Today, I am writing a blog post on math.

I’d like to preface this with the fact that I do not normally write about math, I write about books.

Nevertheless, I’m diverting this blog’s attention for the day to my other passion.

Now, I’m sure you’ve all heard of Goodreads, the online social platform for books & reviewing books & reveling in all sorts of bookish goodness.

And you may have also heard of how some people on this platform, when they see a 1 star review for a book they think doesn’t deserve the 1 star, will **give it 5 stars to cancel the 1 star out**. And this works the other way too, giving 5 stars to cancel a 1 star.

But this idea isn’t mathematically sound. In fact, it’s *so* mathematically incorrect.

Before we continue, I’d like to add a disclaimer about this post. This post **does not involve any personal views on this practice**, except for pure, unadulterated WTF-ery about the way people’s minds work & their complete disregard for mathematics. (Which is understandable because some people are one-side-of-the-brain-oriented, but still.) Of course, I have personal views on this practice, but that isn’t the purpose of this post.

The purpose of this post is to *inform* readers about the craziness of this actual action and why it doesn’t actually achieve what anyone wants it to achieve.

For my purposes, I’ll be using the example of a person seeing a 1 star review and adding a 5 star review, but this mathematical concept works both ways.

And if you’re afraid you’ll be lost in all the math-y logic of it all, **do not worry about not understanding the math**. It’s nothing more than basic addition and division (I do go into calculus just to hang with the cool cats, but it’s really unnecessary and mostly for bragging purposes).

Many people, when they do this, usually have this goal in mind:

**To cancel out the 1 star.**You might be a SJW or just a general do-gooder, and you see someone give a book that’s not out yet a 1 star review for what you perceive is an irrational reason (i.e. when ARCs aren’t out yet). And you think, “Hmm. This isn’t right. This is unfair to the author. Let me give it a 5 star review to cancel it out.” (hint: You’re wrong.) This can go all the way from do-gooder to extreme fangirls who fight over ratings, which I’m not going to get into.

**BUT THIS IS NOT HOW MATH WORKS.** Let’s use an example.

I photoshopped a fictional Goodreads book with a food-related summary to serve our purposes. The things you need to know about it is that it currently has a **4.2 rating and 6 ratings total**.

Now, someone goes and rates my *fabulous* book with a 1 star rating (bringing it up to **7 ratings and a 3.7 average**).

How did I get those numbers? Simple. With **averages**. You add the values of all the ratings up (1, 2, 3, 4, or 5 as the rating value for each) and then divide by the number of ratings.

And so, to find what the average was with 7 ratings, I just used the formula to find the new average. You can read my math in the photo below, or just assume I did my average right.

Now, Do-Gooder Debbie comes around and says, “Hey! That’s not fair. Vicky deserves better than this (thank u boo). She should have a fair playing field for her book.” And then promptly goes to give it a 5 star rating.

And while the sentiment is nice, it doesn’t actually achieve what Debbie wants it to achieve. We end up an **new average of 3.9 stars from 8 ratings**. (Once again, read my math below or just assume I’m right.)

And, as much as I appreciate the gesture. **3.9 stars does not equal my original 4.2 stars, at least, not in this world**. (I wish because maybe then my SAT score would be better.)

And now, you must be going, “Gasp! My efforts have been futile!” And if your goal was to bring me back to 4.2 stars, then yes. Your efforts have been futile. If your goal was to help me out, well you kind of did, but you also may have done the opposite . . . we’ll talk more about this at the end.

Now, you see, there are two more lines of thought that I must pursue (besides whether you helped or not). This idea on a larger scale (one hundred 5 stars to negate one hundred 1 stars) and this idea on an infinitely large scale (searching for that perfect five stars).

We’ll start with an expansion of this topic.

I hope you all know that **the average of 5 and 1 is 3**. So if we give little ol’ me 100 5 stars and 100 1 stars, it’s basically the same as giving 200 3 stars. **Which means my new average is 3.03 stars for 206 reviews**. Which is pretty sucky, because a good Goodreads rating is usually in the 4-point-something range.

I’m not going to write out the math for you, but you can plug in what I did into your calculator to double check, if you’re super doubtful. (Mind you, please keep the parentheses where they belong).

And so, the point of this is, the more times the 5-star-1-star cycle happens, the closer your average approaches the unhelpful number 3.

Which brings me to limits. Yes, that’s right. Calculus.

**BUT WAIT! **Before you go “Oh god, I’m not gonna get this,” and skip to the end of this post, here me out. We won’t be doing *actual *calculus (unless you want to). Just fiddling with an idea that is commonly used in calculus. Just try and follow along, for my sake, okay?

Which brings us to considering what happens when you have not 100 5 stars and 100 1 stars, but 1000 of each. Or 10,000. Or 1,000,000. You’re basically never going to get out of the 3 star range.

So, this is all to prove my point that **as the number of 5-star-1-star cycles increases, the more your Goodreads rating goes closer to 3 stars**.

(If you’ve taken calculus, I assume you understand where I *would *have taken this blog post (limits as x→∞ as the number of 1 & 5 star ratings keep going up). I won’t really be catering to you, but just know I had y’all in mind.)

But this can also apply to ones with purely a 5 star goal. If, for instance, the 1 star raters don’t retaliate and you think, “Gosh, let me get this rating to a perfect 5 stars,” then **the world will be laughing in your face because this will never happen**.

I mean, yes, it will happen in the sense that it rounds up to 5, but think about it some more.

Even if you had a billion 5 stars and one 4 star, **the average still won’t be a perfect 5**. It’ll be 4.9999999…9 (it has an ending point, but the more 5 stars you add, the more nines get pasted on the end).

Of course, Goodreads will just round 4.99 to 5. But in theory, you’ll never have a *perfect* 5 star average rating. You’ll have a 4.9999 which will keep going with the number of 5 star ratings added

(Once again, to my calculus buddies. Consider this:

(yes, you might want to use L’Hospital’s rule. or maybe just basic algebra. whichever.)

And so, if you’re looking for the perfect 5 and you have a non-5 rating, **it’s never gonna happen**. (It’ll do some rounding though!)

By now we’ve considered both lines of thought–an infinite number of 5s to reach the perfect 5 (which will never happen) and an very large number (aka infinite) of 5-star-1-star cycles to end up pushing you somewhere around 3.

The last thing we have to consider is **psychology** to determine whether or not your 5 star rating actually helped me and my *Book of Math* with it’s veggie summary. Whether the 5-star-1-star cycle will actually happen. Because if it doesn’t happen, then you can claim you did something positive (although not *as *positive as you may have wanted because 3.9 ain’t a 4.2). You did something to combat the unfair rating and bring the average closer to what it used to be.

*But*, if other people see your rating and think *you’re *the one being unfair, will this cycle continue? Will the people add a 1 star to spite you, while all you were trying to do was spite the 1 star person?

This is where I leave you off, because I am no psychology expert (but I am pretty darn good at basic algebra and non-complicated limits).

Some things to consider:

- By giving a book (let’s assume that the book isn’t out yet because that’s when this commonly happens) a 5 star (or a 1 star) rating, what are the chances that someone will retaliate, creating a 5-star-1-star cycle?
- And if YOU retaliate, are you prompting a continuation of the cycle?
- If this cycle continues, are you dooming the author (and the people who look at Goodreads ratings) to live in a vaguely unhelpful 3 star zone?

~~Merry Christmas~~ Thank you to all, and to all a good night!

What did you think of today’s post? Were you able to follow along with my train of thought? Please, please, please leave thoughts, opinions, criticisms, pictures of your cat’s butt, *anything* below! This is one of those rare times where I’m begging you for some feedback.

Interesting Post! You can actually work out how many 5 star ratings you would need to negate the 1 star rating in your example using the formula (26.2 + 5n)/(7+n) = 4.2. This comes out to n=4 🤓 So you need to get 3 friends to join you in your five-star rating! 😛

I get your point about the average just tending to 3 though and how by retaliating with a 5 star rating you are continuing the 1-star, 5-star cycle.

Best to just rate honestly when the book is released and you have read it!

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Thank you! Ahaha yes, that’d definitely work for this instance! But when the

truerating moves up or down with honest ratings, the 5 stars would end up skewing the rating again and it all ends up in a giant math mess! Ahhaha I definitely agree-just be honest and ignore everyone else xDLikeLiked by 1 person

Oh man this is awesome. And yes, I did calculus. I am so happy to see a bookworm that likes math xD (and gets it!) Sharing this Sunday 🙂

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oh ahahah thank you! I’m glad you enjoyed this post–I’ve got to let out my math geek side out from time to time xD

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An interesting analysis and definitely one to keep thinking about. Rating wars are never a good thing.

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definitely! it can really end up messing up a book’s “true” rating and almost never ends up well. thanks for stopping by!

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This is an interesting post that I never really thought about with ratings. I can’t stand the rating battles over Goodreads when authors or a book become controversial. Even worse still the people who rate in order to bandwagon without actually touching the book themselves, just for the sake of arguing with the other side. It’s funny now to consider the math and what they’re actually doing is not what they intended, great post!

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I’m glad you liked it! And definitely Goodreads becoming controversial is not fun and it usually ends up in disaster! Thank you!

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A very interesting post. Thank you for sharing.

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Of course! Glad you liked it!

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