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NOTE: The projections and commentary below are subject to change. If necessary, they will be updated on Saturday afternoon to reflect Steve Buzzard's updated roster percentages. Any revisions to existing commentary will be color-coded: Green if new information has changed a player's situation for the better, red if it has changed his situation for the worse.

Welcome back for Week 2 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 what goes into the model, click here. One slight change going forward is that, because the model relies heavily on Steve Buzzard's roster percentage projections for the overall public, there will be two versions of this article posted each week. The draft version will be released on Thursday and include three things:

1. A post-mortem of the prior week
2. The tables for each position, which contain Buzzard's projections as well as those of the model
3. The names of players that the pros are expected to roster significantly more (or significantly less) than the overall public

The final version will be released on Saturday and include an update of the projections, as well as commentary attached to the players listed previously. Because the projections will change between Thursday and Saturday, it's possible that a player listed in the draft version will be replaced by someone else in the final version.

With that bit of housekeeping out of the way, let's move on to this week's projections.

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Quarterbacks

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

Before proceeding to the commentary, return readers will notice that the table looks slightly different this week. Namely, rather than have a "Difference Ratio" column as a means of identifying which players the pros figure to roster at higher (or lower) rates relative to the overall public, the "Overall" column is now also color-coded. This allows for a quicker, entirely visual inspection. A significant difference in color (e.g., Sam Darnold) indicates a significant difference between the two sets of projections, and therefore implies he's a player to which you should pay particular attention. Indeed, these players are the ones most likely to be subjects of additional commentary. Speaking of which...

Sam Darnold ($4,700, 2.2% Overall, 4.4% Pros)

Darnold ticks all the boxes that the model looks for in a quarterback. Darnold's 27.1% probability of achieving 4x value on Sunday leads all quarterbacks. The defense he's facing, Miami, isn't projected to appear on even one percent of lineups. If the public thinks Miami isn't worth rostering at all, then Darnold should be worth rostering heavily; yet he isn't being viewed that way. Quincy Enunwa (11.7%), Jermaine Kearse (5.6%), and Robby Anderson (5.0%) have a combined projected roster percentage of 22.3%, which ranks third-highest in the slate; yet Darnold's own projection ranks 18th among quarterbacks. Those two rankings can't both be correct at the same time. If people think Darnold's trio should be rostered that much, then they should also think the same of Darnold; yet they don't.

One might raise the point that Miami has allowed the fourth-fewest Draftkings points to opposing quarterbacks. But of course that's based on a single game delayed four hours and against a pass offense led by Blaine Gabbert one third of the time. And besides, if it were the case that Miami's pass defense is truly as good as that ranking, then why are they likely to have a roster percentage less than one percent?

Based on the new numbers, Darnold's roster percentage projection has risen from 18th-ranked to 12th-ranked. The aggregate roster percentage of his wide receivers has dropped to 15.9%, which now ranks seventh instead of third. On the bright side, he still has the No. 1 value probability, and the Dolphins defense is still projected to appear in less than one percent of lineups. Darnold remains a value play that the pros are likely to roster more frequently than the field, but there's not as much edge in the play as there existed previously.

Matt Ryan ($5,700, 3.8% Overall, 5.0% Pros)

The model still projects pros to roster him at a rate 1.7 times the field, but he's risen from 12th in expected pro roster percentage to 6th. This is due to two factors. First, his wide receivers now have an aggregate projected roster percentage of 21.1% (ranked 4th), which is up from 17.7% (8th) earlier in the week. Second, whereas Carolina's defense was previously projected to appear in 2.2% of lineups, they're now at less than 1.0%.

Running Backs

Below is the table for running backs:

Alfred Morris ($3,600, 3.6% Overall, 4.8% Pros)

Morris gets a significant bump from having the fifth-highest probability of achieving 4x value among running backs (23.9%). He also gets a slightly smaller bump from the Lions defense being projected to only appear in 2.3% of lineups. Finally, Morris benefits slightly from San Francisco's wide receivers combining for the 12th-lowest projected roster percentage. This last data point typically implies one of two things: Either the public perceives that the pass offense's share of running back targets will be higher than normal or that the run offense will be more productive. Given that Morris is not a pass catcher, one can assume it's the latter in this case.

It's also important to remember that Detroit allowed 177 yards and two touchdowns on 28 carries last week as a large home favorite. This week, they're a large road underdog, which is typically a scenario that Draftkings pros try to exploit.

All of a sudden, everyone's on Morris to the point that he's gone from a value to a fade. The main culprit is the massive increase in his expected overall roster percentage, which rose from 3.6% to 6.0%. But he's also lost his luster due to changes in two other factors the model considers important. First and foremost, the aggregate projected ownership for San Francisco's wide receivers has exploded from 12.7% to 19.6% thanks to the confirmation that Dante Pettis will start in place of an injured Marquise Goodwin. Second, the overall projection for Detroit's defense has risen slightly from 2.3% to 2.6%.

James White ($4,500, 3.3% Overall, 5.1% Pros)

White's situation is nearly identical to that of Morris, except he actually is a pass catcher. New England's receivers combine for only 5.5% projected rostering, which implies that the public perceives a higher relative target share for Patriots running backs. This conclusion is also buttressed by the fact that Jacksonville has one of the best secondaries in the league. If New England is to have success in the passing game on Sunday, it will be via their running backs (and/or Rob Gronkowski). Also related to the matchup, despite their overall quality as well as the benefits of playing at home, the Jaguars' defense is projected to appear in only 2.5% of lineups, which ranks eighth-lowest on the Sunday main slate.

Elsewhere, White himself has the fourth-highest probability of achieving 4x value (25.6%), no doubt due in part to Rex Burkhead (concussion) and Sony Michel (knee) being questionable to play. As Ryan Zamichieli noted in his "The Sharp Report" article this week, another situation pros try to exploit is when one or more other members of a team's backfield are not available for the game.

Like Sam Darnold, the public has caught wind of White's value since Thursday. Unlike Darnold, the roster percentage gap between pros and the field is now completely closed. What happened was that his overall projection increased from 3.3% to 5.9%, and the projection for his opposing defense increased from 2.5% to 3.0%. If that wasn't enough, there's this:

Rex Burkhead (concussion) made progress this week and traveled with the Patriots to Jacksonville, per source. Encouraging sign for tomorrow.

— Jeff Howe (@jeffphowe) September 15, 2018

James Conner ($6,700, 33.8% Overall, 38.2% Pros)

Before discussing Conner's pro projection for Week 2, just a quick note about Week 1. The primary reason Footballguys has decided to include a Saturday afternoon update for this article is exemplified by Conner's situation in Week 1. Because Le'Veon Bell was still expected to play when Buzzard released his initial roster percentages on Wednesday, Conner ended up not even appearing in this article's running back table. However, when the model was rerun on Saturday afternoon after Buzzard's update, Conner's pro projection came in at 35.1%, which ranked only behind Alvin Kamara. Furthermore, this pro projection was a full five percentage points higher than his overall projection, so no doubt he would have been highlighted in the commentary. Thankfully, we have remedied the issue so that it won't happen again going forward.

Which is an apt segue to Week 2, as Draftkings has not fully remedied Conner's salary despite increasing it by $2,200 based on last week's breakout performance. He should be even more expensive to roster. For example, he's still $2,800 cheaper to roster than Kamara despite having a Draftkings points projection only slightly lower. That's a savings that pros usually don't pass up and is manifested in Conner's position-leading 32.6% likelihood of achieving 4x value this week. For comparison, Kamara's is only 18.3% despite playing as a consensus 9.5-point favorite at home against Cleveland. This discrepancy is precisely because of the difference in salaries.

Another factor that increases Conner's pro projection is that the Chiefs defense, which gave up 49.3 points to Chargers running backs last week, is projected to appear in less than one percent of tournament lineups. If the public perceives Kansas City to do that poorly, then they should be rostering Conner -- especially at his current salary -- even more frequently.

Tevin Coleman ($6,700, 31.3% Overall, 36.4% Pros)

Coleman is a late-breaking addition to the John Conner club of chalk running backs that the model expects pros to roster at a higher rate than the public. He gained this status by virtue of Devonta Freeman being declared out for Sunday's game. (Remember: As was mentioned in the above commentary on James White, pros tend to exploit situations in which a running back will benefit from his stablemate's absence.) In terms of the model-related reasons for Coleman's pro projection being higher than his overall projection, the overwhelming factor is that he now ranks second among running backs -- behind only Conner -- with a 30.1% probability of achieving 4x value.

Corey Clement ($3,500, 1.7% Overall, 4.2% Pros)

With Darren Sproles being declared out for Sunday's game, Clement is poised to assume the receiving back role for Philadelphia. On a PPR site like Draftkings, that role is especially coveted. The concomitant increase in his Footballguys projection, which has doubled from 5.2 points to 10.3 points means his likelihood of achieving 4x value has taken a quantum leap from 4.4% (ranked 42nd) to 29.0% (ranked 4th). No doubt related to his increased involvement in the passing game, the combined roster percentage projection for Eagles wide receivers has dropped from 11.1% to 7.9%, which further boosts his projected pro ownership percentage.

Wide Receivers

Below is the table for wide receivers:

Randall Cobb ($4,600, 10.1% Overall, 11.7% Pros)

Compared to the other wide receivers projected for high overall roster percentages, Cobb is a steal at $4,600. The reason why he's only one of a few that pros can be expected to roster at an even higher rate is because his probability of achieving 4x value is a position-leading 32.0%. Also in his favor is that the Vikings defense is projected to appear in only 2.3% of lineups. So again, just to keep driving the point home, the rate at which you roster offensive players should be commensurate with -- and in opposition to -- the rate at which you roster defenses. When it appears that the defense is ranked lower than expected, it's likely the case that either the defense should appear in more lineups or the offensive players competing against them should appear in more lineups. It must be one or the other, as it's mathematically unlikely both discrepancies will prove correct simultaneously.

As is the theme with this Saturday update, the gap between Cobb's overall and pro projections has disappeared since Wednesday. However, this time it's not due to a number of relevant model factors moving in the same direction to a player's detriment. Rather, the reduced edge in rostering Cobb is because Buzzard's projection for the Vikings' overall roster percentage has more than doubled, from 2.3% to 5.3%.

Corey Davis ($5,100, 4.8% Overall, 5.3% Pros)

One suspects Davis' relatively low projected roster percentage is due to Tennessee's vague -- to put it politely -- situation at quarterback. The good news, however, is that Davis' target rate in Week 1 did not depend on who was throwing the passes. Marcus Mariota targeted him seven times before leaving the game with injury, and Blaine Gabbert targeted him six times in one-plus quarters of work. To boot, that 34.2% target share doesn't figure to decrease given the Titans' other target hog, Delanie Walker, is now out for the year.

As opportunity is king in fantasy football, it's not surprising then that the model projects a significantly higher pro roster percentage than his overall rate. Specifically, Footballguys translates it to 14.0 projected points. And combined with his paltry salary, Davis' probability of achieving 4x value comes out to a fifrth-ranked 22.7%.

What's particularly unique about Davis' pro projection being higher than his overall projection is that it's higher despite Houston's defense ranking near the top of projected roster percentages (8.4%, 2nd). In other words, he's actually hurt by one of the key variables in the model, and yet still figures to be one of the pros' value plays on Sunday.

Antonio Brown ($8,800, 31.5% Overall, 39.7% Pros)

Did you roster Keenan Allen at higher-than-projected rate last week despite him being the chalk? If so, congratulations on a profitable week. One of the things keen-eyed readers might have noticed about the model is that players ranked No. 1 at their position according to Buzzard's overall roster percentage projections tend to have a pro projection even higher. Indeed, in developing the model this offseason, one finding that stood out was that the 205 winning tournament players who enter at or near the maximum number of lineups (i.e., employ "mass multientry") don't "fade the chalk" as much as is assumed by avid tournament players. This is simple, unavoidable math in part. If this particular group of contestants is maxing out 150 lineups in a large Draftkings tournament, that means over 30,000 lineups in said tournament will belong to them. (Indeed, maximizing one's percentage of the field is one of the main game theoretical benefits of mass multientry.) So if these pros represent such a large portion of all lineups, it can't be the case logically that they're all "fading the chalk." Otherwise, it would be impossible for those players to end up being the chalk!

Which brings us to Brown, who is this week's wide receiver chalk. Despite his lofty salary, Brown's probability of achieving 4x value is still a sixth-ranked 22.5% because of his lofty Footballguys projection. In addition, after giving up over 500 yards of total offense, over 400 of which came via the pass, Kansas City's defense is projected to appear in less than one percentage of tournament lineups according to Buzzard. Oh, and which wide receiver benefited from the Chiefs' largesse? Last week's chalk, Keenan Allen.

Kenny Stills ($5,700, 6.5% Overall, 5.0% Pros)

Stills was the wide receiver darling of pros last week, and for good reason. With a $4,700 salary, a 26.6% value probability, and going against a Titans defense projected to appear in only 2.0% of lineups, the model projected pros to roster him at 1.5 times the overall rate. Week 2 presents almost the complete opposite situation. Draftkings increased his salary by $1,000, which is the fourth-largest increase for wide receivers in the Sunday Main slate (Emmanuel Sanders +1,200, Tyreek Hill +$1,100, and Keelan Cole +$1,100). This increase coupled with a Footballguys projection of 13.2 points translates to Stills' likelihood of achieving 4x value decreasing by more than half, to 12.5%. In further contrast to Week 1, he'll be facing a New York Jets defense projected to be one of the more highly rostered on the slate (7.2%, ranked 5th).

Tight Ends

Below is the table for tight ends:

George Kittle ($3,800, 20.1% Overall, 24.4% Pros)

Kittle's situation is similar to Conner's vis-a-vis Kamara: Pros are likely to exploit the massive salary difference between Kittle and Rob Gronkowski when their scoring projections are only 3.5 points apart. Indeed, Kittle's 4x value probability (45.6%) leads all tight ends in the Sunday Main slate, whereas Gronkowski's (16.5%) ranks 11th. Both, however, do benefit in terms of projected pro roster percentage because, as has been noted previously, the defenses they're facing -- Detroit at 2.6% and Jacksonville at 3.0% -- are near the cellar in the eyes of the public.

Travis Kelce ($5,900, 7.9% Overall, 5.3% Pros)

This might be a week to reduce your exposure to Kelce in Draftkings tournaments. With a an average Footballguys projection of only 14.8 points at $5,900, he only has a 14.9% probability of achieving 4x value. Furthermore, at a combined 18.6%, Kansas City's wide receiver corps is projected to be the fifth-highest group on the slate. This is likely to increase even further as the Steelers listed cornerback Artie Burns (toe) as questionable and cornerback Joe Haden as doubtful on their Friday injury report.

This indeed has increased further. The previous combined projection for Chiefs wide receivers was 16.7%.

Defenses

Below is the table for defenses:

San Francisco 49ers ($2,800, 2.1% Overall, 3.5% Pros)

San Francisco is a 6-point home favorite against a Lions offense that surrendered 23.0 Draftkings points to the Jets defense last week -- at home no less. Due to the randomness of their scoring and having salaries far below that of other positions, the majority of defenses each week have a greater than 25 percent (i.e., 1 in 4) chance to achieve 4x value. In this case, San Francisco's is 27.6%, which ranks a middle-of-the-road 13th on the Sunday Main slate. Rather, the driver of their increased pro roster percentage relative to the overall public is that their opponent's quarterback, Matthew Stafford, has the fifth-lowest projection according to Buzzard (1.9%). Again, if people think Stafford won't do well enough to be worth rostering, then they must think the 49ers defense will do well, and therefore should be worth rostering at a rate higher than 2.1%.

It's fitting that the final update follows the overall theme: San Francisco is no longer a value likely to be exploited by the pros. The decreased discrepancy between the two roster percentage projections is almost entirely due to Matthew Stafford going from 1.9% overall to 3.2% overall.

What's more, it seems that the entire slate of defenses has reached an equilibrium state between the two projection systems. The only defense that's wildly off -- as indicated by the color-coding -- is New Orleans. But Cleveland just announced their intention to release Josh Gordon, so far be it from this writer to recommend fading them.

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