The Official Semi-Log Scale of Weeb Enjoyment

I’ve found that in rating anime, things tend to be “it’s shit, but this is even more shit, and jesus christ this is all shit but they can’t all be 1’s either,” so I end up giving 4’s to things that are just. Really. Bad. They just aren’t WORSE than other things, so I can’t justify giving them 1’s.

The same goes for the upper end. I give some really, really good shows like 6’s or something because I can’t justify them being equally as good as another show. But that’s not reflective of how much I liked watching it.

See, the problem is that we assume a direct linear relationship of any given anime on a very limited scale that directly relates how objectively good an anime (with subjective ratings, of course…) to how much you subjectively enjoyed it. A 10/10 anime, while only 1 number higher on the scale, gives me infinitely more enjoyment than a 9/10 anime.

So, in order to rectify this problem for my personal self, I present an alternative:
a semi-log plot with the logarithmic scale along the x axis.

Now, you might ask, what is a semi-log plot?
Honestly, it’s pretty simple. It’s a logarithmic graph where only one of the axes (x or y) is scaled logarithmically (usually to base 10). The other axis is scaled linearly.
In this case, the x-axis is the one that is plotted on a logarithmic scale.

For this purpose of Weeb Enjoyment, the x-axis will be a “how good is it” rating on a scale of 1-10. HOWEVER, because this is a logarithmic scale, x will actually be a function of y–namely, x=log(y), assuming that log is the base-10 algorithm. This means that the value of y, at x=10, will be 10000000000, or 10 trillion. The y-axis for us will represent How Good This Shit Actually Is. That’s a scale from 1-10 trillion, which is a far sight better than 1-10. You can graph this expression in your calculator by using f(x)=10^x. (but don’t, because that really won’t get you anywhere)

Because the default log expression of x=log(y) is really…imperfect for how much I like things (and seriously, a scale from 1 to 10 trillion is way more precise than we need for our purposes), we need to modify the equation.
First, we realize that the base does not, in fact, have to be 10, though for purposes of computing, it is easiest to be base 10 (unless we want to work with the natural log, and I don’t in this case). Also, how the graph looks can be modified by putting a multiplier in front of the exponent, which is how we’ll handle the graph so that it can be base 10.
Then, to account for how graphing this shit actually looks, we’ll put in a function multiplier and move down the graph a little. The resulting equation?


The resulting graph looks like this:


Now, why 0.213446, you might ask?
Because that’s the number that gives approximately f(8)=100.
Any anime up to 8 on the regular linear scale can be rated on the enjoyment scale of 0-100, 0 being total shit and 100 being yeah, this a damn good anime. And, to me, an anime of totally “meh and just half okay”–a perfect five–does not give that much enjoyment. At all. So the 21.349 score it gets on the enjoyment scale is actually pretty accurate.

But above 8? Oh boy, we getting into the masterpieces here. You don’t just enjoy them, they aren’t just good–they are another level. This graph reflects that, because from 8-10, the scale goes from 100 to 270.5. Boys, this is the elite part of the graph. This is where you start picking and choosing. This is the cream of the crop. This is where the graph actually matters. These are the anime you would die for. This is where the distinction “this anime is too good to be with the plebs, but not good enough for it to be in my top ten” comes into play.

The range of 100-270.5 isn’t meant to be taken on the same level as range 0-100. Anything above 100 means that I had a damn good time watching it. It’s all about semantics and decimals from there on out, which I think is awesome. Any rating I give above eight will be allllll about that enjoyment, which means the corresponding “enjoyment number” from 100-270 is actually far more important than a decimal number from 8-10.

Link to graph for those interested

So yes, let’s use a better graph with better representation of what anime is really like.


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