WHR… and how it really differs from Elo/Glicko

23 Jun , 2020,
Jason

If you’re a frequent visitor, you may have noticed that we’ve added four purely mathematical variants of named rating systems to the ranking pages.  Two versions of Elo, Glicko-1 and the latest being WHR.

You’ll see some basic info within our FAQ page and can Google for more.  To make a long story super short, Elo is the grandfather of most like systems.  It has been around for ages and is super simple.  Elo doesn’t care about inactivity or inconsistencies.  The process starts from day 1 and moves chronologically throughout time, every competitor starts with a starter rating, which is then modified with each result.  Glicko-1 is a very similar system to Elo, except it has the concept of “rating deviation” which allows competitors’ ratings to deviate more or less, given when they fought last.  There is also a second version of Glicko, which tosses in a factor called volatility — it is a major complication with extremely limited benefit.

In comes WHR.  Again, it is based on Elo, but is setup to take numerous passes throughout history.  With each pass, it “learns” from what happened in surrounding events.  This makes it an excellent system for reviewing the past and in trying to determine when a competitor was really at their peak.  Whether it paints a more accurate ranking picture… who knows?

Using the four systems we have in place, let’s take a look at the following events and the rankings at the end of the story.

Fighter A [W-SD] Fighter C – Day 1
Fighter B [W-KO] Fighter D – Day 1
Fighter A [DRAW] Fighter B – Day 30

Fight Matrix

#1 Fighter B (11.6 pts)
#2 Fighter A (10.9 pts)

Fighter C & D both below the starter rating of 10 and don’t qualify for a ranking.  With the standard system, we draw the line at 10 and toss out the slop.  Mathematically, C would be marginally ahead of D as he lost a split to a debuting fighter and did not get knocked out.

 

Elo “K170”

#1 Fighter A (1085)
#1 Fighter B (1085)
#3 Fighter C (915)
#3 Fighter D (915)

In basic Elo, a win is a win.  As a result, you have two sets of ties.

 

Elo “Modified”

#1 Fighter B (1102)
#2 Fighter A (1081)
#3 Fighter C (954)
#4 Fighter D (862)

The “modified” version of Elo has some smarts built in.  As a result, B comes out on top as he got a KO win.

 

Glicko-1

#1 Fighter B (1077)
#2 Fighter A (1028)
#3 Fighter C (990)
#4 Fighter D (904)

Pretty much agrees with the modified Elo version, but less aggressive like the basic version.

 

WHR

#1 Fighter B (1058)
#2 Fighter A (1016)
#3 Fighter C (1003) (0-1 record, above starter rating)
#4 Fighter D (935)

This is the only version which pushed Fighter C above the starter rating (1000).  Why?  This highlights the real argument for using WHR….

Since Fighter A drew with Fighter B, who got a KO win (instead of a split decision), this retroactively increased the quality of Fighter C’s close loss to Fighter A.  Marvin Vettori is a fighter who benefited from this in reality.  Due to his split decision loss against Adesanya, he’s tied somewhat closely to Adesanya’s success and has a #11 ranking in the WHR system.  However, this linkage becomes weaker as time increases between this bout and present.  In WHR, every result has a trickle down effect.  The WHR system is run ~60 times against the entire MMA history every time the rankings are updated to analyze how results affect other results, etc., and so forth.

Do I think WHR is the magic bullet for predicting MMA?  No.  It probably isn’t a viable ranking system either.  However, it is an incredible system to take a look at the past, with all the knowledge as we have it today.