Ergodic theory usually has several papers in Annals and Inventiones each year, and is regularly mentioned when the work of recent Fields medalists is described (e.g. Avila, Lindenstrauss, Mirzakhani) but I would estimate the number of ergodic theorists who contribute regularly to MathOverflow as being below ten. MathOverflow has issued three bronze badges for answers to ergodic theory questions, and no silver badges.