Does accuracy increase linearly when you add more factors/features to a random forest? I have read in various machine learning books that adding more data should result in a more accurate model. Is this rule the same for adding more factors/features to the model as well? So, should I expect the accuracy of a random forest to increase linearly as I add more instances or factors to my model? Any references/resources are appreciated.  
 A: Linearly, no. One obvious reason is well explained in the comments. Let's further assume it increases linearly as you add more features and it gets saturated at 100 %. Then, random forest would be our silver bullet for any ML problem, but it's not. Let alone random forest, no algorithm provides you with such confidence. It's even not guaranteed to increase the accuracy when you add features and depending on how you tune and validate, you might end up decreasing your accuracy/or any other success metric as well.
A: A cheap way to make a feature is to randomly sample values. These values can be drawn from any probability distribution you can imagine. But whenever these features have no relationship to the outcome, I wouldn't expect these features to improve the quality of the model; and if they do improve the model, this effect must be spurious because they have no relationship to the outcome.
This reasoning is true for random forests and any other model -- "add more features" is only useful when those features have some relationship to what you're trying to predict. Likewise, it’s not surprising when a model is improved (or at least not made worse) by including additional relevant predictors, so random forest is not remarkable in that regard either.
