My Week 6 ownership targets

Last week I constructed 100 unique FanDuel lineups, and I posted the number of lineups that I wanted each player to appear in. (I did not hit the targets exactly, but was generally within 10% in either direction.)

I'm not sure I'll keep doing that every week, but I'll do it again at least this week.

Last week one commenter remarked that my list looked like a DFS popularity contest. That is somewhat true. It was a list of players who held the most value in my view (given their expected production and their FanDuel salaries), and there is definitely a positive correlation between value and popularity. But not a perfect correlation -- which is why it's possible for skilled DFS players to beat FanDuel contests over the long run. (If NFL players were owned exactly as often as they should be, everyone would just be pushing entry fees back and forth while paying rake.)

Popularity isn't bad, though. Devonta Freeman was popular in this week's Thursday contests, and I'm quite glad that I owned him even more often than the field did. The idea that uniqueness should be specifically sought out when building GPP lineups is, I believe, a popular misconception.

Uniqueness doesn't matter at all. Ownership percentage matters -- but uniqueness is the wrong word for what matters about it. (And not just in the overly pedantic sense that uniqueness, like pregnancy, is strictly binary.)

The players you should be looking for are under-owned players, but under-ownedness and uniqueness are different concepts.

Real DFS is complicated, so let's consider a simplified toy game to examine the relevant principle.

Suppose we have a 100-person contest with a tournament-style payout structure (you can make it winner-take-all for simplicity; it doesn't matter), and each lineup consists of a single player -- either the Broncos defense or the Raiders defense. Suppose the Broncos defense is a 2-1 favorite to outscore the Raiders defense, and suppose that 80% of the entrants will own the Broncos.

It is easy to see that the lineups with the Raiders will win money, on average, while the lineups with the Broncos will lose money. (Two-thirds of the time, 80% of the lineups will split the prize pool; one-third of the time, 20% of the lineups will split the prize pool. The latter group is the one that is +EV.)

The Raiders defense was more unique, and that's the one that was profitable. Does that mean that uniqueness is beneficial?

No. What made the Raiders defense profitable was that its 33% win rate was greater than its 20% ownership, and in that sense they were under-owned. But it's not at all the case that unique players are inherently under-owned while chalk players are inherently over-owned. Change the numbers from the example a bit -- make the broncos 7-1 favorites to outscore the Raiders rather than 2-1 favorites, and now it's the Broncos, even at 80% ownership, that are under-owned while the Raiders, at 20%, are over-owned.

In general, uniqueness might be correlated with under-ownedness. That's an interesting empirical question that is worth looking into. But the correlation would not be perfect in any case, and there may be plenty of situations where 60%-owned guys might be under-owned because they are actually 70% likely to outscore similarly priced players at their position -- as may well have been the case with Devonta Freeman this week.

(See also: similar thoughts on this topic from Steve Buzzard and John Lee.)

So we want to roster under-owned players more often than our opponents, and over-owned players less often than our opponents. There are a few different ways we might accomplish this, and an analogy to poker strategy might help.

In poker, exploitive play is distinguished from game-theory-optimal play. With exploitive play, you're trying to identify and take advantage of specific mistakes your opponents are making, and you'll depart from standard play yourself in order to do so. With game-theory-optimal play, you're trying to avoid making mistakes yourself -- to avoid being exploited by others -- and in the process you'll automatically benefit from others' mistakes even without specifically adjusting your play in response to them. It's helpful to have both styles of play in your arsenal, but the general oversimplification is that you'll maximize your win-rate against bad opponents by playing exploitively, and you'll do better against other experts by using something more like game-theory-optimal strategy.

It occurs to me that a similar distinction exists in GPP strategy. In GPPs, as we said above, it helps to own under-owned players and to fade over-owned players. There are two ways to do this. (1) You could try to determine how frequently a player should be owned, then try to anticipate how often he will actually be owned, and then go out of your way to roster under-owned players and avoid over-owned players. Or (2) you could try to determine how frequently a player should be owned, and then try to own him with that optimal frequency. In so doing, you will automatically have a higher ownership percentage of under-owned players and a lower ownership of over-owned players than the field -- all without ever paying attention to anticipated ownership percentages at all.

I'm partial to the second method. It might leave some money on the table when there are genuine ownership anomalies from time to time. But for the most part, the big crowds aren't usually off by that much all that often. So my time might be better spent working on my own evaluation of a player's optimal ownership frequency instead of worrying about how often other people are likely to own him.

Another commenter from last week asked me if this 100-lineup strategy made me any money in Week 5. I don't think it did, but it's hard to say without a more careful analysis than I've done so far. To be sure, I won money in Week 5 -- 113% ROI including the value of tickets won in qualifiers -- but that was mostly due to luck (as just about any one-week results, good or bad, will be), significantly due to just building good lineups heavy on high-value players, and probably very little due to this particular diversification strategy.

What I'm hoping this strategy will be good for -- aside from just getting a great number lineups into play, which is kind of fun in itself -- is reducing the variance of my results by having more of my bases covered. The tradeoff is that I should expect a lower long-term percentage-ROI as I diversify away from the highest-value players. But a lower variance means I can wager more without increasing my risk of ruin, and wagering more (as long as I have a positive expectation) means winning more money. So my aim is to sacrifice percentage-ROI in order to bet a larger percentage of my bankroll -- and hope that even though I'll win less as a percentage of what I bet, I'll win as much or more in absolute dollars.

This has gotten longer than I intended, so I'll shut up and give you my current ownership targets for Week 6.

LeVeon Bell	33
Larry Fitzgerald	32
DeAndre Hopkins	32
Matt Forte	29
Rob Gronkowski	27
Arian Foster	22
Adrian Peterson	21
Julian Edelman	20
Eric Decker	17
Antonio Gates	17
Dion Lewis	16
Allen Robinson	15
Stephen Gostkowski	15
Mason Crosby	15
NY Jets	15
Justin Forsett	14
Jeremy Maclin	14
Kamar Aiken	14
Seattle Seahawks	13
Brandon Marshall	12
A.J. Green	12
Emmanuel Sanders	11
Allen Hurns	11
Tyler Eifert	11
Tom Brady	10
Greg Olsen	10
Demaryius Thomas	9
Caleb Sturgis	8
Tennessee Titans	8
Giovani Bernard	7
DeMarco Murray	7
Randall Cobb	7
Keenan Allen	7
Cam Newton	6
Aaron Rodgers	6
Eddie Lacy	6
T.Y. Hilton	6
Odell Beckham Jr	6
Donte Moncrief	6
Jordan Matthews	6
Calvin Johnson	6
Gary Barnidge	6
Travis Kelce	6
Matt Prater	6
Denver Broncos	6
Minnesota Vikings	6
Carson Palmer	5
Eli Manning	5
Andy Dalton	5
Chris Ivory	5
Frank Gore	5
Carlos Hyde	5
John Brown	5
Mike Wallace	5
Antonio Brown	5
Jarvis Landry	5
Delanie Walker	5
Blair Walsh	5
Chandler Catanzaro	5
Nick Folk	5
Detroit Lions	5
Cincinnati Bengals	5
Green Bay Packers	5
Blake Bortles	4
Russell Wilson	4
Teddy Bridgewater	4
Philip Rivers	4
Jay Cutler	4
Marcus Mariota	4
Ryan Tannehill	4
Sam Bradford	4
Colin Kaepernick	4
Ryan Fitzpatrick	4
Alex Smith	4
Duke Johnson	4
James Jones	4
Kendall Wright	4
Larry Donnell	4
Ryan Succop	4
Steve Hauschka	4
Chicago Bears	4
Jacksonville Jaguars	4
Baltimore Ravens	4
Josh McCown	3
Andrew Luck	3
Matthew Stafford	3
Danny Woodhead	3
Marshawn Lynch	3
Charcandrick West	3
Melvin Gordon	3
Ted Ginn	3
Travis Benjamin	3
Charles Clay	3
Richard Rodgers	3
Brandon McManus	3
Justin Tucker	3
Mike Nugent	3
Josh Brown	3
Adam Vinatieri	3
Phil Dawson	3
Washington Redskins	3
New England Patriots	3
Arizona Cardinals	3
Cleveland Browns	3
Philadelphia Eagles	3
Michael Vick	2
Peyton Manning	2
Kirk Cousins	2
Joe Flacco	2
Brian Hoyer	2
Antonio Andrews	2
Ameer Abdullah	2
Anquan Boldin	2
Rueben Randle	2
Marquess Wilson	2
Jamison Crowder	2
Golden Tate	2
Zach Ertz	2
Jimmy Graham	2
Jordan Cameron	2
Jason Myers	2
Nick Novak	2
Dan Carpenter	2
Andrew Franks	2
Chris Boswell	2
Robbie Gould	2
Houston Texans	2
San Francisco 49ers	2
Shane Vereen	1
C.J. Anderson	1
Lamar Miller	1
LeGarrette Blount	1
Rashad Jennings	1
Chris Thompson	1
Chris Johnson	1
Michael Floyd	1
Malcom Floyd	1
Eddie Royal	1
Sammy Watkins	1
Doug Baldwin	1
Pierre Garcon	1
Marvin Jones	1
Torrey Smith	1
Rishard Matthews	1
Cecil Shorts	1
Kyle Rudolph	1
Martellus Bennett	1
Crockett Gillmore	1
Julius Thomas	1
Josh Lambo	1
Cairo Santos	1
Travis Coons	1
Dustin Hopkins	1
Buffalo Bills	1
Miami Dolphins	1
Carolina Panthers	1
Pittsburgh Steelers	1
Kansas City Chiefs	1
NY Giants	1