As a basis for evaluating the likelihood of that outcome, the empirical probability, relative frequency, or experimental probability utilizes the number of occurrences of an outcome within a sample collection. It is possible that the incident will occur on the basis of the findings of the collected data. The empirical probability, in a more general context, measures probabilities from experience and observation. An empirical probability is closely connected to an event’s relative frequency.

The formula for Empirical Probability:

Empirical Probability = Number of Times Occurred / Total No. of Times Experiment Performed

Where:

Number of Times Occurred refers to the number of times a favorable event occurred;

Total No. of Times Experiment Performed refers to the total amount of times the event was performed.

Example of Empirical Probability

By following more assumptions in the form of a statistical model, the empirical probability can be enhanced: if such a model is fitted, it can be used to estimate the probability of the event described. Empirical proof must be obtained in order for a hypothesis to be proven or disproved. There are two other major types of probabilities, apart from empirical chance:

• Classical probability – Classical probability refers to probability which is based on formal reasoning (also called a priori or theoretical probability). The classical chance, for instance, of having ahead in a coin toss is ½.
• Subjective probability – Subjective probability refers to likelihood-based on experience or personal opinion. For instance, if an analyst assumes that “there is an 80% chance that in the next month the S&P 500 will reach all-time highs,” he/she is using subjective probability.

Using real market data, an empirical analysis will be carried out. For instance, on the capital asset pricing model (CAPM), several empirical studies have been performed, and the results are slightly mixed. A benefit of using empirical probabilities to estimate probabilities is that this method is relatively free of assumptions. In certain investigations, the model holds in true circumstances, yet most examinations have refuted the model for anticipating returns. An immediate gauge could be found by checking the quantity of men who fulfill the two conditions to give the exact likelihood of the joined condition.

The empirical probability would be either 0 percent or 100 percent if a person wanted to know the probability of having ahead in a coin toss but used only one sample. A drawback exists in calculating probabilities that are either very close to zero or very close to one by using empirical probabilities. Although the model is not entirely accurate, that is not to suggest that the use of the CAPM is not correlated with any utility. For example, CAPM is also used to measure the weighted average cost of capital of a business.

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