the-fact quantity: it is measured retrospectively, by counting what actually happened, and not by reasoning about what should happen.

The mental image is that of a logbook. Each result is recorded as the trials go by, then one looks at what share of the total belongs to each outcome. This share, between 0 and 1, can also be expressed as a percentage and sums up, at a glance, the actual behavior of the experiment.

The calculation is a simple division: the number of times a result appears divided by the total number of trials. If tails comes up 47 times in 100 flips, its frequency is 47 divided by 100, that is 0.47 or 47%. The sum of the frequencies of all the outcomes of a single experiment is always 1, since it covers the whole set of trials.

The distinction from probability is essential. Probability is a theoretical value, fixed in advance by the nature of the experiment; frequency is an empirical value, which varies from one series to another. On a fair coin, the probability of tails is exactly 0.5, but the frequency observed on a given sample will rarely be exactly 0.5.

The two notions come together thanks to the law of large numbers: the more the number of trials increases, the more the observed frequency approaches the theoretical probability. A common trap is to judge an experiment rigged on the basis of a small sample, when a gap between frequency and probability is perfectly normal over few trials.

Frequency is the natural tool for checking the fairness of the site's draws. By rolling a virtual die, flipping a coin, or running a number generator a large number of times and recording the proportions obtained, one can observe their convergence toward the expected probabilities.