Doctors use statistics to advance medical knowledge; we use a medical analogy to introduce statistical inference "from scratch" and to highlight an improvement. Your doctor, perhaps implicitly, predicts the effectiveness of a treatment for you based on its performance in a clinical trial; the trial patients serve as controls for you. The same logic underpins statistical inference: to identify the best statistical procedure to use for a problem, we simulate a set of control problems and evaluate candidate procedures on the controls. Now for the improvement: recent interest in personalized/individualized medicine stems from the recognition that some clinical trial patients are better controls for you than others. Therefore, treatment decisions for you should depend only on a subset of relevant patients. Individualized statistical inference implements this idea for control problems (rather than patients). Its potential for improving data analysis matches personalized medicine's for improving healthcare. The central issue--for both individualized medicine and individualized inference--is how to make the right relevance robustness trade-off: if we exercise too much judgement in determining which controls are relevant, our inferences will not be robust. How much is too much? We argue that the unknown answer is the Holy Grail of statistical inference.