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PFF WAR: Modeling Player Value in American Football
Submission ID: 1548728
Track: Other Sports
Player valuation is one of the most important problems in all of team sports.  In this paper we use
Pro Football Focus (PFF) player grades and participation data to develop a wins above replacement
(WAR) model for the National Football League.  We find that PFF WAR at the player level is more
stable than traditional, or even advanced, measures of performance, and yields dramatic insights
into the value of different positions.  The number of wins a team accrues through its players’ WAR
is more stable than other means of measuring team success, such as Pythagorean win totals.  We
finish the paper with a discussion of the value of each position in the NFL draft and add nuance to
the research suggesting that trading up in the draft is a negative-expected-value move.
1. Introduction
Player valuation is one of the most important problems in all of team sports. While this problem has
been addressed at various levels of satisfaction in baseball [1], [23], basketball [2] and hockey [24],
[6], [13], it has largely been unsolved in football, due to unavailable data for positions like offensive
line and substantial variations in the relative values of different positions. Yurko et al. [25] used
publicly available play-by-play data to estimate wins above replacement (WAR) values for
quarterbacks, receivers and running backs. Estimates for punters [4] have also been computed, and
the most-recent work of ESPN Sports Analytics [9] has modified the +/- approach in basketball to
college football beginning in the fall of 2019.  Pro Football Reference’s [20] Approximate Value (AV)
is the most widely used open-source measure for player value, and although the currency is not
“wins”, it is a very useful measure by which to compare players across positions and seasons.
Pro Football Focus (PFF) [19] offers hope in the area of player valuation due to its unique player
grades, which provide play-by-play participation and performance data for each player on the
football field, from the quarterback to the gunner on the punt team. These grades have been
transformational in the football community - from appearing on NBC's Sunday Night Football to
playing a part in contract negotiations for players and teams. The PFF grades have become the go-to
place for establishing how good a player is at playing football. An open question remained as to how
well it could establish how valuable a player is.  A quarterback with a 67 PFF grade as a passer is not
worth the same to his team as a running back with a 67 grade as a rusher. Furthermore, a left tackle
with a 67 grade in 100 snaps is not worth the same to his team as a left tackle with the exact same
grade in 1000 snaps.
Therefore, a player valuation model needs to incorporate a) how well the player played b) what the
player did and how important is doing that well, and c) how often did the player do the various
things he did. In this paper we introduce PFF Wins Above Replacement (PFF WAR). PFF WAR is
computed using PFF's player grades and participation data in conjunction with a Massey matrix
model [15] infused with machine learning [12] to determine how important each facet of play is in
football. We find that, on balance, this WAR metric is very stable season-to-season during the PFF
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era (2006-present), although this stability varies by position group. Defensive backs and wide
receivers are the most valuable non-quarterbacks on average, but the former’s WAR estimates are
far less stable than those from other positions on the defense.
We find that the total team wins implied by WAR are more stable than actual wins earned and
Pythagorean-implied win totals [11] and that the total number of wins above replacement
generated during a rookie contract falls off monotonically with draft position.  However, differences
between quarterbacks and non-quarterbacks are significant enough for both teams to win a trade
involving draft picks.
2. The Massey Rating System
2.1.Original Formulation
The Massey rating system [15] is a matrix-based system of evaluating the overall performance of
teams in a league by assuming that the overall strength of a team is a product of a) the interactions
between teams in a given league and b) the existing strengths of the teams with which a given team
interacts. Modeling a) is done by the construction of the Massey matrix, which is an n by n matrix,
where n is the number of teams in the given league. The ith term along the main diagonal of the
Massey matrix is the total number of games played by the nth team in the league during a given
period of interest (usually one season). The i,jth element of the matrix is the number of games
played between team i and team j during that same period, multiplied by -1. It's clear that every
Massey matrix M is a symmetry matrix, and each of the columns of the Massey matrix sum to zero.
Modeling b) is done by using an n-dimensional vector of team strengths over the period of interest.
In the original Massey framework, this amounted to the total net points for that team, which was
positive if that team scored more points than its opponents during the season and negative if they
scored fewer. It's clear that the vector of team strengths f sums to zero.
The resulting rating vector, r, for which the ith element is the overall rating for the ith team in the
league during the period of interest, solves the matrix-vector equation:
𝑀𝑟 = 𝑓,                (1)
which represents the assumption that each team’s strength is a linear combination of the difference
between its strength and those of each of its opponents. Offensive and defensive ratings can be
extracted from r in a straightforward way by using the positive and negative parts of f.
2.2.Adjusting Massey Ratings Using PFF Grades
The Massey rating system is lacking in some contextual places. For example, a team with a
substantial number of defensive touchdowns or touchdowns generated by the offense but from the
aid of a short field will actually have a higher offensive Massey rating than they should, while a team
whose offense constantly puts them in short fields or gives up points themselves will have a lower
Massey defensive rating than they should. Special teams touchdowns scored are counted on the
offensive side, when often they are very much influenced by a team’s defense.
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Additionally, football is a noisy game to begin with, where passes that should be intercepted can
bounce off a defender's hands into those of a receiver for an offensive touchdown. Perfect passes
are dropped, and fumble luck persists for an entire season in many cases. These issues can, in many
ways, be addressed with PFF grades. In the PFF system each player is assigned a grade between -2
and 2, in increments of 0.5, and this grade can be classified as passing, rushing, receiving, run
blocking, pass blocking, screen blocking, run defense, pass rushing or coverage, as well as a
plethora of special teams designations.  Each player earns a grade for avoiding penalties on offense,
defense and special teams as well. An example of a +0.5 grade earned by a quarterback is an
accurately-thrown completion traveling 10 yards on third down and nine yards for a first down,
while an example of a -0.5 coverage grade is applied to the cornerback who was beat on said play
for the reception (or even in the case the pass was dropped).
Thus, we can get around some the noise issues inherent in the Massey model through using PFF
grades. While most positively-graded plays by quarterbacks will result in completions and/or
touchdowns, and negatively-graded throws incompletions and/or interceptions, capture much of
what score differential captures, the noisier plays will be given null (zero) grades, and plays that
“should" have resulted in a different outcome will be graded accordingly, making the vector f that
uses them part of a model that is more predictive than the original version.
To create f for our PFF Massey model, we first normalized the grades in each facet of play by season
(a fixed effect) and season-long position (a random effect [17]) at the play level. We needed to
normalize by the former because our grading system has evolved since its inception to comply with
feedback from team clients and consultants. We controlled for latter because summary statistics
within the same facet (e.g. pass blocking) were different between different positions (e.g. guard and
tackle). After normalization, the average player at a position will earn a zero cumulative grade in
each facet of play over the course of a season.
We then used a random forest model [12] to scale PFF facet grades by their variable importance
relative to adjusted team wins in each season (including playoffs).  Adjusted records are computed
by giving a team credit for a full win or loss if the score differential was nine or more, and half a win
and half of a loss otherwise.  Some facets of play needed to be split up due to grades generated at
different positions yielding different value relative to team wins (e.g. .  The three most-important
facets are passing, receiving by wide receivers and coverage by defensive backs, followed by the
remaining non-special teams’ facets (offensive penalty grade is more important than defensive
penalty grade, which is consistent with the theme that offense is more important than defense [3]).
Once the vector f is built, PFF Massey ratings are computed by solving an equation analogous to (1).
Metric Cor(Metric year n+1) Cor(Win Pct year n) Cor(Win Pct year n+1)
PFF Massey total 0.45 0.73 0.35
PFF Massey offensive 0.46 0.67 0.33
PFF Massey defensive 0.37 0.50 0.25
Table 1: Pearson correlation [22] coefficients between PFF Massey ratings and PFF Massey ratings in subsequent years,
win percentage in concurrent and subsequent years (including playoffs).
Some model diagnostics on the PFF Massey ratings are in Table 1.  The second column in Table 1
shows what has been known for some time [3], that offense is what wins games in football more
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than defense does. The third column shows that all three PFF Massey ratings offer some predictive
power with respect to (unadjusted) total team wins in subsequent seasons, despite not accounting
for changes in front office, coaches or players.
3. Player Valuation
3.1.Wins Above Average
The first step in a wins above replacement model is the derivation of a wins above average (WAA)
model. The reason for this is that a replacement player is a difficult concept to define, but a team of
replacement-level players is more straightforward. Furthermore, on the player level, the following
equation holds:
𝑊𝐴𝑅 = 𝑝𝑙𝑎𝑦𝑒𝑟 𝑤𝑖𝑛𝑠 − 𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑝𝑙𝑎𝑦𝑒𝑟 𝑤𝑖𝑛𝑠
= 𝑝𝑙𝑎𝑦𝑒𝑟 𝑤𝑖𝑛𝑠 − 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑙𝑎𝑦𝑒𝑟 𝑤𝑖𝑛𝑠                                                    (2)
+ 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑙𝑎𝑦𝑒𝑟 𝑤𝑖𝑛𝑠 − 𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑝𝑙𝑎𝑦𝑒𝑟 𝑤𝑖𝑛𝑠.
The first two terms of the last expression are exactly WAA, which varies by player.  Given a known
fixed snap count for each facet, the final two terms above are fixed league-wide, making WAA the
necessary entity to compute in this situation.
To compute WAA for a player, we compute the PFF Massey ratings for his team(s) twice - once with
his grades present in the data set and once with them replaced by a 0 (average) - graded player
with the same number of snaps in each facet of play. The wins above average for each player is then
the difference in the number of wins implied (via a linear regression model) between the two PFF
Massey ratings.
WAA estimates were computed for each player from 2006 to 2018, which amounts to over 25,500
player seasons. Year-to-year correlations in WAA for all positions (with no snap restriction) is 0.41,
while players who played 250 or more snaps (on offense and/or defense) in season n (with no
restriction on year n + 1) had a WAA that correlated at a rate of 0.48 (0.58 for quarterbacks).
3.2. Wins Above Replacement
To compute the last two components of (2), we need to define thresholds for a team of average
players and a team full of replacement-level players. We assume a team of average players will win
an average of eight games, while a team of replacement-level players will win an average of three
games, leaving 171 total wins above replacement to allocate per season (including playoffs).
We assume that all 171 of these wins are found on either the offensive or defensive side of the ball
(e.g. an average special teams player is a replacement-level player), and are apportioned according
to the weights in the PFF Massey ratings on a per-snap basis for each facet. Each player's WAR is
therefore his WAA value plus the sum of all his per-snap apportionment of the 171 total WAR
multiplied by his number of snaps in each facet of play. Since 8 > 3, a player's WAR will always be
higher than his WAA, but the difference will be bigger for players that a) play more snaps and b) are
utilized in more-important roles.
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Table 2 contains the mean and standard deviation in WAR values for each position for players than
play above the 60th percentile or more snaps in a given season at their position (for quarterbacks,
this is just over 500 snaps), along with the year-to-year stability of WAR for each position. Notice
that, as expected, quarterback is by far the most-important position, and as a measurement of
quarterback play, WAR is the most-stable we’ve seen.  For example, ESPN’s QBR [10] is correlated
year-to-year at a rate of 0.43, which is roughly the same as expected points added on passing plays
(0.45, [25]).  Both metrics are drastic improvements over traditional quarterback rating (0.37).
None of these values rival that of PFF WAR during the same time period, though.
Wide receiver is the second most-valuable position, in many ways because they must capitalize on
the process generated by quarterbacks in the form of accurate throws, but also can generate
substantial value on expected, or even inaccurate, throws by making contested catches or
generating yards after the catch. They can also lose their team significant value if they fail to catch
accurate passes, and hence higher coefficient of variation in their WAR values relative to the
quarterback position.
While the value of edge and interior players are similar on average, variation is higher at the edge
position, since pressure (lack of pressure) from the edge is more valuable (detrimental) than
pressure from the interior (Figure 1 (a) [7]).  The more a player is in coverage, the more valuable
they are, which is consistent with a conclusion we have that coverage is more valuable than
pressure, all else being equal [8].  What earns the trench players a place back in the discussion is
their substantial reliability in the way of year-to-year correlation in WAR, a virtue that players
playing further away from the ball on defense cannot claim.
Position n Mean in
WAR
Coefficient of
Variation in WAR
Year-to-Year
Correlation in WAR
QB 994 1.63 0.70 0.62
RB/FB 2373 0.10 0.64 0.53
WR 2864 0.28 0.84 0.52
TE 1621 0.18 0.62 0.66
T 1543 0.09 1.09 0.49
G 1604 0.10 1.11 0.57
C 708 0.10 1.08 0.50
DI 2559 0.06 1.34 0.68
ED 2259 0.06 1.54 0.61
LB 2721 0.11 0.83 0.51
CB 2733 0.23 0.91 0.29
S 2169 0.23 0.77 0.30
Table 2:  Average WAR values, coefficient of variation in WAR values and year-to-year correlation in WAR values for each
of the broad position categories in the National Football League.  Abbreviations are as follows:  Quarterback (QB), running
back/fullback (RB/FB), wide receiver (WR), tight end (TE), tackle (T), guard (G), center (C ), interior defensive player
(DI), edge defender (ED), linebacker (LB), cornerback (CB), safety (S)
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Figure 1:  Distributions of seasonal WAR for positions along the defensive line (a) and the defensive back seven (b).
Thresholds are 250 snaps for each position.
It is surprising that the average WAR values for each of the offensive line position designation are
similar, but the similarity in average value between guard and tackle is due to the existence of a few
guards generating outlier-level values, as tackles generate the most high-but-not-outlier values,
while centers the most moderately-high ones (Figure 2 (a)). Running backs can add some value
(even with their low snap counts) due in large part to their receiving. That said, it's telling that the
sum of an average offensive line’s WAR is roughly five-times that of an average running back, and
an average wide receiver’s is roughly three-times higher.  Tight ends are both more valuable than
running backs on average and more stable than any position group other than interior defensive
linemen.  As previously stated, wide receivers have the potential to add a great deal of value, but
also to cost their team value due to their ability to turn positively-graded passes from their
quarterback into negative plays for an offense due to drops or poorly run routes (Figure 2 (b)).
Figure 2:  Distributions of seasonal WAR for positions along the offensive line (a) and the offensive skill positions (b).
Thresholds are 250 snaps for each position.
Using every player in the sample and 250 as the snap threshold in the first season of the year-to-year
comparison, WAR is correlated at a rate of 0.74 league-wide - which is better than almost every
individual player metric or PFF player grade that we've studied at the NFL level.  For example, Pro
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Football Reference’s [20] Approximate Value metric, the current standard singular number by
which we evaluate performance of NFL players, is correlated at a rate of 0.64 since 1960, and 0.65
during the PFF era (2006-present).
4. Applications
4.1. Implied Team Wins
With WAR estimated for every player on every team since 2006, we examine how many wins a
team “should" have had based on the quality of their players during a season by summing the entire
team's WAR values and adding three wins. Much like analysts use Pythagorean implied win totals
[11] to find over- and underachieving teams, analyzing the discrepancy between a team's actual
wins and those that would be implied by aggregating its player's WAR can help us understand how
lucky/unlucky the team was, how good/poor its coaching performed during the season, or where to
look for possible places in which the whole is more or less than the sum of the parts in the game of
football, so to speak.
Figure 3 (a) shows the distribution in the differences between actual wins (including playoffs)
versus those implied by PFF WAR, which includes substantial variability. Some notable
discrepancies include the 2006 Chicago Bears (8.3 implied wins versus 15 total wins) and the 2007
Green Bay Packers (8.8 versus 14). Both teams included quarterbacks that did not grade very well
in our system in Rex Grossman and Brett Favre, and both failed to win even eight games the
following season.  The 2006 Detroit Lions (8.2 versus 3), 2017 Cleveland Browns (6.0 versus 0)
were both teams whose players performed far better than their win-loss record (a finding
consistent with Pro Football Reference's Expected W-L based on points for/against [20]).  Both
teams won seven games the following year. Teams in the seven-to-nine-win range that also win a
playoff game will have a higher discrepancy by virtue of having played an extra two or more games,
as will teams in the 10-11-win range that don't make the playoffs.
Figure 3:  The differences between actual team wins (including playoffs) and wins implied by PFF WAR (a).  Year-to-year
stability in wins implied by PFF WAR, with correlation coefficient r = 0.50.
While it's difficult to draw any causal conclusions with respect to coaching efficacy, the Kansas City
Chiefs have averaged more than two wins over those implied by WAR during head coach Andy Reid
era (2013 - present), which is the most over that time period. Arizona was a top-five team during
Bruce Arians' tenure with the Cardinals (0.97 wins above implied).  It's a surprise to absolutely no
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one that the Cleveland Browns have managed just under three wins per season under that implied
by WAR during the entire PFF era (2006 - present).
Unsurprisingly, wins implied by PFF WAR are more stable season-to-season (r = 0.50, Figure 3 (b))
than actual wins (0.36, similar when one doesn't include postseason) or total team AV during that
same time (r = 0.42).  Wins implied by PFF WAR predict total wins the following season better than
total wins do even without roster adjustments and adding roster adjustments (without
incorporating projections for rookies) yields better predictive power than Pythagorean win totals
do (r = 0.43 versus r = 0.42) in predicting wins from one season to the next.
4.2. WAR per Draft Position
The Jimmy Johnson draft chart [20] is widely cited in the NFL media and was based on the
monetary cost of acquiring each draft pick. With PFF WAR at our disposal, we're able to look at
history and determine how much, on average, should be expected from a player on his rookie
contract by virtue of being drafted at a certain position in the NFL draft. Using the sum of a player's
WAR for the first four years for each player drafted (regardless of whether they were playing for
the team that drafted them) as a proxy for a player's rookie-contract WAR, we fit a LOESS [5] curve
between draft position and the WAR and standard deviation in WAR (Figure 4). Notice, as one can
expect, the payoff for picking a quarterback is, on average, higher than picking a non-quarterback.
The variance is higher as well, though, and many quarterbacks taken in the draft are below
replacement level as a result.
Figure 4:  Early-career WAR as a function of draft position during the PFF era (2006-pres.), excluding players drafted in
2016 and beyond.
Since different positions offer different utility to different teams, the analyses of draft trades is a far
more nuanced one that “the value of picks a, b, and c minus the values of picks x, y, and z”. Take, for
example, the 2018 pre-draft trade between the New York Jets and the Indianapolis Colts, which
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netted the Jets the third-overall pick in exchange for the sixth-overall pick, the 37th-overall pick, the
49th-overall pick and a 2019 second-round pick (which turned into the 34th overall pick in the
2019 NFL draft). Assuming that the Jets were open to taking any position with the third pick, and
you'd be left with the conclusion that, assuming a conservative [16] 25 percent discount rate on
future picks, the Colts won the trade more than 75 percent of the time for an average almost oneand-a-half WAR during the course of the player's rookie deals (Figure 5).  However, if we assume
that the third-overall pick is a quarterback (which it was - the Jets picked Sam Darnold of USC) the
Jets actually win the trade more than 65 percent of the time and generate roughly one-and-a-half
WAR in the process. This exercise, which is along the same lines as the NFL's own Michael Lopez’s
research [14], shows that draft picks can have different utility for different teams. The Colts,
possessing a franchise quarterback (at least at the time) in Andrew Luck, needed a volume of picks
to re-stock their roster at other, less valuable positions. The Jets needed a quarterback and all the
value that that brings and paid a substantial price for it with respect to the Colts. Both teams “won"
that trade.
Figure 5:  Outcome distributions for the 2018 Jets-Colts trade when assuming the Jets take a quarterback with the leading
pick (left) and assuming they take a player from any position (right).
One can also look at expected draft position and determine which team did the best with the picks
they used during the PFF era (Figure 6).  Only drafts from 2006 to 2015 were used since the full
four years for players drafted from 2016 onward have not been completed.
While there are some biases that skew this analysis (for example, a team that trades away or
accumulates picks frequently), over this long a timeframe the results coincide with results on the
field over the past decade and a half, with the Seattle Seahawks gaining the most WAR above
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expectation and the Cleveland Browns the least.  Even after quarterbacks are taken out of the
analysis, the Seahawks are the top team and the Browns the bottom, but teams like Minnesota,
Green Bay and New Orleans move ahead of teams that drafted quarterbacks who’ve had success
(e.g. Atlanta).
Figure 6:  Early-career WAR accumulated by team over what is expected at each draft position.  Quarterbacks are included
in this analysis.
5. Discussion
In this paper we derived an estimate for every player's WAR at the NFL level using PFF data dating
back to 2006. We found that, as expected, quarterbacks contribute the most to their team's success,
and this contribution is more stable season-to-season than his other statistics. We also found that
players further away from the football are, on average, more valuable to a team than players closer
to the ball, but that value comes at the cost of predictability from year to year on the defensive side
of the ball. We found that good tackles add more value than good guards and good centers, but the
existence of dominant players in the latter groups make the mean values similar. The same holds
true on the defensive line, where edge players are generally more valuable, but players like J.J. Watt
and Aaron Donald have skewed the data in favor of interior players with their outlier play. It's very
hard for a tight end or a running back to add the value of a high-level wide receiver, but equally
difficult to produce values as far beneath replacement as the worst player at the position as well.
Season Player Position Team WAR
2011 Drew Brees QB NO 5.54
2017 Tom Brady QB NE 5.48
2006 Peyton Manning QB IND 5.17
2011 Aaron Rodgers QB GB 4.75
2006 Drew Brees QB NO 4.64
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Table 2:  Who has been the most valuable player in the PFF era?  The top five players in terms of PFF WAR from 2006-
present.
Team strength can be well captured by summing the collective WAR of its players, and this number
is more stable season to season than actual wins or those implied by things like Pythagorean win
percentages [11]. Teams that consistently overperform the sum of their PFF WAR values are those
with coaches that are considered among the league's best, while teams that consistently
underperform said numbers have been franchises with more than their fair share of dysfunction
during the PFF era.
Player value decreases monotonically with draft position, as expected, but decreases differently for
the quarterback position than it does for all other positions, rendering the historical Jimmy Johnson
draft pick trade chart less meaningful than it was back when the passing game was less important.
We demonstrate how the differential utility of a franchise quarterback can create "win-win"
situations for trade partners on draft day, using the 2018 Jets-Colts trade as an example.  Thus,
while the seminal conclusions of Massey and Thaler [16] still hold when considering all positions,
trading up for a quarterback appears to be a drastic exception.
Future work includes using these valuations of players to model and recommend salaries for
players after their rookie contract is complete. The NFL has a rookie wage scale [18] that limits the
amount that players in their first four or five years can make, independent of position and tied to
where they were selected. Differences in the value of each position therefore manifest themselves
in a) where a player is initially drafted and, more drastically, b) the duration, size and percentage of
guaranteed money doled out in deals subsequent to their rookie deal. We find that offensive tackles
and defensive edge players are paid more than their WAR numbers suggest, while quarterbacks,
receivers and cornerbacks are paid less, so a model for recommending player compensation will
likely need to be regressed to the market using positional factors for the time being. Models
currently in development in this area are showing promise and will be the subject of a future
manuscript.
Season Player Position Team WAR (rank)
2006 LaDainian Tomlinson RB SD 0.34 (113th)
2007 Tom Brady QB NE 4.50 (1st)
2008 Peyton Manning QB IND 3.66 (1st)
2009 Peyton Manning QB GB 4.10 (1st)
2010 Tom Brady QB IND 2.61 (8th)
2011 Aaron Rodgers QB GB 4.75 (2nd)
2012 Adrian Peterson RB MIN 0.30 (137th)
2013 Peyton Manning QB DEN 4.45 (1st)
2014 Aaron Rodgers QB GB 3.87 (2nd)
2015 Cam Newton QB CAR 2.88 (5th)
2016 Matt Ryan QB ATL 3.52 (3rd)
2017 Tom Brady QB NE 5.38 (1st)
2018 Patrick Mahomes QB KC 4.39 (1st)
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Table 3:  The NFL MVPs during the PFF era, along with their PFF WAR values and where that WAR value ranked league
wide.
Player valuation remains one of the most challenging problems in sports analytics, especially
football. From the non-stationary nature of the sport, to the fact that different positions mean
different things to different teams and schemes, the problem of assigning a value to each player in
the National Football League will likely never be fully solved. However, with the aid of PFF data,
which takes into consideration much of the vast and ever-changing play-by-play context that has
alluded traditional statistics, we're able to estimate a value for each player in the currency in which
they are ultimately judged on the football field: wins. This should have wide-ranging implications
throughout the football and analytics community and be a jumping-off point for future approaches
in this space.
Position Player Season Team WAR
QB Drew Brees 2011 NO 5.54
RB LaDainian Tomlinson 2006 SD 0.34
WR Antonio Brown 2015 PIT 1.36
TE Rob Gronkowski 2011 NE 0.68
T Tyron Smith 2015 DAL 0.37
G Evan Mathis 2013 PHI 0.46
C Jason Kelce 2017 PHI 0.46
DI J.J. Watt 2013 HOU 0.57
ED Calais Campbell 2018 JAX 0.42
LB Bart Scott 2008 BAL 0.39
CB Darrelle Revis 2009 NYJ 1.19
S Jairus Byrd 2012 BUF 0.86
Table 4:  Highest WAR values during the PFF era by position.  Estimates adjusted since previous submission due to model
updates.
References
[1] Baseball Reference. “WAR Explained”. https://www.baseballreference.com/about/
war_explained.shtml. 2019.
[2] Basketball Reference. “NBA Win Shares”.  https://www.basketball-reference.com/about/ws.
html. 2019.
[3] Burke, B.  “Does Defense Win Championships?” http://archive.
advancedfootballanalytics.com/2008/01/does-defense-win-championships.html.  2008.
[4] Clement, S. “The Relationship Between Punting and Winning in the NFL.”  https://www.
fieldgulls.com/2018/5/7/17327282/punt-wins-above-average.  2018.
[5] Cleveland, W.S.   “LOWESS: A Program  for Smoothing Scatterplots by Robust Locally Weighted
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