# Factional LEIs Done The Gwent Masters Way

#### Introduction

In the recent Top5 Best Factional Scores article summing up the Season of the Wild Hunt best factional achievement I introduced new quantity: Factional LEI (fLEI). This parameter is supposed to measure the efficiency of Pro Ladder climb done with a single faction. It was defined in analogy to LEI (Ladder Efficiency Index) as follows:

$fLEI = \frac{fMMR-2400}{\sqrt{fGAMES}}$

(where fGAMES is number of games played with faction). The values of fLEI appeared to be hardly relatable to general LEIs. Luckily, this drawback could be fixed fast and in style.

#### Math

Let’s look again into the expression for general LEI:

$LEI = \frac{MMR-9600}{\sqrt{GAMES}}$

Now, let’s imagine that total MMR is composed of 4 fMMR scores identical with the one for faction considered. Then MMR = 4*fMMR and GAMES = 4*fGAMES.

$LEI = \frac{4fMMR-9600}{\sqrt{4*fGAMES}}$

Square root of 4 is obviously equal to 2. Let’s divide numerator and denominator by 4 and change naming from LEI to fLEI:

$fLEI = 2 \frac{fMMR-2400}{\sqrt{fGAMES}}$

Newly defined fLEI is simply the one used in charts, but multiplied by 2! The new one has clear interpretation by relation to LEI. From now on I would use the new fLEI exclusively and recommend you to do the same!

For example let’s take the highest fLEI score in the Wild Hunt Top5 charts. Player Lord-Dana achieved 29.2 old fLEI with amazing 2546 fMMR in 25 games placements. If we multiply this value by 2, we get new fLEI = 58.4.

Let’s compare this value with Masters 3 LEI Highscore: 53.3 by Pajabol in the Season of the Viper. As we could see, by repeating Lord-Dana placements on each faction we could achieve tremendous, colossal, cosmic, enormous, monumental, prodigious, titanic, planetary, greatest efficiency achievement in Gwent Masters history: LEI = 58.4!

…ah wait, it is 0.7 LEI below TailBot’s score in the Season of the Bear in Masters 2. Nevermind.

#### Closure

Thanks for reading! New improved fLEI is there and ready to use. Stay tuned!

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