[Math] Conditional K-Factors, Low reliability and MMR [More Math, Practical Math, Do you find Math fun?]

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[Math] Conditional K-Factors, Low reliability and MMR [More Math, Practical Math, Do you find Math fun?]

Posting this here for reference. Trophies can be tricky to understand. Because. Math. But feel free to comment.

Empires uses a K-Factor of 61.

The highest trophy adjustment is +60/ -1, the lowest is +1/ -60.

Elo’s K-Factor

K-Factor is one constant Arpad Emmerich Elo did not have to worry about a lot. Matches involving rankings usually required the presence of a judge, and a scorekeeper, so frequency of matches, and opponent pool, were fairly stable.

Players sitting on high rankings and playing less and less the higher the rank were the top problems.

But subsequent applications usually tweaked K-Factor significantly. Battle frequency, team/ hero strength and opponent pools having a huge impact.

Conditional K-Factors

Live PvP usually uses conditional K-Factors

Season start

The first 30-50 battles of the Season, K-Factor is double

Example
1st Battle of the Season for Player A, Empire’s K-Factor would be 122

Players are usually very active at the start of a new Season.

Lower arenas

In lower arenas, K-Factor is increased +25% to +100%

Example
Bronze arena has K-Factor +100%

1st Battle of the Season for Player A, Empire’s K-Factor would be 244 in Bronze arena.

1000th Battle of the Season for Player A, Empire’s K-Factor would be 122 in Bronze arena.

Elo’s math was never designed for teams/ heroes of such large variation in strength. It still works surprisingly well.

But MMOs had to find other ways to adapt the math to their situation. Especially since building up a Rank #1 team often takes years, even with periodic catch up events.

Adjusting K-Factor based on arena helps deal with the unreliability of Elo’s rating when players are squished together at the bottom, helps with Elo rating deflation when new power ups are introduced ( troops, Barracks, Classes, Costumes, etc. ) and helps with players returning in large amounts when an update comes out for a game.

Hidden public rank or low reliability

Conditional K-Factor, Live PvP, may hide public rank, and trophies, for the first 3-12 battles of a Season ( if Seasons ), Week ( if weekly quests) or day ( if daily quests).

Players are shown their public rank, and trophies, after the battle, but not before.

Example
1st Battle of the Season for Player A, rank, trophy adjustment and trophies, of opponent would be hidden.

This is usually to emphasize known times of high fluctuations in rankings when Elo’s math has the highest chance of being wrong due to increased battle frequency and rapid swings in size of opponent pools.

MMR or private ranks

Live PvP can have multiple private ranks. These are called Match Making Ranks (MMR) and are not visible to the player.

Example
A wizard hero might have a MMR versus wizards and an MMR versus warriors.

Elo’s math was developed for two opponents with equal tools. It still works surprisingly well for MMOs. Separate MMR help deal with opponents that may have a huge advantage against an entire class of opponents or situations were battle rules are drastically different.

If applied to Empire, MMR would probably break down as the following:

MMR defense team
MMR attacking versus purple center
MMR attacking versus yellow center
MMR attacking versus blue center
MMR attacking versus green center
MMR attacking versus red center

I am not sure why MMR are not visible, but considering the way most MMOs have a very vocal minority, I will guess a combination of trade secrets and hiding it from trolls.

Resource intensive

I am beginning to see another reason why Devs went with computer defense instead of live PvP. Live PvP is a lot more coding and server CPU cycles.

2 Likes

Hey… I try to be clear. I show my work whenever I can. :wink:

1 Like

I’m here for very long, know the game pretty well and still don’t understand anything about your post :face_with_monocle:

But i pretend i understand everything showing my other glasses :nerd_face:

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@Elpis LMBO, I was going to challenge @Gryphonknight in a game battle (mock) because he assaulted my limited understanding. :upside_down_face::joy::joy::joy::joy: Although to be fair he did ask “Do you find math fun”. I do! Thank You for trying to educate me, I did understand a bit​:facepunch:t3:

:Fistpunch:* Argggg…:grin:

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