Wednesday, August 19, 2015

Value Expectations and Pricing Tiers

During the process of ranking players based on their consistency of value, we’ve uncovered a bit of a bootstrap paradox, to borrow the term. How is that we can ask an expensive option to give us the same return on investment as a cheap option? Theoretically, the more a player cost the less likely he is to hit value. The inverse of that isn't necessarily true either. So this isn't a mutually exclusive scenario. Wouldn’t it be more logical to weight value by price?

For the purpose of this exercise, we’re going examine things with a guaranteed prize pool viewpoint. Therefore, hitting value means at least 3x salary. Three-times valuation drives up our final score to at least 180 points—20 points per roster spot—a cashable score in most weeks. 

But projecting 20 points per roster spot isn’t the same thing as achieving 3x value for every player. It’s unreasonable to ask Aaron Rodgers to hit 3x with a salary of 10,400 (he came damn close in Week 14). Instead, our value expectations should descend with each increase in pricing tier. Here is a weighted table broken down by three separate tiers that calculates expected value with a minimum of 20 points as the baseline: 
What I like about this is it gives us a way to deconstruct blanket averages and connect the dots of a winning strategy. We shouldn’t look at salaries and think “how realistic is it that Rodgers scores 31.2 points and justifies his $10,400 price tag?”, because we no longer need 31.2 points to reach value expectations. Instead, we need 19.97 points. That’s a major difference. 

But as nice as all of that sounds, we have a logic problem. Logically speaking, asking 20 points of your kicker and 20 points of your defense is unreasonable. If we’re normalizing value expectations based on price point, it’s only fair to normalize positional expectations as well.

We learned from the Cracking FanDuel eBook that winners of last year’s Sunday NFL Million tournaments averaged 13.9 points for kickers and 15.7 points for defenses—just under 15 points per. Projecting 15 points for a non-skill position is a lot more reasonable than projecting 20. But the 10 points we just dithered from kickers and defenses will have to be reconciled by other positions.  

Said reconciliation increases our value expectations by 1.5 points across the board. Instead of just needing 20 points from nine positions, we now need 21.5 points from seven positions. Here’s an updated table that removes non-skill players from consideration and is normalized accordingly:
We can now apply projections to weighted value expectations based on a player’s salary. Obviously, a $5,000 player isn’t going to be projected to score 21.5 points. But you can at least use value expectations as guide when building lineups and determine the likelihood of, to use our earlier example, Rodgers exceeding expectations to cover a player that might fall short.

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