MHB Calculating 5-Star Ratings to Reach 4.85 Rating

[loso6699]

Hello guys I was going to ask a question regarding 5 star ratings its a hard one for me but it could be simple for you guys here it is,

I've got 1115 ratings ( 5 star max 1 lowest )

* What I know so far is my total rating is 4.80
* 696 of these are 5 star ratings
* some of the 1115 have not rated not sure how many but not too many 100-150 max i'd say

Questions, how many 5* ratings would I need to get rating up by 0.01 my aim is 4.85 rating or 4.9 to make it easier I just want a estimate to figure out where i'am

thanks

 

[I like Serena]

Hello guys I was going to ask a question regarding 5 star ratings its a hard one for me but it could be simple for you guys here it is,

I've got 1115 ratings ( 5 star max 1 lowest )

* What I know so far is my total rating is 4.80
* 696 of these are 5 star ratings
* some of the 1115 have not rated not sure how many but not too many 100-150 max i'd say

Questions, how many 5* ratings would I need to get rating up by 0.01 my aim is 4.85 rating or 4.9 to make it easier I just want a estimate to figure out where i'am

thanks

Hi loso6699! Welcome to MHB! ;)

Suppose we have $N$ actual votes $x_i$ where $i=1..N$.
So $N \le 1115$.
Then the rating is:
$$\text{rating} = x_{average} = \frac {\displaystyle\sum_{i=1}^N x_i}N = 4.80$$
It follows that the sum of all actual votes is:
$$\sum_{i=1}^N x_i = 4.80 N$$

Now suppose we add $n$ extra votes of $5$ stars.
Then the new rating will be:
$$\frac {\displaystyle\sum_{i=1}^N x_i + 5n}{N+n} = \frac {4.80 N + 5n}{N+n} = 4.81 \quad\Rightarrow\quad
4.80 N + 5n = 4.81(N+n) \quad\Rightarrow\quad
(5 - 4.81)n = (4.81-4.80)N $$
So:
$$n = \frac{0.01 N}{5-4.81} \le \frac{0.01 \cdot 1115}{5-4.81} = 58.7
$$
That means that with 59 extra votes of 5 stars, the rating is guaranteed to go up by 0.01.

If the actual votes was, say, 100 less, then we can do the same calculation with $1015$ instead of $1115$.
And if we want to go up by $0.05$, we can replace $0.01$ and $4.81$ by $0.05$ respectively $4.85$.