Photo: Grace Hollars, USA Today Sports

NOTE: The pro projections below are first posted on Thursday, then updated on Saturday afternoon. On Thursday, commentary will be limited to early impressions. A more-detailed discussion of specific players will be added on Saturday afternoon.

Welcome back for Week 16 of Footballguys' new feature that uses a statistical model to project the roster percentages of "professional" tournament players on Draftkings. If you're curious about the full methodological details of the model, click here. The most important detail to keep in mind, however, is that the "professionals" in question were identified using a clustering algorithm and can be characterized by the following statement: Compared to the rest of the population, these 205 pros play more, they win more, and they do both consistently.

Quarterbacks

Below is the table for quarterbacks. In this and all subsequent tables, "Overall" is Steve Buzzard's projection of roster percentage. "Pros" is the model's projection of roster percentage for Draftkings pros only.

Early Impressions

There's still plenty of time for things to change, but I went back and checked, and this is the first time all season that the highest pro projection at quarterback is actually below the overall projection. (In a bit of symmetry, Andrew Luck barely missed the mark just last Thursday.) The reason why Luck gets this ignominious distinction is because he ranks 8th (of 21) right now in 4x value probability (25.0%) and 12th in the combined rostership projection of his wide receiver corps (14.7%). In other words, at such a high salary, Luck requires a higher point total to achieve 4x. But how is he going to score that many points if only one of his wide receivers -- T.Y. Hilton -- is worth rostering?

You might be saying, "Wait a minute. Eric Ebron's at 13.8% projected rostership this week! He should count!" Aside from the fact that including tight ends in this calculation was rejected when building the pro projection model last offseason, even agreeing for the sake of argument that Ebron should count, how does Luck get to 300 passing yards (i.e., the three-point Draftkings bonus) primarily via only Hilton and Ebron? Even including running backs as well as tight ends, the Colts' pass offense has not had a single game in which two pass catchers had 100-plus receiving yards. Furthermore, out of 448 team games so far this season, such a phenomenon has only occurred 27 times across the entire league, or a mere 6 percent of the time:

• Pittsburgh (4) = Weeks 2, 3, 6, and 11
• Kansas City (3) = Weeks 2, 6, and 11
• Minnesota (3) = Weeks 2, 4, and 8
• Chicago (2) = Weeks 4 and 10
• Houston (2) = Weeks 2 and 4
• New Orleans (2) = Weeks 1 and 3
• Tampa Bay (2) Weeks 1 and 10
• Eleven teams tied at 1

And if we don't include running backs (i.e., just going with the apples-to-apples, Hilton-Ebron-like comparison), it's only happened 22 times, or 5 percent of the time. So, to drive the point home, given their current overall roster percentage projections, Luck almost certainly needs both Hilton and Ebron to reach 100 yards receiving in order to reach 300 yards passing himself, and neither the leaguewide or Colts specific frequencies suggest that's highly unlikely to happen.

SATURDAY UPDATE: Luck's situation has improved slightly since Thursday, but the pro projection model still views him unfavorably. Luck's probability of achieving 4x value increased to 25.3%, and the aggregate projected rostership for his wide receiver corps increased to 15.2% (or 30.3% if you want to include Ebron). Projected rostership for the Giants defense also decreased slightly, from 1.4% to 1.2%.

Nick Foles ($4,700 salary, 9.0% overall roster projection, 10.4% Pro Projection)

Foles' favorable standing according to the model is almost entirely due to his second-ranked 38.0% probability of achieving 4x value. Outside the model, his matchup against is one of the best on the Sunday Main slate, what with Houston having allowed the most fantasy points to opposing quarterbacks over their past five games. And those five games include a strong game against Washington in Week 11 (189 passing yards, 1 touchdown, and 2 interceptions allowed). Since then, the Texans have allowed an average of 338 passing yards per game.

Dak Prescott ($5,700, 8.5%, 9.9%)

Prescott's 33.7% probability of ahcieving 4x value ranks just behind Foles in third. He also benefits in the model from Tampa Bay's defense being projected to appear in less than one percent of tournament lineups. That said, Prescott's matchup may not be all it's cracked up to be. That's because, since the Buccaneers fired defensive coordinator Mike Smith after a Week 6 loss, Tampa Bay has flipped from a passing funnel to a rushing funnel. In their first five games, they allowed an average of 356 passing yards -- including a 300-yard passer in all five -- but only 84 rushing yards. In the ensuing nine games, they've allowed an average of only 204 passing yards -- including not a single 300-yard passer -- but nearly double the rushing yards as before (153). As yardage bonuses are key to winning Draftkings GPPs, it might be adviseable to rely more on Ezekiel Elliott in your Sunday Main slate lineups.

Running Backs

Below is the table for running backs:

Early Impressions

It's a miracle! After almost all of the past three months involving the "chalk" spot being filled by inexpensive running backs, this is now two weeks in a row that Ezekiel Elliott, a decidedly not inexpensive running back, tops the table. And just like last week, the reason is that his probability of achieving 4x value is abnormally high for a player of his ilk. In fact, last week, he ranked 16th among running backs in the Sunday Main slate, at 13.4%. This week, he ranks -- wait for it -- 16th again, at 14.1%, in a much easier matchup.

SATURDAY UPDATE: Elliott's even more chalky than he was earlier in the week. According to the pro projection model, that's because his 4x value probability has risen from No. 16 to No. 11. It's now 16.3%, which is almost unheard of for a running back with his salary.

Nick Chubb ($5,500 salary, 19.2% overall roster projection, 17.8% Pro Projection)

and Marlon Mack ($5,500, 12.4%, 9.3%)

After Elliott, there are a slew of running backs that the pro projection model views less favorably than the overall public. But the model is by no means perfect, so at least one of them has to defy the odds. This author's picks are Chubb and Mack for a variety of reasons. First, they both have 4x value probabilities that rank in the Top 10 of the position: Chubb's is 20.1% (7th); Mack's is 17.0% (10th). Second, they're both facing defenses projected to appear in only around one percent of lineups. Likely related to this, they're both playing as home favorites of a touchdown or more. And speaking of the matchup, the Bengals and Giants rank in the bottom quartile of the league in terms of points allowed to opposing running backs, both across the full season and over their last five games.

And in the case of Mack, it's worth pointing out the game theory angle of rostering him heavily so as to counteract the chalkiness of Andrew Luck, T.Y. Hilton, and Eric Ebron.

Matt Breida ($4,200, 3.4%, 6.9%)

and Kenyan Drake ($3,900, 3.3%, 5.6%)

These two are grouped together here because their situations, both in and out of the pro projection model, are strikingly similar. They're both inexpensive running backs projected for low rostership who are playing at home. Both are involved in the passing game and are facing defenses that have allowed exactly 8.3 Dratkings points per game via running back receptions. With respect to the model, Breida (42.7%) and Drake (29.4%) rank first and second on the slate in terms of 4x value probability. If you're looking for salary relief and a modicum of contrarianism, they're two big values that allow you to pivot away from some of the more expensive, popular running backs not name Ezekiel Elliott. In fact, they're perfect complements to Elliott insofar as they're precisely the running backs that will allow you the salary cap space to roster Elliott in the first place.

Wide Receivers

Below is the table for wide receivers:

Early Impressions

Robby Anderson is the darling of the pro projection model this week for one reason: He ranks No. 1 among wide receivers with a 32.3% probability of achieving 4x value.

SATURDAY UPDATE: Anderson is even chalkier now and viewed even more favorably by the pro projection model because his 4x value probability has increased to 34.1%, which is still No. 1 among wide receivers on the Sunday Main slate.

Davante Adams ($8,500 salary, 10.5% overall roster projection, 8.9% Pro Projection)

A la Elliott vis-à-vis running backs, the model doesn't view many wide receivers favorably immediately below Anderson in the table. Adams stands out among this group due to having a 4x value probability of 20.7%, which ranks eighth. And like Elliott, this is absurdly high for a wide receiver with Adams' salary. In terms of his matchup, the Jets rank third-worst in points allowed to opposing wide receivers, both over the course of the full season and over their past five games. Individually, Pro Football Focus has assessed Adams as having the fifth-best cornerback matchup of the week.

Tight Ends

Below is the table for tight ends:

Early Impressions

Zach Ertz topping the table and being favored by the pro projection model vis-à-vis his overall projection is one of the more perplexing statistical developments of the year in this space. In terms of 4x value probability, he ranks 10th of 18 tight ends in the table (15.6%). And in terms of the projected roster percentage for his opposing defense (Houston, 3.0%), he ranks 11th. One could make the Elliott-esque argument about that actually being an outlier due to Ertz's salary, but Eric Ebron ranks higher on both metrics a nearly identical salary.

SATURDAY UPDATE: Ertz's pro projection has increased, but his overall/pro gap didn't increase because his 4x value probability has decreased from to 14.4% (still ranked 10th among tight ends).

Chris Herndon ($3,100 salary, 7.9% overall roster projection, 8.1% Pro Projection)

If you want to pivot away from Ertz and Ebron, there are three tight ends in favorable situations, both in terms of the model and in terms of their matchups (Herndon, David Njoku, and Austin Hooper). The one who shows best is Herndon, who ranks No. 1 on the Sunday Main slate with a 24.4% probability of achieving 4x value. And according to Pro Football Focus, he has the fourth-best individual matchup, and this advantage is mirrored in Austin Lee's normalized strength of schedule, which shows that the Packers have allowed the second-most fantasy production to tight ends over their past five games.

Defenses

Below is the table for defenses:

Early Impressions

New England is the darling of the pro projection model this week for one reason: They rank No. 1 among defenses with a 68.0% probability of achieving 4x value. But this isn't just the highest 4x probability on the Week 16 Sunday Main slate. It's the highest of any defense on the Sunday Main slate all season. The only other defenses above 60 percent were Dallas (at Seattle) in Week 3 and Green Bay (vs. Arizona) in Week 13. Of course, Dallas scored 2 Draftkings points and Green Bay scored 3 points in those two games, so some skepticism here is reasonable.

SATURDAY UPDATE: The only thing that's changed since Thursday is that their opposing quarterback, Josh Allen, has seen his overall rostership projection increase from 4.2% to 5.2%, which is a negative indicator in the model.

Los Angeles Rams ($3,200 salary, 9.8% overall roster projection, 9.3% Pro Projection)

As was the case with running backs, there's a heap of defenses after the absolute chalk that the pro projection model views less favorably than the overall public; and the model has to be wrong on one of them. The Rams are who this author is putting his money on. Nevermind that colleague Steve Buzzard won the Fanduel championship last week with a defense facing Arizona. The Cardinals have allowed the most Draftkings points per game to opposing defenses this season. And working against the likes of Aaron Donald and Ndamukong Suh, Pro Football Focus has this matchup in the trenches as the most lopsided of the year. This must be a contributing factor to Josh Rosen being the only main slate quarterback projected to appear in less than one percent of lineups, which, it should be noted, provides a boost to the Rams defense in the model. Oh, and so does the fact that they rank second behind the Patriots with a 53.6% probability of achieving 4x value.

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