We discuss the problem of the design of encoding profiles for web streaming. In this application, the video is normally embedded in a web page, and based on user preferences, e.g. browser stretch factor, full-screen mode, etc., the area that it occupies on the screen may be different. When multiple viewers tune to the same web page, this creates a distribution of possible player sizes. The key idea of this paper is to consider such distribution as input to the problem of the design of encoding profiles for web streaming. The objective is to maximize the average quality that can be experienced by a population of viewers. We define this problem mathematically, show that it belongs to a class of non-linear constrained optimization problems, and show how it can be solved practically. Examples of optimal profiles generated for different videos, networks, and player models are also provided. Provided results demonstrate the significance of accounting for player size distributions in the design of encoding profiles for web streaming.