Uploaded August 2023 | Updated September 2026, 1 week ago
Here, we derive the mathematics behind the Elo rating system, and talk about how they're used in Chess, Pokémon, and various digital video games. We also briefly discuss alternatives to Elo, such as Glicko, league systems (as in League of Legends or other games in its genre), and Smogon's GXE, and the advantages and distadvantages these systems may have.
References:
Elo, A. "The Proposed USCF Rating System, Its Development Theory, and Applications", (1967): uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1967/1967_08.pdf#page=26
Elo, A. "The USCF Rating System, A Progress Report", (1960): uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1960/1960_03_1.pdf
"FIDE Rating Regulations effective from 1 July 2014": web.archive.org/web/20140701031750/http://www.fide.com/fide/handbook.html?id=172&view=article
Zarel "Everything You Ever Wanted to Know About Ratings", (2016): smogon.com/forums/threads/everything-you-ever-wanted-to-know-about-ratings.3487422
Spirit of the Law "How Elo Ratings Are Calculated", (2017): youtube.com/watch?v=GTaAWtuLHuo
Glickman, M. "The Glicko system": glicko.net/glicko/glicko.pdf
Glickman, M. "Example of the Glicko-2 system", (2022): glicko.net/glicko/glicko2.pdf
X-Act "GXE (GLIXARE): A Much Better Way of Estimating A Player's Overall Rating Than Shoddy's CRE", (2009): smogon.com/forums/threads/gxe-glixare-a-much-better-way-of-estimating-a-players-overall-rating-than-shoddys-cre.51169
Image Credits:
Manim Community Edition: https://www.manim.community/
League of Legends logo, by Riot Games, Public domain, commons.wikimedia.org/w/index.php?curid=85762404
Chess piece, by Cburnett, CC BY-SA 3.0, commons.wikimedia.org/w/index.php?curid=1499808
Pokémon Showdown logo, by unknown, Fair use, play.pokemonshowdown.com
Elo, by unknown, Fair use, en.wikipedia.org/w/index.php?curid=21291794
ELO, by TyrystorELO, Public domain, commons.wikimedia.org/w/index.php?curid=9883142
Magnus Carlsen, by Этери Кублашвили (Eleri Kublashvili), CC BY-SA 3.0, commons.wikimedia.org/w/index.php?curid=120906569
Bobby Fischer, by Bert Verhoeff for Anefo - Dutch National Archives, CC0, commons.wikimedia.org/w/index.php?curid=22577887
Special Thanks:
Mishi, Lucia, and Alessandro for participating in the inaugural Competition to Highlight Elo Systems Simply
Michelle for coming up with a non-monotonically-increasing function
Here, we derive the mathematics behind the Elo rating system, and talk about how they're used in Chess, Pokémon, and various digital video games. We also briefly discuss alternatives to Elo, such as Glicko, league systems (as in League of Legends or other games in its genre), and Smogon's GXE, and the advantages and distadvantages these systems may have.
References:
Elo, A. "The Proposed USCF Rating System, Its Development Theory, and Applications", (1967): uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1967/1967_08.pdf#page=26
Elo, A. "The USCF Rating System, A Progress Report", (1960): uscf1-nyc1.aodhosting.com/CL-AND-CR-ALL/CL-ALL/1960/1960_03_1.pdf
"FIDE Rating Regulations effective from 1 July 2014": web.archive.org/web/20140701031750/http://www.fide.com/fide/handbook.html?id=172&view=article
Zarel "Everything You Ever Wanted to Know About Ratings", (2016): smogon.com/forums/threads/everything-you-ever-wanted-to-know-about-ratings.3487422
Spirit of the Law "How Elo Ratings Are Calculated", (2017): youtube.com/watch?v=GTaAWtuLHuo
Glickman, M. "The Glicko system": glicko.net/glicko/glicko.pdf
Glickman, M. "Example of the Glicko-2 system", (2022): glicko.net/glicko/glicko2.pdf
X-Act "GXE (GLIXARE): A Much Better Way of Estimating A Player's Overall Rating Than Shoddy's CRE", (2009): smogon.com/forums/threads/gxe-glixare-a-much-better-way-of-estimating-a-players-overall-rating-than-shoddys-cre.51169
Image Credits:
Manim Community Edition: https://www.manim.community/
League of Legends logo, by Riot Games, Public domain, commons.wikimedia.org/w/index.php?curid=85762404
Chess piece, by Cburnett, CC BY-SA 3.0, commons.wikimedia.org/w/index.php?curid=1499808
Pokémon Showdown logo, by unknown, Fair use, play.pokemonshowdown.com
Elo, by unknown, Fair use, en.wikipedia.org/w/index.php?curid=21291794
ELO, by TyrystorELO, Public domain, commons.wikimedia.org/w/index.php?curid=9883142
Magnus Carlsen, by Этери Кублашвили (Eleri Kublashvili), CC BY-SA 3.0, commons.wikimedia.org/w/index.php?curid=120906569
Bobby Fischer, by Bert Verhoeff for Anefo - Dutch National Archives, CC0, commons.wikimedia.org/w/index.php?curid=22577887
Special Thanks:
Mishi, Lucia, and Alessandro for participating in the inaugural Competition to Highlight Elo Systems Simply
Michelle for coming up with a non-monotonically-increasing function
![[RF5] How to Craft QUAD-ABILITY ACCESSORIES – Teachers Guide to Rune Factory 5](https://i.ytimg.com/vi/Ew14AqBw4A8/mqdefault.jpg "[RF5] How to Craft QUAD-ABILITY ACCESSORIES – Teachers Guide to Rune Factory 5
gotten through most of the game, back to video-making!!")
![[RF4S] A Teachers Guide to Weapons, Tools, and Staves - Advanced Forging Mechanics, Range, Status](https://i.ytimg.com/vi/GriWfQSPyyM/mqdefault.jpg "[RF4S] A Teachers Guide to Weapons, Tools, and Staves - Advanced Forging Mechanics, Range, Status
These videos keep getting longer and longer... scope creep is a real thing. But yeah, so here we revisit light ore, elements and rarity, properly go over status, range, tools, and magic, and where to get the important materials. Hopefully you enjoy!!
0:00 Introduction and Revision
4:24 Differences between Armour and Weapons - Bonuses
7:40 Why Rarity is important for Weapons
9:31 Status Effects
12:23 Status Materials (Holy Spore, Melody Bottle, Chimera Tail, Giant Golden Turnip)
15:40 Elements and Elemental Crystals
16:55 Shade Stone
21:01 Range Mechanics
22:05 Range Materials (Glitta Augite and Racoon Leaf)
24:56 Summarising Range
27:25 Drain Materials (Legendary Scale, Love Crystal)
29:05 Other Materials (Invisible Stone, Scrap Metal+)
32:18 High Rarity Materials and Locations (SPOILER SECTION)
38:44 Upgrading Tools
40:26 Light Ore, Sacred Pole, and other Tools
42:40 Upgrading Staves
48:18 Example Weapon: Max Attack
49:55 Example Weapon: Range and Status
50:36 Example Weapon: Love, Drain, and Attack
51:23 Conclusions and Summary
Crafting Playlist: https://www.youtube.com/playlist?list=PLzcYp4bo2JIQfMXHo9uyoITIca7ew34En
RF4S Datamining Compendium (with Rarity Values): https://docs.google.com/spreadsheets/d/1UPdNZGUyHLMOTYWqz5KJYCnR0ZnsMENifPi4UAVZeV8/
HELL Mode without Crafting: https://youtu.be/mPRIPCQJYW0")
