I opened the Fight Matrix Program for the Moicano and Nolan card on 31 October with a coffee and no real plan, and ended up staring at one row for twenty minutes. The lightweight main event, Renato Moicano (listed under his family name, Carneiro) against Tom Nolan. Four rating systems, all four picking Moicano, and no two of them agreeing on by how much.
Elo K170 had him at 73.16%, the modified Elo a hair higher at 73.65%, Glicko-1 at 76.16%, and WHR way out ahead at 82.17%. Same two men, same records, and a nine point spread between the most careful number and the boldest.
So why run four systems side by side? Because each one answers a slightly different question, and most of those questions were first asked over a chessboard, by people who never thought about a cage.
A physics teacher in Milwaukee
Arpad Elo was born in 1903 in Egyházaskesző, then part of the Kingdom of Hungary, and came to the United States with his parents in 1913. He taught physics at Marquette University in Milwaukee from 1926 until 1969, a really long time to spend in one building, and in between classes he won the Wisconsin State Championship eight times.
US chess already had a rating system, put together by Kenneth Harkness in 1950, and Elo thought he could do better. His version was approved at a US Chess Federation meeting in St. Louis in 1960, FIDE took it up for the whole world in 1970, and Elo kept doing FIDE’s calculations himself into the mid-1980s. Imagine being the one guy whose sums decided who the best chess players on the planet were!
The clever bit, the one every fight model still leans on, is that an Elo rating is really a prediction wearing a number, because the gap between two ratings turns straight into an expected score. A 100 point edge works out to about 64%, 200 points to about 76%, and 400 points to something like 91%. Back on the program, Moicano’s Elo K170 rating sits 174 points above Nolan’s and comes out at 73%.
The K that decides everything
After every result the rating moves, and the size of that move is set by the K-factor. Elo’s own values were 16 for masters and 32 for everyone weaker, and FIDE today uses somewhere between 10 and 40 depending on how established a player is.
Going by the name, Fight Matrix’s Elo K170 runs with a K of 170. A hundred and seventy! It looks enormous next to chess, and after a minute’s thought it makes total sense. A busy chess player can sit down for a hundred rated games in a year. A busy fighter might possibly get three. Nudge the rating by a chess sized amount per fight and a fighter would retire long before the number caught up with him.
The price is that one strange night counts for a lot. A flash knockout, a first-round cut stoppage, a terrible weight cut, all of them hit at full force, and the formula can’t know which were flukes. The Elo Modified line sneaks in a bit more context, and the program’s notes say it “includes any considered fight-specific advantages, such as home advantage.” The win percentages also fold in the favourite’s share of the chance of a draw, a really nice bit of honesty in a sport where draws hardly ever happen.
How sure is the number?
In 1995 the statistician Mark Glickman put his finger on what Elo leaves out. Two players can carry the same rating and deserve very different amounts of trust. One has played five hundred games. The other has played six and won all six.
His Glicko system gives every rating a second number, the rating deviation or RD, which is basically how much the system believes its own estimate. A brand new player starts with an RD of 350, the system admitting it has no clue yet. Add and subtract 1.96 times the RD and you get a 95% range, so a player rated 1500 with an RD of 50 is expected to truly sit somewhere between 1402 and 1598. The less sure the system is, the further one result moves you, and the RD shrinks as evidence piles up.
Fight fans make this argument at the bar every weekend. The unbeaten regional prospect and the thirty fight veteran can look equally good on paper, and everybody knows one record is way more solid than the other. Glicko just writes the doubt down. It holds the potential to explain why the Glicko-1 line is a couple of points bolder than the Elo lines, though that is my guess and not anything the page says. Lichess, Chess.com and Counter-Strike 2 all run on some form of Glicko, so an awful lot of people get rated by Glickman’s maths without ever hearing his name.
Coulomb and the problem of looking back
Elo and Glicko share one habit. They update one result at a time and never look back. Beat a nobody in 2019, watch that nobody become a champion by 2022, and the points you got in 2019 stay exactly what they were. Every fan who has said “people forget who he beat early on” is complaining about this flaw, whether they know it or not.
In 2008 Rémi Coulom presented a Whole-History Rating at the Computers and Games conference in Beijing. WHR goes back over the whole rating history of every player and works it all out again together, so an old win can gain value years later when the opponent turns out to be good. Coulom tested it against Elo, Glicko and Microsoft’s TrueSkill and reported better predictions than all three, with a new game still added in under a thousandth of a second.
That is the system that came out boldest on the Moicano row, at 82%. Which kind of fits, since WHR is the one that has gone back and re-read everybody’s whole career, opponents included.
Every ranking gets mail
None of these systems can fix how people feel about where they land. Elo’s critics have long pointed out that a rating gives people a reason to stop competing, since sitting still is the safest way to protect a high number, and Wizards of the Coast ended up dropping Elo for Magic: The Gathering in favour of a points system. Anybody who has watched a champion wait out a division will recognize that one right away!
Anyone who runs a public ranking, a fight database, a gym ladder, a regional promotion’s matchmaking list, knows the other half of it. The mail. The manager who swears his fighter was robbed. The cousin. The guy who found a 2014 amateur result you missed and is definitely right about it. When two or three people handle that inbox in their spare time, a help desk like Maxdesk turns the emails into tickets and doesn’t bill per agent, so the friend covering Saturday nights gets their own login instead of a shared password.
Where the maths went next
Ratings did not stay on the chessboard for long. The same idea, score something from its results and let the number predict the next one, runs across video game matchmaking, sports models and a good deal of casino software, where affiliate platforms such as MAP track which partner site sent which player and what that player turned out to be worth. More or less Elo’s habit of trusting results over reputation, sat in a back office.
Then there is the one place ratings stop working. The slots at a UK mobile casino like Jackpot Mobile Casino carry no rating at all, because each spin is settled by a random number generator with no memory of the spin before it. No form, no K-factor, no history to go back over, and the RTP on a game is a long-run average across a huge number of spins that stays put however your evening goes. A cold run does not make the next spin due, worth remembering for anyone who spends the week reading fight models and stands a chance to start seeing patterns everywhere. Set a budget before you start and stop when it is gone.
Four numbers, one fight
So the spread on that one row is the systems doing their jobs. Elo and its modified cousin read the recent results, Glicko adds how sure it can really be, and WHR looks at the whole history from where we stand now. Fight Matrix prints all four side by side and lets you see where they part ways, honestly the most useful thing on the page.
Arpad Elo built his formula for chess players in Wisconsin, and more than sixty years later it is sizing up a lightweight main event on Halloween. On the night the cage gets the last word, the way it always does, and afterwards all four numbers update, one of them all the way back to the beginning.