I am attempting to create a user ranking system for a trivia game I am developing. Essentially, users are asked a question with only two possible answers to choose from, giving them a 50/50 chance of answering correctly. I would like to rank them based on the following variables: 1) Question Accuracy; and 2) Total Questions Answered. My intent is to allow the user to answer an unlimited number of questions. However, I would like the overall rankings to rank all users against each other despite the number of questions answered. The problem I foresee is a user could have earned a high accuracy rating (say 69%) based on answering a significant amount of questions, and still be ranked below a user who answers a minimal amount of questions and has only a slightly higher accuracy rating (70%) due to chance.
How do I give more weight to User A in the rankings? I would argue that they deserve to be ranked higher based on the sheer amount of questions answered in comparison to User B.