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The past few weeks, I've been presenting the highest and lowest probabilities of achieving value given three parameters:

1. A player's FantasyScore salary.
2. A player's projected FantasyScore points according to Footballguys.
3. The variance in weekly FantasyScore points among players at a given position.

In total, there have been 297 games played by quarterbacks so far in 2015. For each quarterback game, I (a) calculated the in-advance probability of achieving value in a DFS cash game, and (b) determined whether or not the the actual performance achieved value. Next, I formed 10 groups of predicted probabilites. Why? Think about it. If I predicted a 4.9% chance of a specific quarterback achieving value in a cash game, how many quarterbacks could possibly have that exact predicted value on a scale of 0-to-100 percent? Not many; hence grouping.

Once I grouped these quarterback performance in 10 percent intervals (i.e., 0-to-9 percent, 10-to-19 percent, and so on), I made the following graph of predicted results vis-a-vis actual results:

In this chart, the x-axis (i.e., the bottom) represents the predicted probability intervals (i.e., 0-to-9 percent, 10-to-19 percent, and so on), while the y-axis (i.e., the left) represents actual results for quarterback performances in 2015. If we plot one against the other for the 297 weekly FantasyScore performances by quarterbacks this season, we get the blue line with blue diamond almonds -- sorry, markers. The red line represents a 1-to-1 correspondence between predicted and actual results, and so it's the ideal associated with what the blue line should be.

As you can see, the blue (actual) line adheres closely to the red (what we want it to be) line. The only large discrepancy is when my system predicts a value probability of 10-to-19 percent. But guess what: That group only has 8 cases, and so its "off-ness" can be attributed (for now) to small sample size. Truth be told, so can the "0-9," "80-89," and "90-99" groups.

And so what's the lesson here? When you see a quarterback in one of my tables with a probability of achieving cash game value between 20 percent and 69 percent, believe it. Otherwise, lean towards believing it, but remain skeptical: More data is required. 

quarterbacks

Below are the quarterbacks with the highest (and lowest) probabilities of achieving value in cash games and GPPs:

Is this table telling you to stake your Week 11 DFS hopes on Matt Hasselbeck? No. It's simply saying that, if you wish to go for value at quarterback this week, Hasselbeck is far and away the best option. Truth be told, the matchup differences between high-value quarterbacks suggest that Alex Smith (at San Diego) is your best value bet in cash games, while Hasselbeck (at Atlanta) is your best value bet in tournaments. San Diego has the worst pass defense, but Atlanta's isn't all that better, and the game script may very well dictate a higher-than-normal pass-run ratio for Indianapolis. Or, given the dropoff from Andrew Luck, the Colts might actually run the ball more often than normal. But hey, that kind of uncertainty means variance, which is (another reason) why I'm saying Hasselbeck's best use is as a value play in GPPs.

In terms of unlikely value, I would avoid the trios on both sides of the table, especially Rodgers and Dalton, the latter for his bad matchup (on national television no less, if you believe in that sort of thing) and the former for his combination of high salary and injured throwing shoulder.

running backs

Below are the running backs with the highest (and lowest) probabilities of achieving value in cash games and GPPs:

OK. Here's one of those rare situations wherein almost all of the high-value targets in the table aren't worth rostering. Carlos Hyde could only muster 4.0 points against the Seahawks in San Francisco, so Draughn -- who is no Carlos Hyde -- at Seattle seems like fool's gold. Thompson at Carolina? No thanks. Baltimore running backs? No thanks. Gordon? Wake me up when he does something of note. The only option I'd consider is Rawls, but (obviously) only if we get advance warning that Marshawn Lynch either isn't playing because of his abdominal injury or will be on a snap count of some sort.

Just as much pessimism lies on the low-value side. Of the seven running backs listed, the only one worth taking a chance on is Adrian Peterson because a) Green Bay's rush defense ranks 28th according to Football Outsiders, and b) he's Adrian F***ing Peterson.

wide receivers

Below are the wide receivers with the highest (and lowest) probabilities of achieving value in cash games and GPPs:

All hands on deck for Inman, and, as a contrarian value play, one of the two Seahawks wide receivers. San Diego has a pass-happy offense and they're facing the 28th-ranked pass defense. Meanwhile, Seattle has the antithesis of a pass-happy offense, but they're facing the the 31st-ranked pass defense...at home...in a one-side rivalry game dominated by their side.

On the other side of the ledger, if there was one wide receiver that I'd roster despite low value, it would be Dez Bryant, especially in GPPs. When a wide receiver and his quarterback are both coming off injuries (and perhaps prematurely so), it's complete reasonable to avoid both. That said, Bryant's been back for 3 weeks, and the one thing missing from his fantasy scoring potential has been a competent quarterback. Enter Romo. If anywhere near fully healthy, there's a better-than-in-the-above-table chance that Bryant achieves value at Miami, who -- oh by the way -- ranks 26th in pass defense. 

tight ends

Below are the tight ends with the highest (and lowest) probabilities of achieving value in cash games and GPPs:

I'm all-in on Ertz with respect to lineups including a high-value tight end. You should be too. Here's an article wherein a massive Buccaneers fan explains why.

In contrast, I'm bearish on taking a chance on any of the tight ends that are unlikely to achieve value. According to Football Outsiders, Carolina is the 4th-most efficient pass defense against the position, so Reed is a no-go. Similarly, Denver's ranked 9th, so Bennett's a no-go; Philadelphia ranks 3rd, so Cameron's a no-go; and Arizona ranks 1st, so Eifert's a no go.

If I all-of-a-sudden found myself in the same predicament as Christopjer Walken in The Deer Hunter, I'd go with Bennett as the contrarian play, simply because of the disparity between the trajectories of these two teams.

defenses

Below are the defenses with the highest (and lowest) probabilities of achieving value in cash games and GPPs:

From the table, we can see that whether you're playing a cash game or a GPP is of no consequence: The Top 3 values are the same in both formats, as are the Bottom 3. But which to use, you ask? On the high-value side, the defense worth rostering is Chicago: The Broncos rank dead-last in offensive efficiency and are starting their backup quarterback on the road in a game on their schedule between a division rival and the undefeated New England Patriots.

On the low-value side, none of the three matchups seem to provide a benefit above and beyond the expense.

WEEK 11 DRAFT LISTS

Finally, to supplement the statistics-based strategies I recommended earlier in the season, here are the VBD draft lists you should use for FantasyScore's Draft-N-Go (DNG) games:

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