The Basics | The Algorithm | Mission & Vision | Support
Hierank incorporates zero legacy bias or opinion bias
(It’s not poll-based).
It considers the ENTIRE ecosystem of play – every single score.
It’s self-balancing, with all outcomes indexed in-relation to all other outcomes.
It is self-reconciling, increasing in certainty each week.
General Walk Through
This guide won’t give every intricacy, but by the end, you’ll understand the Hierank algorithm’s guiding principals, what most values mean, and how they interact.
I. Foundation
First, if we claim to know how to rank for best, we better define what that is. Hierank’s definition:
Best
Having the highest probability to decisively defeat any given opponent.
Better
Having higher probability to decisively defeat any given opponent.
Worse
Having higher probability to decisively lose to any given opponent.
In these terms, “BEST” looks like the following:
Winning…
[success]
…big or easily against the majority…
[force]
…and in the most-difficult challenges.
[grit]
II. Building Blocks
Hierank rewards the aforementioned activities (or penalizes their opposites), with assigned values, and sums all of those activities over the entirety of the season.
It uses the following values within each contest to represent the ideas of success, force, & grit, and to overall-rate each performance:
Dominance Factor
(success, force)
Comparative Factor
(force, grit)
Hierarchical Factor
(grit, success)
(0 Perf Quot = 50 Game Pow).
So what do these values mean?
Dominance Factor
The Dominance Factor represents how dominant the Winner was over the Loser.
Each receives an equal-but-opposite Dominance Factor in that contest, the Winner’s positive & Loser’s negative. This value is closer to 0 for tight contests, and greater-in-magnitude for blowouts.
Dominance Factor is determined by a non-linear function of the score-spread and score-ratio, with additional bonus for shutouts. For every Overtime period played, the game’s DF is halved.
A team’s Dominance Factors over the course of the season can be averaged to give a Dominance Average, which reveals how well a team handled their specific opponents, generally. This rewards consistency over blowouts better than a PF-PA analysis does, and adds valuable in-game context to the W-L record.
Like the Dominance Average, every stored value in Hierank is derived from the Dominance Factors of multiple match-ups.
To accurately rank a huge pool of 255 teams though, each with very-limited clashes (12-15 maximum), we need to step beyond direct team-to-team match-ups, and think bigger. We still need more context.
We still need more context, unless you want to believe Princeton is the second-best team in the country…
Comparative Factor
The Comparative Factor represents how well the subject team performs against each opponent, compared to all other teams that opponent faced.
Rather than only make direct comparisons with our team & 9-12 other teams…why not with 81-144 other teams?
And before you object with, “Transitive property in sports isn’t a thing!” consider:
This may be true in a point-for-point sense, or when three or four competitive teams end up in a Rock-Paper-Scissors loop due to match-up conditions; but the hierarchy of Great-beats-Good-beats-Mediocre-beats-Poor, who in-turn gets crushed by the Great, has naturally formed in the vast majority of environments since the dawn of competition.
Counter-examples are memorable because they are rare; but across the sum of all transitive observations, very strong assessments can be made.
Using other opponents’ results helps develop a baseline for expected performance, just like in any scientific testing. This gives more context to our Dominance Factor, and allows us to compare our subject team against a much greater portion of the field.
It would take forever to manually compare each second-degree match-up, but luckily, math is awesome:
Thanks to the associative & cumulative properties, we can take the difference between our subject team’s Dominance Factor in the match and the Dominance Factors of every team that has faced our opponent thus far. But rather than look into the Dominance Factor of every team that faces our opponent in those matches, we can take the numeric opposite (+/-) of our primary opponent’s Dominance Average to get the same cumulative result.
Math is awesome.
Hierarchical Factor
Description in-process