Similar projects/products

[Henry Harrison]

FantasyCruncher: They provide ceiing/floor projections, which is a naive way of estimating probability distributions. Piggy-backing on them would be very useful, unfortunately they just recently started a pay model. Still, we can probably learn something from them.

Lineup Lab: They provide a knapsack optimizer similar to FantasyCruncher. It's worth playing with as a knapsack optimizer could be used to create a reference point for any given game slate, to compare all other lineups to.

Post here with any other links you want to share.

[Robert Del Vicario]

I have some code kicking around with an optimizer and Ceiling / Floor calculations implemented. I'm pretty sure FC is just projection +/- 2x season FP standard deviation. it wouldn't be hard to extend to produce multiple portfolios of players (e.g. 100 lineups).

[Henry Harrison]

That's boring then, if FC just uses standard deviation.

What's your strategy for estimating ceiling/floor?

As far as the optimizer, I think the basic starting point is a knapsack optimizer that produces multiple lineups, but that's trivial. I'm going to assume if that's what someone wants to do they can already do that. Let's build on that. See the thread on portfolio strategies for some ideas. One basic idea coul be an optimizer that adjusts each player's value every time he's included in a lineup.

[Devin McCabe]

Numberfire includes confidence intervals:

https://www.numberfire.com/nfl/fantasy/fantasy-football-projections/

[Robert Del Vicario]

I do the same floor / ceiling calculations though I use linear solver to build teams. It makes it easy to construct sub-optimal lineups because you just loop through the number of teams you want to produce constraining each subsequent team to be just a bit worse than the last.

However if we really want to calculate a floor ceiling it seems to me that it is a pretty complex problem with 3 moving parts:

1. We have variability in player performance

2. We have covariance between players on the same team

3. We have covariance between teams

The other issue is that i can't buy fractional shares of players so traditional portfolio optimization methods in finance won't work. I might be wrong, but it sounds like it'll make for a pretty gnarly optimization problem. All of that to say that I don't have a good way to calculate it!

[Nathan Braun]

In terms of player performance densities, I just wrapped up my second season running Bayesian Fantasy Football:

http://www.bayesff.com/bayesian101/

It's not perfect (don't currently allow for different shape parameters by player), but we're working on it.  I think it does pretty well.  It's something I charge for now, but I'm interested in seeing where this project is heading and would potentially be interesting in collaborating.

[Devin McCabe]

Thanks, I hadn't come across your site before. How are you picking the initial parameters for a player's first start? Some other type of projection?

[Nathan Braun]

The initial rankings are based on ADP, check out this article here (requires a login, but it's free):

http://www.bayesff.com/draft/

Basically, within each position group, and using historical data, I fit a relationship between ADP and weekly performance (along with some other factors, like opponent points allowed) within a gamma distribution (so the scale parameter is a function of ADP).  The shape parameter is free.  So, to start the season I plug in players' ADPs and get the initial, week 1 rankings.

[Henry Harrison]

Devin: Cool, I've added a field to nfldb-projections to store variance, which we can compute from those confidence intervals.

Nathan: Your site looks awesome. I like your approach to estimating probability distributions, it gives me some ideas of where to start. I hope we get far enough along that you'll want to collaborate. I think what I'd like to do is something similar but model the distribution of deviations from projections, allowing us to use as a baseline the work of other experts, and therefore automatically track factors like opposing defenses.

[Henry Harrison]

Robert: I agree that it's a touch optimization problem. It's certainly not linear once we start considering distributions. Which is why I've been leaning away from an automatic solver like a linear optimizer but rather visual aids. That will keep the human element in the loop  (and also make the problem tractable for us). But it also means that we won't be coming up with closed-form solutions and I don't think we'll ever be confident that our strategy is optimal in any kind of formal sense.

As far as your points, 1-3 are fairly easy--I just posted correlation matrices in the probability-distribution thread. Of course it would be nice to be able to vary them by specific pairs of players but for now I think correlation by position will get us pretty far. As for 1, I haven't done that, but it doesn't seem like that hard a problem, at least for a rough estimate.

Traditional portfolio theory won't work, for the reasons you mentioned but also because we're not trying to maximize total fantasy-points but rather the payouts from our lineups. That nonlinearity in there is killer. Still, I think some of the insights from portfolio theory are applicable in a general sense.

[Devin McCabe]

http://thespread.us/

There are some nice posts in this blog about methods for NFL projections. K-means clustering is something I plan on trying soon. That might also be an effective way to specify the prior distribution for players in the aforementioned Bayesian model, for instance.

[Spencer Cushman]

Nathan this is really cool. How do you then take the distributions to ultimately form your lineup?