# Expected Playoff Games Played

Projected playoff fantasy points based on expected number of games played.

One of the most important sources -- if not the most important source -- of arbitrage in playoff fantasy football is in accurately projecting how many games each team is going to play. Last postseason, I detailed a system for doing just that.

And looking back at how the 2014 playoffs actually turned out, the system did quite well. One way to test its accuracy is to compare the expected games for each team that my system projected versus the expected games for each team that was implied by the actual Vegas lines in the games they actually played. For instance, going into last year's playoffs, my article projected 2.30 expected games for Seattle based on the following likelihoods for them playing a given number of games:

• Probability of playing exactly 1 game = 18.7%
• Probability of playing exactly 2 games = 32.4%
• Probability of playing exactly 3 games = 48.9%
• Probability of playing exactly 4 games = 0.0% (They had a first-round bye, so 4 games was impossible.)

The math to convert the above probabilities into expected games is (18.7% * 1) + (32.4% * 2) + (48.9% * 3) + (0.0% * 4) = 2.30.

In comparison, the probabilities based on the Vegas lines for games Seattle actually played were as follows:

• Probability of playing exactly 1 game = 19.6%
• Probability of playing exactly 2 games = 21.2%
• Probability of playing exactly 3 games = 59.2%
• Probability of playing exactly 4 games = 0.0%

And the math to convert these probabilities into expected games is (19.6% * 1) + (21.2% * 2) + (59.2% * 3) + (0.0% * 4) = 2.40.

Based on the above, my system was off by 0.10 expected games, which is good enough for me, especially when you remember that, going into the Wild Card round of last year's playoffs, I didn't know the actual line for any of the games Seattle would end up playing. Now, if we repeat this exercise, calculating "expected game error" for all 12 teams, we get the following list:

Teamproj Exp GVegas Exp Gabsolute Error
SEA 2.30 2.40 0.09
NWE 2.15 2.19 0.04
DAL 2.12 1.91 0.21
DEN 2.00 1.70 0.30
GNB 1.97 1.85 0.12
PIT 1.88 1.59 0.29
IND 1.81 1.82 0.01
CAR 1.81 1.82 0.01
BAL 1.64 1.54 0.11
CIN 1.52 1.41 0.11
ARI 1.42 1.31 0.11
DET 1.39 1.31 0.07
AVG 0.12

The bottom row shows that the average error across all of last year's playoff teams was 0.12 expected games, from which we can reasonably conclude that my system did a good job of projecting Vegas lines in future rounds (and therefore, future win probabilities; and therefore, expected games). The two biggest misses were because Pittsburgh lost as a 60-40 favorite to Baltimore in the Wild Card round and Denver lost as a 70-30 favorite to Indianapolis in the Divisional round. However, if you clicked on the link to last year's column, you'll notice that Baltimore was actually one of the teams I identified as having an expected games total higher than what was implied by their (No. 6) seed. The other team I identified as such was Dallas (i.e., a No. 3 seed that ranked ahead of two No. 2 seeds in expected games). They, like Baltimore, held a fourth-quarter lead on the road in the Divisional Round, only to see controversy -- to put it politely -- dash their hopes and prevent my system from producing even better results. Maybe that's what it's actually good at projecting: soul-crushing defeat!

## expected playoff games played

Alright, after looking back, it's time to look forward to this year's playoffs. The procedure I used last year to calculate expected games is the same, except for one wisdom of crowds-related component. This season, Fivethirtyeight.com and ESPN Stats & Info have joined Football Outsiders as statistical outlets that publish playoff win probabilities, so I'm now sourcing them as well. Furthermore, for the purposes of calculating Wild Card win probabilities, in addition to those implied by the Vegas lines, I'm also including as a source the probabilities implied by Pro Football Reference's Simple Rating System (SRS) because the combination of Vegas lines and SRS-implied lines ended up giving me great personal satisfaction in Footballguys' Staff Confidence Pool this season. (Just kidding. Again, it's because the more sources, the better.)

So, without further ado, here are the expected game totals for each team in this year's playoffs:

ARI 27.2% 38.8% 34.0% 0.0% 2.07 2.41
CAR 37.2% 24.1% 38.7% 0.0% 2.01 2.40
NWE 38.3% 31.2% 30.6% 0.0% 1.92 2.23
KAN 37.6% 33.9% 13.8% 14.7% 2.06 2.20
DEN 43.7% 25.0% 31.3% 0.0% 1.88 2.19
SEA 40.0% 32.1% 12.9% 15.1% 2.03 2.18
CIN 49.0% 30.9% 10.6% 9.5% 1.81 1.90
PIT 51.0% 27.5% 11.8% 9.7% 1.80 1.90
GNB 44.5% 42.7% 8.6% 4.2% 1.73 1.77
WAS 55.5% 32.4% 8.6% 3.5% 1.60 1.63
MIN 60.0% 28.1% 7.3% 4.5% 1.56 1.61
HOU 62.4% 25.8% 7.8% 3.9% 1.53 1.57

In case you didn't read last year's article, here's how to read the table. In the header row, P(1), for example, means "the probability of playing exactly one game," P(2), means "the probability of playing exactly two games," and so on. EXP G is the number of expected games, and ADJ EXP G is the number of expected games if you're playing in a contest where fantasy points accumulated in the Super Bowl counts double. (Again, refer to last year's article if you want to see how I calculate this ADJustment to EXP Games.)

So, take Arizona, for instance. They have a 0.0% probability of playing four games because it's impossible for teams with a first-round bye to do so. Meanwhile, they have a 27.2% chance of playing exactly one game (i.e., losing in the Divisional round), a 38.8% chance of playing exactly two games (i.e., winning their Divisional round game, but losing the NFC Championship game), and a 34.0% chance of playing exactly three games (i.e., winning both their Divisional round game and the NFC Championship game). Applying the math I did earlier in this article, this set of probabilities means the Cardinals can be expected to play 2.07 games. And for contests that double-count Super Bowl points, Arizona's 2.07 expected games is the equivalent of 2.41 games after adjusting for their 34.0% chance of making the Super Bowl [i.e., P(3)].

In a typical postseason (with last year being a prime example), higher seeds are more likely to win any given game because they're at home and they're probably the "truly" better team. As has been discussed extensively over the past few days, however, this week's matchups (and potential matchups in upcoming weeks) are (and will be) rife with conflict between statistics and seedings. Two teams stand out as having being seeded due to their record far lower than what their statistics suggest: Kansas City and Seattle. According to Football Outsiders, the Seahawks were the most efficient team in the league for the fourth consecutive season (per DVOA) and are the second-most likely to win it all this season, but insurmountable early-season hiccups have made them the No. 6 seed in their conference. Similarly, Kansas City is the No. 5 seed in the AFC despite ranking 5th among all teams in both DVOA and Super Bowl win probability. It's not just Football Outsiders that holds these views, by the way. Fivethirtyeight has Seattle No. 1 overall with the 5th-highest Super Bowl win probability, while Kansas City's ranked 4th and 6th, respectively. Per Pro Football Reference, Seattle and Kansas City are the 2nd- and 4th-best teams in the NFL, respectively.

On the flip side, Denver is overseeded in comparison to their metrics: 8th in the league per DVOA, 5th per Fivethiryeight, and tied for 8th among playoff teams per Pro Football Reference. And by virtue of only being able to play three games maximum, their expected games total falls below both Seattle's and Kansas City's. Even if you're playing in a "Super Bowl counts double" format, the Broncos only ascend into a virtual tie with them.

All of the above illustrates what I think most experts would agree is the key to dominating playoff fantasy contests. NFL rules dictate that four playoff teams can only play three games, while eight can play four games. Most people are going to try to load their roster with players from those three-max teams because a) they're usually the best teams, and b) they start the playoffs closer to the Super Bowl. Therefore, the shortest path to playoff fantasy victory, regardless of format, is to attack your opponents from both sides: Correctly identify the four-max teams that will overperform their seed and correctly avoid the three-max teams that will underperform their seed. It's easier said than done, and as much art as science, but hopefully my expected games system will be the science part that helps you get it done.

## projected playoff fantasy points

But that's not all!

Like last year, I've used the expected game totals above to calculate expected FFPC points for both standard (EXP PTS) and "Super Bowl counts double" (ADJ EXP PTS) contests. For the vast majority of players, I've simply multiplied their scoring averages over Weeks 13-16 by the expected games total for their team. The exceptions were players for which injuries have affected their Week 13-16 scoring averages and/or their expected playoff games. In their cases, I did several hours of research to produce better approximations of their expected points.

As an example of forming an educated guess about a player affected by injury in Weeks 13-16, take Tyler Eifert. He missed Weeks 13, 15, and 16, so his relevant scoring average would only be based on one game; that's not ideal. At the same time, all games prior to Week 13, and even the game in Week 14 that he did play, were started by Andy Dalton, who is out this week (and perhaps beyond), so calculating an average using games prior to Week 13 wouldn't be a good reflection of how much he scores with A.J. McCarron at quarterback. Therefore, as loathe as I am to use stats from Week 17 for anything besides attempts at humor, both Cincinnati and their opponent, Baltimore, played their starters the entire way, so I included Eifert's points against the Ravens -- along with his points from Weeks 10-12 -- in his four-game average.

As an example of forming an educated guess about a player whose expected games total will be affected by injury (and will produce cascading effects for other players), take Houston's wide receiver situation. Studying Houston's snap counts, I noticed two recent phenomena relevant to their likely usage rates in the playoffs: 1) Jaelen Strong gets Cecil Shorts' snaps when he's out, but plays about 12 snaps when Shorts is healthy; and 2) Keith Mumphery gets Nate Washington's snaps when he's out, but barely sees the field when Washington's healthy. Aside from Strong having more talent than Mumphery, this pattern occurs (presumably) because Strong can play the second slot receiver in a four-wide formation (and give Shorts a breather in three-wide sets from time to time), while Mumphery is "line up outside or bust." Therefore, with Shorts healthy and Washington likely out against Kansas City, I prorated Mumphery's points-per-snap average to the average number of snaps Washington plays when healthy, and gave Strong his usual modicum of 12 snaps when Shorts is healthy. For subsequent weeks, I'm assuming Washington will be fine, and so Mumphery then goes from a Washington-level number of snaps this week to virtually absent.

Can these educated guesses be wrong? Of course. That's why, in the table below, I've put in bold, red font all of the expected points (and adjusted expected points) for players about whom I made an educated guess. I've also put in bold, blue font one player whose Week 13-16 scoring average was totally unsustainable, so I opted to use his Week 1-16 average instead. Move any of these players up or down in your own personal rankings as you wish:

Cam Newton QB CAR 65.9 78.5
Russell Wilson QB SEA 64.2 68.9
Carson Palmer QB ARI 45.3 52.7
Tom Brady QB NWE 44.7 51.8
Kirk Cousins QB WAS 45.5 46.5
Ben Roethlisberger QB PIT 38.7 40.8
Alex Smith QB KAN 38.0 40.7
Aaron Rodgers QB GNB 33.0 33.8
Teddy Bridgewater QB MIN 29.3 30.2
Peyton Manning QB DEN 24.7 28.8
Brian Hoyer QB HOU 26.7 27.4
Andy Dalton QB CIN 21.4 22.6
A.J. McCarron QB CIN 11.6 12.2
David Johnson RB ARI 53.7 62.6
Jonathan Stewart RB CAR 36.5 43.5
James White RB NWE 27.7 32.1
Marshawn Lynch RB SEA 26.8 28.8
Steven Jackson RB NWE 24.5 28.4
Jeremy Hill RB CIN 19.6 20.6
James Starks RB GNB 19.4 19.9
DeAngelo Williams RB PIT 18.5 19.5
Charcandrick West RB KAN 18.2 19.5
Ronnie Hillman RB DEN 16.3 19.0
Adrian Peterson RB MIN 18.5 19.0
Eddie Lacy RB GNB 17.7 18.1
C.J. Anderson RB DEN 15.3 17.9
Giovani Bernard RB CIN 14.3 15.0
Alfred Blue RB HOU 13.9 14.2
Alfred Morris RB WAS 11.2 11.4
Pierre Thomas RB WAS 10.3 10.5
Brandon Bolden RB NWE 7.9 9.2
Chris Thompson RB WAS 7.8 8.0
Matt Jones RB WAS 6.4 6.5
Jordan Todman RB PIT 5.1 5.4
Fitzgerald Toussaint RB PIT 3.2 3.4
Will Johnson RB PIT 1.1 1.2
Doug Baldwin WR SEA 53.3 57.2
Antonio Brown WR PIT 51.2 53.9
Ted Ginn Jr WR CAR 40.2 48.0
Julian Edelman WR NWE 37.3 43.2
Jeremy Maclin WR KAN 39.6 42.4
Michael Floyd WR ARI 35.0 40.8
Demaryius Thomas WR DEN 34.5 40.3
Tyler Lockett WR SEA 34.5 37.0
John Brown WR ARI 30.7 35.8
Emmanuel Sanders WR DEN 29.2 34.1
A.J. Green WR CIN 31.8 33.5
DeAndre Hopkins WR HOU 26.9 27.6
Larry Fitzgerald WR ARI 22.1 25.8
Martavis Bryant WR PIT 24.4 25.7
Danny Amendola WR NWE 21.7 25.2
DeSean Jackson WR WAS 24.6 25.2
Jermaine Kearse WR SEA 22.9 24.6
Markus Wheaton WR PIT 22.4 23.7
Marvin Jones Jr WR CIN 21.6 22.7
Pierre Garcon WR WAS 21.6 22.1
Corey Brown WR CAR 16.9 20.1
Albert Wilson WR KAN 18.7 20.0
Jerricho Cotchery WR CAR 15.8 18.8
James Jones WR GNB 17.9 18.4
Brandon LaFell WR NWE 15.1 17.6
Randall Cobb WR GNB 17.0 17.4
Devin Funchess WR CAR 12.5 14.9
Davante Adams WR GNB 13.2 13.6
Stefon Diggs WR MIN 13.0 13.4
Jarius Wright WR MIN 11.5 11.8
Mike Wallace WR MIN 11.5 11.8
Jordan Norwood WR DEN 8.8 10.3
Mohamed Sanu WR CIN 9.5 10.0
Cecil Shorts WR HOU 9.2 9.5
Nate Washington WR HOU 8.7 8.9
Jamison Crowder WR WAS 6.6 6.8
Keith Mumphery WR HOU 2.9 3.0
Jaelen Strong WR HOU 2.4 2.4
Greg Olsen TE CAR 34.7 41.4
Rob Gronkowski TE NWE 34.7 40.3
Jordan Reed TE WAS 30.0 30.6
Tyler Eifert TE CIN 25.9 27.3
Travis Kelce TE KAN 25.2 27.0
Heath Miller TE PIT 24.0 25.3
Richard Rodgers TE GNB 19.1 19.6
Owen Daniels TE DEN 15.0 17.5
Kyle Rudolph TE MIN 16.0 16.5
Darren Fells TE ARI 11.6 13.5
Cooper Helfet TE SEA 11.3 12.2
Ryan Griffin TE HOU 9.8 10.1
Luke Willson TE SEA 5.0 5.3
Chandler Catanzaro K ARI 22.5 26.3
Chris Boswell K PIT 22.5 23.7
Stephen Gostkowski K NWE 20.0 23.2
Graham Gano K CAR 15.5 18.5
Steve Hauschka K SEA 17.0 18.3
Brandon McManus K DEN 15.4 18.0
Mike Nugent K CIN 16.7 17.5
Blair Walsh K MIN 16.3 16.7
Cairo Santos K KAN 12.2 13.1
Nick Novak K HOU 12.2 12.5
Dustin Hopkins K WAS 12.2 12.5
Mason Crosby K GNB 9.1 9.3
Arizona Cardinals D ARI 36.2 42.1
Kansas City Chiefs D KAN 27.2 29.2
New England Patriots D NWE 20.7 24.0
Carolina Panthers D CAR 18.6 22.2
Pittsburgh Steelers D PIT 20.3 21.4
Denver Broncos D DEN 17.8 20.8
Cincinnati Bengals D CIN 16.3 17.1
Houston Texans D HOU 15.3 15.7
Seattle Seahawks D SEA 14.2 15.3
Green Bay Packers D GNB 14.7 15.0
Minnesota Vikings D MIN 14.5 14.9
Washington Redskins D WAS 12.8 13.1

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