An implementation of http://www.evanmiller.org/bayesian-ab-testing.html with no depenedencies

bayesab.js

function probabilityBBeatsA(aa, ba, ab, bb) {
  var probability = 0.0;

  for(var i = 0; i < ab; i++) {
    var product = Math.log(1 + (aa + ba)/(i + bb));
    var j = 1;
    var start = i+1;

    [bb, ba, aa, i].forEach(function(steps){
      var stop = start + steps;
      while(start < stop) {
        product += Math.log(start++)
        product -= Math.log(j++);
      }
      start = steps;
    });

    probability += Math.exp(product);
  }

  return probability;
}

Updated to use logs, to avoid Infinity issues.

Updated to have the right name (BBeatsA, not ABeatsB)