Hi,
First, thank you to the organisers for a great competition and it is nice that you take on your own calculation of scores instead of the default itch.io method.
It may just be a matter of what is meant by words, but if my basic understanding of weighted average is intact, I think you have given more weight to the 5 first categories than first stated and less to the last three. More specifically, I calculate that you have effectively given 18,1% to the first five categories and 3,19% to latter.
To quote you:
”The results were generated by taking the raw scores for each category and applying our weighting to calculate to overall score”
I would calculate the total score like this:
[abbreviations: W=writing,St=story,C=characters and so on]
=0,17*W+0,17*St+0,17*C+0,17*I+0,17*P+0,05*U+0,05*H+0,05*Su
=0,17*(W+St+C+I+P)+0,05*(U+H+Su) [Eq. 1]
EDIT: There was a repeated typo in the formulas above. 5% should of course be written 0,05 and not 0,5. Sorry for the confusion.
The resulting number would then be less or equal to 5 stars. The winner got a score of around 20 and it is perfectly okay to multiply with a factor to make the decimals stand out clearer.
But it seems like you have done the following:
=0,85*(W+St+C+I+P)+0,15*(U+H+Su)
In my understanding, this corresponds to giving the first 5 categories higher weight than the stated 17% each.
More specifically, the percentages add up to 5*85% +3*15% = 470% which explains why the final score can be above 5 stars. In my terminology [Eq. 1] this also means that the first five categories each have a weight of 85/470=18,1% and the last categories each have a weight of 15/470=3,19%. In addition, this score was effectively multiplied with 470% = 4,7.
Example using The Impossible Stairs:
4,7*(0,181*(4,5+4,23+4,39+4,54+4,31)+0,0319*(1,81+3,85+2,31)) = 19,9
I don't know if it is a mistake or just another way of expressing weights, but as I see it, you have effectively reduced the weights of the last three categories to 3,19% instead of 5%. If this calculation was what you planned all along, then feel free to stick to it – it probably won't matter much. I just thought I would tell you this in case you wanted to correct it.