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The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.
These values are used to calculate an E value for the estimate and a standard deviation (SD) as L-estimators, where: E = (a + 4m + b) / 6 SD = (b − a) / 6. E is a weighted average which takes into account both the most optimistic and most pessimistic estimates provided. SD measures the variability or uncertainty in the estimate.
Sports ratings systems use a variety of methods for rating teams, but the most prevalent method is called a power rating. The power rating of a team is a calculation of the team's strength relative to other teams in the same league or division.
A Bayesian average is a method of estimating the mean of a population using outside information, especially a pre-existing belief, [1] which is factored into the calculation. This is a central feature of Bayesian interpretation. This is useful when the available data set is small. [2] Calculating the Bayesian average uses the prior mean m and a ...
In decision theory, the weighted sum model (WSM), [1] [2] also called weighted linear combination (WLC) [3] or simple additive weighting (SAW), [4] is the best known and simplest multi-criteria decision analysis (MCDA) / multi-criteria decision making method for evaluating a number of alternatives in terms of a number of decision criteria.
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For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().
The rating percentage index, commonly known as the RPI, is a quantity used to rank sports teams based upon a team's wins and losses and its strength of schedule. It is one of the sports rating systems by which NCAA basketball , baseball , softball , hockey , soccer , lacrosse , and volleyball teams are ranked.