Ekestimos Scale

The Ekestimos Scale versus Approval

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English Ekestimos Scale
The Four Standard Languages
Egonyota Pasaru Yijeekestimos
Serakafph Xaxex Ekestimos iŝa
yukũa|Elaga ütæk|Qvalsa {{{yukũa!Elaga ütæk!Qvalsa}}}
Cipogrtesaj Adinekestimos

The Ekestimos scale or the Ekestimos normalization is a review scale based on arbitrary numbers and desperately trying to normalize them. The main thing about the Ekestimos scale is that it is trying to normalize the rather extreme values that humans (and to an even greater extent, the kilis) give to things such as Fictions.


Let us take a movie for an example. I'll make it an Earth movie so you'll kind of know what it is. Gisitolo II: Akus ek Fälën. [1] Or, GS2:AF for short, because typing stuff like that is hard.

Now, GS2:AF is a very polarizing movie. Some like it, some don't. I have picked about ten different people, and they give me a score for the movie. They know that they have to give a score between -1 000 000 and +1 000 000 and there will be no more than two trailing zeros. (That means certain integers are banned, but a nearby decimal may be given.)

Out of those ten people, five were very avid GS fans and they gave scores like +941 223, +894 224, +971 000.5311, +932 227 and +943 004. The next four people are professional critics and as GS2:AF does not leave a good impression there, it got dismal numbers such as -431 228, -774 004, -416 234, and -885 034. The last one thought it was durr-hurr and gave a +100 884.

Now people tend not to use the middle numbers: watch as I create a table to indicate this:

Distribution of opinions of ten different people
Score less than Cumulative frequency
-1 000 000 0
-800 000 1
-600 000 2
-400 000 4
-200 000 4
0 4
200 000 5
400 000 5
600 000 5
800 000 5
1 000 000 10

See those long lulls between rises? That's human nature.

Now what the Ekestimos scale does is to alleviate that problem by processing the numbers slightly.


The old score is translated into the new score using this formula:

$ y = 1 000 090.8 \tanh \frac{x}{200 000} $

When plotted, this gives the graph above, only sideways. x is the original value, y is the new value.

You can see how this immediately reevaluates something. Let's face it, movies, music, books — you may like them, but it'll never be to the extent that you will no longer live without it, like you would if you have seen God or something like that (not that seeing God is uncommon in the Pseudoan Empire.) When a reviewer gives GS2:AF something like -300 000, it's fairly reasonable, but the diehard fans that will never give a score less than 900 000 for anything they like and never give a score greater than -900 000 for anything they hate, those probably have never seen anything like the Gibraltar Falls seven hundred thousand years ago.

Moving on.

What we do next is to transform all the numbers.

Values Before and After Ekestimos Normalization
Original New
+941 223 349582.5988
+894 224 288 443.0769
+971 000.5311 421 593.8927
+932 227 334 897.2737
+943 004 352 746.4322
-431 228 -92 271.2256
-774 004 -206 012.6604
-416 234 -88 616.4879
-885 034 -279 632.3385
+100 884 20 243.8207

This is the First Ekestimod Normalization value. Further adjustments may be made using the same formula, because some species are more prone to exaggerating than others.


  1. For purposes of protecting their identities they are Pseudoanized. Doesn't mean that the original name is still hidden in here somewhere.