How to calculate the ELO system of rating

I don't think i need to further emphazie on what a rating is, so i would get right in by telling you the two main types of rating system and how to calculate one of them.

So lets begin,

There are two main rating system used to calculate the approximate strength of every chess player which are;

1. The ELO Rating System

2. The Glicko Rating system

Today we are going to be dwelling on the ELo System

ELO Rating system is named after its creator Arpad Elo, a Hungarian-born American physics professor, and is also used in other competitive games other than chess to calculate the relative skill of every player in such games.

It is true ELO system has some downfalls thats the reason why Glicko rating system was invented but is still very popular and used by chess organizations like FIDE, USCF, FICS, ICC e.t.c.

So thats why i am going to teach you how to calculate it

All you need are three(3) basic material:

1.Paper

2.Pen

3.Calculator (Scientific)

So get your material and lets begin

Every player has a rating, and is expected to move higher or go lower (Exception (Unrated)) and every new rating is determined by the outcome of a game and the rating of both player.

So ELO system has 2 formulars which i would breakdown for you, first you need to learn this

R_A- Real Rating of Player A

R_B- Real Rating of Player B

E_A- Expected outcome of player A ( Percentage of win)

E_B- Expected outcome of player B (Percentage of win)

K- Weighing Factor( Normally- 15, Top Level- 10, beginners- 25 i advice you stick with 15)

Round - It is adviced u round up all decimal rating

S_A- Outcome of game for player A ( win - 1, Draw 0.5, Loss-0)

S_B- Outcome of game for player B

R_A_N- New Rating of player a

R_B_N- New Rating of player b

ok once you get that i think it time to start calculating

There are 2 main steps

1. Finding the E_A and E_B ( Percentage of win)

2. Finding the new rating of both players

First i would give you the formular then an example

1. Finding the E_A and E_B

formular: for player a we say 1/1+10^(R_B-R_A)/400

for player b we say 1/1+10^(R_A-R_B)/400

now this may seem very confusing but it pretty easy when you understand it so let use an example

A 1583 rated player plays with a 1572 rated player according to the formular we first have to find the E_A and E_B so lets start with A

formular: 1/1+10^(R_B-R-A)/400

solution

1/1+10^(1572-1583)/400

as thought in high school we are going to start with the bracket so get your calculator (Scientific) and lets begin

we say 1572 - 1583 which gives us -11

next step we divide -11 by 400 which gives us -0.0275

now we say 10 raise to power -0.0275 which gives us 0.938642036...

now we add one to it which gives us1.938642037..

now the divide 1 by our result

which gives us 0.515824985 multiply that by 100 and round up to get your E_A of player a RESULT: 52%

now for player b

we have: 1/1+10^(1583-1572)/400

as usually start with the brackets 1583 - 1572 gives us 11divide 11 by 400 and we get 0.0275 we say 10^0.0275 which gives us 1.065368864... then add 1= 2.065368864...

divide 1 by ans and we have a result multiply that by 100 and round up leaving us with 48%

so E_A - 52%

and E_B - 48%

now time to find the new rating of both players (note the ELO is slightly different from Glicko if the Rating deviation is normal then they give the same result (Rating deviation is caused by lack of playing rated or not playing at all))

now to calculate R_A_N: we say R_A + round(up) +K*(S_A - E_A)

in this game white won (Player a) so the S_A(game outcome) is 1

now lets calculate this(Please refer to the notation if possible write them down)

according to the formula we have

1583 + up +15*(1-52%)

now we go step by step

firstly we say 1-52% which is equals to 0.48 now the remove that bracket and say 15 x o.48 which gives us 7.2 and thats it just add 7.2 to 1583

1583 + 7.2 = 1590.2 (don't forget to round up)

= 1590 there we have it has easy has nothing

for player B we say

1572 + round + 15*(0-48%)

0-48% = -0.48

-0.48 x 15= -7.2

1572+(-7.2) = 1564.8 (Don't forget to round up)

therefore we have 1565

so there you have i hope you guys understood what i did if you did please comment and if you didn't please tell me why and i will try to improve.

Thanks