PROJECTIONS ARE NOT PRICES, Part 1
Winning at playing fantasy baseball has two obvious components:
Player Projections and Player Pricing.
It is, one assumes, most helpful to have the best projections, because they tell us what players are going to do. The best set of projections would give you the best idea of who is going to be good this year, and who is going to be not so good, and this information should give you an edge over someone who doesnâ€™t have such good projections (or no projections at all).
Plus, good projections should lead to better prices. If you know better than anyone else what the players are going to do in the coming year, you should be better able to value a home run, for instance, in the context of all the other home runs hit, and so on and so forth for all the categories. This would give you a better price in each category for each projection and overall more accurate prices for all players.
This is how good projections are thought to lead to winning fantasy teams, but it just isnâ€™t so. At least not when it comes to the conversion of projections into prices to pay at auction. The fact is that accurate projections are a map of regression to the mean. In making accurate projections we average out the highs and lows of a playerâ€™s history, in order to better identify his baseline, which is the core description of his true talent.
A perfect illustration of this comes from the projection of at bats. In any given year six to 10 hitters will accumulate more than 700 PA. These are, obviously, guys who have and hold the leadoff position in the lineup, on good teams, all year long. But when one uses regression analysis to look at past history of players with more than 700 PA in a year, the math comes back that that sort of player will have 630 PA in the subsequent year.
What the formula does is look at the, letâ€™s say, 10 hitters with 700 PA each (for a total of 7000 PA), and notes that on average in subsequent years a player in that group will have, on average, 630 PA. Now this could break out in a variety of ways. Nine might have 700 again, and one 0, or 5 might have 700 and five might have 560. The specifics are changeable, but the point is that based on the actual history of baseball players over the past 40 years or so, what we know is that on average each of the top 10 PA guys in one year will have 10 percent fewer at bats the next year.
What we also know, is that most of the leading PA guys in one year will be the leading PA guys the next year, with about 700 or more.
And what we donâ€™t know is which player or group of players is going to fail and bring down the average PA of the group.
So, is a good projection the one that gives each of the 10 players 630 PA, spreading the risk between them?
Or is a good projection one that gives each of the 10 players 700 PA, getting more of them individually right, but making the misses that much more wrong?