Aggregate Performance Metric, Pt. III  Examples
Posted by: source
(Saturday, November 7, 2020)
For the previous articles, see Aggregate Performance Metric, Pt. I  Overview and Aggregate Performance Metric, Pt. II  Breakdown.
Here are a few simple examples to illustrate how it could work for a 6v6 match given a rank displacement scale of 0.025 (2.5%). In each example, the number of players is 12 and the match rank is 18,000. As a result, Î± ~0.833 and Î² ~0.167 which means that 15,000 points will be distributed for player impact and 3,000 points will be distributed for team success.
Example #1: Balanced, Win/Loss, Kills = 10
In this example, the teams are assumed to be balanced as every player starts with a rank of 1500. There are two standout players with respect to impact, player_a and player_g, the latter of which plays exceptionally well despite a match loss. Since there is only one category counted towards impact points, the weighting is irrelevant.
Example #2: Balanced, Win/Loss, Kills = 10 and Revives = 5
This example is exactly the same as the previous one, except that revives are factored into the player impact calculation in order to better characterize the impact of medics. The difference is reflected in their consequent rank where player_a and player_g, two killfocused players gained less points while player_k lost less points. The rest of the players who had an average number of revives moved slightly towards the mean.
Example #3: Unbalanced, Win/Loss, Kills and Revives
This example has the same statistics and outcome of the previous two, but starts with rankings that more accurately reflect the skill levels of the players; the team ranks skew towards the winning team by 500 points. As a result, a number of players lose points despite their team winning since they have a belowaverage impact on the match.
Example #4: Unbalanced, Tie, Kills and Revives
The last example is the same as the previous except for that the match result is a tie. The axis team overcomes their rank disadvantage to tie the match which earns them points relative to that disadvantage. At this point, the distribution of points after the match is very reasonable with only a few outliers which highlights the importance of assigning weights fairly among a wellrounded (but not excessive) set of statistical categories.
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