Comparing player percentages effectiveness with different sample sizes I have a spreadsheet of player data. One of the categories of player data is pass percentage. Pass percentage is calculated as follows:
AccuratePasses/TotalPasses

In total I have around 400 players to compare, however the sample size of passes between each player is very different. For example on player may have executed 1592 passes (1426 of which were accurate), and another may have executed only 7 passes (of which all were accurate). 
How can I use the data I have to extrapolate a score or ranking based on the player effectiveness or likelihood of being effective. At the moment I have a formula to do this as follows:
PlayerAccuratePasses-(PlayerTotalPasses*(AverageAccuratePasses/AverageTotalPasses)

I did not pull this formula together and want to be sure that this makes sense mathematically to produce a score of who is the most effective passer.
 A: I think the best way to takle the problem is to take a Bayesian approach.
Your scoring metric $S$ is going to be the expectation of the parameter of a Bernouilli distribution which represents the intrinsic accuracy of the player.
As a prior distribution, you can take the conjugate prior that is the beta distribution with parameter $\alpha$ and $\beta$. You choose them such as expectation and variance are equal to the sample mean and sample variance of the data. 
The final posterior expectation of the accuracy becomes (using wikipedia):
$S=E(\Theta) = \frac{\alpha + n_{acc}}{\alpha + \beta + n_{tot}}$
where $n_{acc}$ (resp. $n_{tot}$) is the number of accurate (resp. total) passes of the player considered.
The formula behaves quite nicely if the number of passes $n_{tot}$ is low / high.
A: You seem to be conflating a measure with its margin of error. 
Passer accuracy is measured by the first fraction you quote:
AccuratePasses/TotalPasses
You can then look at things like confidence intervals to see how well estimated the proportion is. 
I think trying to combine them into one measure is a mistake, but you could, I suppose, compare the lower confidence limit (not necessarily 5%, could be some other number). 
