I have six predictions from six different sources. Each prediction has a percent probability that the prediction will happen, as well as a historical accuracy percentage.
Here's a table of my problem:
This is the link to the table: https://docs.google.com/spreadsheets/d/1fioSBZiucRwsyeUD4foi2Bt2tBAUXSpv9Esvgksm_mk/edit?usp=sharing
An example of how to read this would be TF predicts the likelihood of a 0 is 63% and has been historically correct 43% of the time.
I want to find if the prediction should be 1 or 0 by weighting predictions with more historical accuracy. For example, TF predicts 0 with a probability of 63%. It has a historical accuracy of 43%. In contrast, LINE predicts 1 with a 81% probability and the same 73% historical accuracy. I want the overall prediction between these two sources to be 1 because LINE has a higher probability than TF and a higher historical accuracy.
So, my question is: how can I mathematically find the average prediction weighted by probability and historical accuracy?
Thanks in advance!
https://en.wikipedia.org/wiki/Weighted_arithmetic_mean Above is reference. The basic formula is $p=\frac{\sum p_ia_i}{\sum a_i}$. Where $p$ is the probability you want and $p_i,a_i$ are the individual probabilities and accuracy.