Multinomial Distribution World Premier League Soccer Game Outcomes.

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Multinomial Distribution World Premier League Soccer Game Outcomes

Multinomial Distribution Used to model a series of n independent trials, where each trial has k possible outcomes (categories) The probability of i th category occurring on any given trial is p i subject to p 1 + p 2 + … + p k = 1 The random variable Y i denotes the number of trials in which the i th category occurred: Y 1 + Y 2 + … + Y k = n Note that once we have observed Y 1, Y 2, …, Y k-1, we have Y k = n - Y 1 - … - Y k-1 similarly, p k = 1 - p 1 - … - p k-1

Multinomial Distribution – Mathematical Form - I

Multinomial Distribution – Mathematical Form - II

Multinomial Distribution – Mathematical Form - III

Examples – World Premier Soccer Leagues Nations: England, France, Germany, Italy, Spain (2013) League Play: Each team plays all remaining teams twice (once Home, once Away) Games can end in one of 3 possible ways with respect to Home Team: Win, Draw (Tie), Lose

Probability Calculations

Distribution of Number of Points in Sample Points are assigned such that a Win gets 3 Points, Draw gets 1, Loss gets 0