the world of the ELO rating system - LMLlml.org.uk › wp-content › uploads › 2016 › 08 › koroliuk_mariia.pdf · Koroliuk Nicholas R Moloney. ELO rating in the real life screenshot

the world of the ELO rating system

Mariia 
Koroliuk

Nicholas

R Moloney

ELO rating in the real life

screenshot from the movie “The Social Network”

A -rating Ra B -rating Rb

- expected score (for A)

S - gained score (for A)a

- new rating for A

vs.

…and in the chess

experience

K = 40 (30 before july 2014,25…)

30 games 18th birthday

2300

K = 20 K = 10

2400

K factor (FIDE official since July 2014)

(whatever happens first)

issues

• Game activity versus protecting one's rating

• Selective pairing

• Ratings inflation and deflation. Example, Around 1979 there was only one active player (Anatoly Karpov) with rating >2700, September 2012 - guess? 44

DataData comes from https://ratings.fide.com that

publish the records every 3 months since 2001 and every months since September 2012.

https://ratings.fide.com

Distribution of different ratings

Data

Typical evolution over time

time (1=3 months period since Jan 2001)

ELO

ratin

g

selected players , that plays actively and around 30 years old at t=0

AR(1)?

Linear around (0,1/2) with m=0.0014

theoretical prediction:
coefficient: 1-mlk=0.78 for L=10 (games) K=15
(average parameters)

We proved, that the score evolution for stable active player is an AR(1) process both empirically and theoretically with parameter alpha of 1-mKL (m- scope of the curve, L -average amount of games per time interval) and variance that depends on how much player vary in good days and bad days.

Estimation Results 1 -variance

stronger players plays more stable

Estimation Results 2 -alpha

predicted level

only regular players born from 1970 to 1975

?

WHO IS THIS GUY?

Palac,

Mladen

time

ELO

ratin

g

played a lot!

around 50 games

Recalculate alpha:

coefficient: 1-mlk=0.4 for L=50 (games) K=10

diffe

renc

e fro

m th

e m

ax

learn

ing p

eriod sta

ble period (AR(1))

decline

Learning periodWe also proved, that if person enters the list with some fixed stable level starting from smaller level learning much evolve in exponential speed.

However, predicted speed of learning is always higher that empirical speed. 


The explanation is that 
We are improving while learning.

extreme values

Is there some possible maximum?

What are the chances for a really-really strong player (more

that 3000) being born in next year?

Generalized Pareto Model: really good fit- helps to explore events, that never

happened

data stops here,

but the model could be

continued

What is the chances

the event of person

with 3000 ELO will appear?

p=4e-10


exampleconditional probability on p>2600

1-(1-p)^n=0.1 —> nlog(1-p)=log(0.9)

—> n=2E8 


now there is p=7e4 players in FiDE list.

on whole earth,

there is 7E9 people
(which means

that
1 out of 100000

plays chess professionally)

so there need to be 1E10 professional players ->
1E12 people

SADLY, there was only 1E11 people ever on the earth

NOt to add on a sad point, as was said:

“A theory has only the alternative of being

right or wrong. A model has a third

possibility: it may be right, but irrelevant.”

and not every prediction is a true one.

THank you and time for questions