How Many Hours of Study Before You Can Reach a Certain Elo

How Many Hours of Study Before You Can Reach a Certain Elo

Formula: y = 1733 exp ( ( x -1559.4 ) / 678 ) - 173.3

Where: y is the number of hours of study and x is the Elo rating

Hi

Hey, I'm new here, just exploring the site. I wanted to ask: How did you come up with this formula/expression?

From the Article How Many Hours Of Chess Study Does It Take To Be A Grandmaster? By NM SmarterChess
I saw a graph like this

I noticed that the graph is kinda similar to a natural logarithm graph

The following graph confirms it.

Then I manipulate the equation.

First, we will find the comparison between number of hours of study and the natural logarithm graph.

I assigned the value 4 as synonymous to the number of hours Nakamura spent before achieving grandmaster title which is (14-7.5) *20 *52 which is 6760

But as we approach x, we approach negative infinity, so I selected 0.1 because it has the right value that fits the graph which is -2.3

Then, the number of hours, xi = k * ( x - 0.1)

Substitute: xi = 6760 and x = 4

We find k = 1733

Then, xi = 1733 * ( x - 0.1 )

Next, we will find the comparison between Elo and the natural logarithm graph.

y = ln(x)

Then we found that the lower limit of y is -2.3, so

yi = k *( y + 2.3 )

We plug in yi = 2500 and y = ln(4) which is 1.386

We find k = 678

Then we manipulate the equations

x = xi / 1733 + 0.1 and y = yi / 678 -2.3

We plug in both equations:

yi / 678 - 2.3 = ln (xi / 1733 + 0.1)

Since we want to know the number of hours to study to reach a certain elo, we separate xi to the left by manipulating the equation

exp ( yi / 678 - 2.3 ) = xi / 1733 + 0.1

xi = 1733 ( exp ( yi / 678 - 2.3 ) - 0.1 )

Simplify,

xi = 1733 ( exp ( ( yi - 1559.4 ) / 678 ) - 173.3

y = 1733 ( exp ( ( x - 1559.4 ) / 678 ) - 173.3

Nice work mate, hope you keep it up and have a good day