Using Monte Carlo Simulation to Calculate Match Importance

Abstract

This article presents a new method of calculating match importance. Match importance is defined as strength of relationship between the match result and a given season outcome. Probabilities of all necessary match result-season outcome combinations are estimated by Monte Carlo simulation. Using actual results of 12 seasons of English Premier League and betting odds, it is shown that both match result and season outcome predictions are realistic. The method provides results that are close to Jennett's approach; however, it does not require ex post information and can be used for any type of season outcome.

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“…Mathematical certainty is a coarse measure of the swing value (Lahvička, 2015). Only 6.0% of team‐games are mathematically certain, most of which occur by the 15th game of a season.…”

“…This incentive-based definition differs from past works saying that a game is important if its outcome has a large impact on end-of-season-outcomes (Geenens, 2014;Schilling, 1994). For example, Lahvička (2015) defines importance as the "strength of relationship between the match result and a given season outcome." According to Lahvička, a game that features a strong team against a weak one is unimportant because the outcome is almost certain.…”

“…This incentive‐based definition differs from past works saying that a game is important if its outcome has a large impact on end‐of‐season‐outcomes (Geenens, 2014; Schilling, 1994). For example, Lahvička (2015) defines importance as the “strength of relationship between the match result and a given season outcome.” According to Lahvička, a game that features a strong team against a weak one is unimportant because the outcome is almost certain. In contrast, we assert that such a game can still have a large swing value for one (or both) of the teams, as will be the case if the outcome of the game has a large impact on a team's chance to qualify for the playoffs.…”

“…According to Table 1, the swing value varies between zero and 0.41, with a mean value of 0.17 and a standard deviation of 0.9. Figure 4 depicts swing values for games 1–15, broken down into five categories akin to Figure 1 of Lahvička (2015). Swing values vary at each stage of the season and as the season progresses.…”

“…The swing represents the increase in the probability that the team qualifies for the post-season playoffs from winning a given game. The swing value generalizes the notion of mathematical certainty (i.e., whether a team can still influence its qualification status) and expands on other measures of game importance used in the literature (Lahvička, 2015;Lei & Humphreys, 2013;Scarf & Shi, 2008;Schilling, 1994). Computing exact swing values requires considering all possible future path-dependent game outcomes, which is beyond computational possibility.…”