Flaw In ESPN NFL Game By Game Projected Player Points

Last year I played in an ESPN Fantasy football league, and too frequently relied on their week by week projected points to set my line-up. As a mathematician it did not take me long to notice the statistical flaw in ESPN's weekly projections, and that it was all about touchdowns. They do not include fractional points for expected touchdowns, making it either a 1 or a 0 (in some rare cases 2). I have heard on the ESPN Fantasy Focus Football podcast that this is done because "you can't score half a touchdown", but in the wonderful world of statistical "expected value" you absolutely can score half a touchdown. If a player has a 50% of scoring 1 TD, then his expected TDs should be 0.5 not 0.

Winning in Fantasy football is all about scoring TDs, as the team with the most TDs will more often than not win their week. By doing it this way ESPN's statisticians are creating an artificially large gap between players expected to score 1 TD and 0 TDs. For example, if you used 50% probability as the dividing line between 1 and 0; and player 1 has a 49% chance of scoring a TD and player 2 has a 51% chance of scoring 1 TD, the gap in ESPN expected points would be 6 (holding other stats constant). In reality, player 1 should have an expected value of 2.9 and player 2 should have an expected value of 3.1, instead of 0 and 6. By rounding to the nearest touchdown they are skewing the actual expected value. That's fine when projecting results for a full 16 game schedule, but on a game by game basis  (where 95% of players true expected TDs is less than 1) you will get a far higher margin of error than if you used fractional TDs.

Fantasy football is a game of inches that can't always be measured in yards. I'd like to be able to use ESPN projections instead of having to check Yahoo rankings before setting my ESPN line-up.