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Average Value Theory or How I Learned to Stop
Worrying about Projections and Love the Draft. by: Christopher Annunziata
and Wade Iuele ©2002 If you are unfamiliar with the principles of Value
Based Drafting (VBD), please read the article found at the link below first: http://www.footballguys.com/bryantvbd.htm The VBD tool allows you to compare the values of
players at different positions in order to display their relative worth. To create a VBD list, you must first have a
list that projects the number of fantasy points (FP) you expect each draftable
player to score. This can be either one
you create, or one you obtain from another source, like FootballGuys.com. Regardless of how well you have created projections
in the past, the fact remains that your projections will always be
incorrect. That inaccuracy may range
from minor (a few FP) to horrific (like projecting the top player at any
position to score 100 more FP than anyone else in the history of that
position). If any one person could
consistently predict player performance with 100% accuracy, we would no longer
have a reason to participate in fantasy football, and the bookies would go out
of business. The problem
is not that the projections will be wrong, but that error in their creation can
cause a ripple effect throughout your VBD list. It is because of errors in projections that the most
important mid-season fantasy football activities are free-agent or waiver-wire
pickups and player trades. What good is
it to project FP if you are off on your calculations by as much as 20% (or
more)? That error can translate into
almost 2-3 FP per game, meaning that you may have ranked a player at least one
tier higher or lower than he should be. A player’s projected FP affects his VBD value, which
affects the relative value of the players around him. If, during the projection process, you overestimate or
underestimate a player’s potential to a high enough degree, you can affect your
VBD values to the point where they are longer an adequate draft-day tool. If you have the misfortune to make a
radically incorrect projection for your baseline player, you have not only
corrupted the VBD values for that position, but likely your entire VBD list. Projections will invariably contain widespread
error, because the process of creating projections is thoroughly
subjective. Each time you make a
subjective decision regarding numerical values, variables, and calculations,
you expose yourself to a potential for error.
Regardless of your method for creating projections,
you will invariably read and synthesize a great deal of information and
ideas. Based on articles you read on
the net, football analysis on TV, or even the dreaded “gut-feeling,” you
develop a belief that a player will do better this season, or that he’ll do
worse, or that he’ll perform roughly at the same level. You pay attention to a player’s new (or old,
or aging) teammates, the team’s strength of schedule, how many times they have
to play last years toughest defense, the player’s propensity for hangnail
injuries, coaching staff changes, O-Line changes, etc. The reasons you have for this belief are
really not relevant. It is enough that
you have opinions. Based on your opinions, you will select the
variables that are important in calculating performance based on your leagues
scoring rules and assign numerical values to them for each player. Those variables and the values assigned to
them may not be completely arbitrary, as they may fall within an acceptable
range of outcomes based on your opinions and possibly even past
performance. However, they are still
subjective. After a series of calculations and perhaps
adjustments to those values, you hope to have compiled a list of statistics
that generally conform to the opinions you had about those players. Like most, you will likely tweak these
numbers because somewhere in the back of your mind you believe that this player
will “do better” this season or that player will “do worse”. Therefore, you “adjust” your stats to meet
your expectations. With every subjective decision you make in
developing a projection, there is a possibility of error; and the greater the
number of variables on which you base your projections, the greater the number
of potential errors. Therefore,
creating player projections might not be the best way to quantify player values
for use with a VBD system. Each time
you make a subjective decision regarding numerical values, variables, and
calculations, you expose yourself to a potential for error. A more objective method can help you limit your
error: Average Value Theory, or “AVT”. AVT assumes that over a course of time, actual FP
scored by each position remain fairly constant, independent of the player who
scored them. While historical data is not a perfect predictor of future
performance, over the past few seasons the data shows that the number of FP
scored remains fairly consistent. Therefore, if one can show, within an acceptable
margin of error, that the #4 RB is likely to score 225 FP, and the #5 RB is
likely to score 214 FP, one should be able to assign those values in lieu of
making an independent projection. We do
not assert that the values generated using AVT represent an actual projection
of how well any player will actually perform, but rather that, based on
historical data, values remain fairly constant at each positional rank. If the absolute values remain fairly
constant, so then does their relative value, and the true indication of their
worth. Because a “true” Fantasy Football article contains
lots of graphs and charts, the following charts show the distribution of the FP
scored by each player for the past six (6) seasons. We first eliminated the names of the players that created those
stats, and plotted the number of FP scored for each position, sorted by rank,
i.e., RB1, RB2, etc. All 6 years were
plotted together. The Y-axis shows the number of FP, and the X-axis is the rank
of said player. The scoring system is as follows: 1
point per 10 Yards Rushing 1
point per 10 Yards Receiving 1
point per 25 Yards Passing 6
points per TD (Rush, Rec., or Pass) Top 35 Quarterbacks – FP
1996 to 2001
Top 35 Running Backs – FP
1996 to 2001
Top 50 Wide Receivers – FP
1996 to 2001
Top 25 Tight Ends – FP 1996
to 2001
While the data seemed to fit a consistent
logarithmic regression curve, there were some irregularities. The variation in the values is addressed
later on when we attempt to calculate a margin of error. The only major discrepancy worth discussing
was the 2000 RB point explosion, where 17 RB’s scored more than 200 FP, and the
top 31 RB’s averaged 30 more FP than the Top 31 RB’s in 1999, an increase of
17%. However, after last season, it
appears that the RB’s have returned to earth. We then calculated the average values (AV) for the
top players each position. This
generated a list of FP that corresponded to various ranks. For example, here are the AV’s for the top
10 at each position for the 96-98 seasons:
In order to “validate” the data, that is, determine
how accurately the Average Values for the previous years would predict the
final FP for the following season, we compared what AVT would have projected
for the 1999, 2000 and 2001 seasons to the actual results. For 1999, we used the Average Values for the 1996-98
seasons; for 2000, we used the 1996 to 1999 seasons; and for 2001, we used the
1996 to 2000 seasons. We then took the
absolute value of the difference between the AV and Actual FP, and divided by
the Actual FP to get a margin of error (± x%).
We also calculated the effect that such an error
would have on that player’s FP by calculating the error in terms of FP per game
(FPG). For example, if the AVT
predicted 132 FP for a certain player, and that player actual scored 128 points
that season, the margin of error was 3.1% and a difference of four (4)
points. Four points over the course of
a sixteen (16) game season represents a mere 0.25 FPG. Ex.:
The chart below shows the average margin of error
and average FPG error for 1999, 2000, and 2001 for AVT.
All in all, the results were
very encouraging. However, two things
stand out: the increased error in the 2000 RB values and the increasing
discrepancies for QB’s. After last
season, it appears that the 2000 season may have been an anomaly. Few can honestly admit that they could have
accurately projected that increase in scoring by RB’s across the board. There may be a variety of reasons for the
fluctuation in FP at the QB position: inconsistent number of games played (some
seasons many QBs play 16 games, other seasons only a few); new offensive
systems (the “Martz factor”); or injuries at surrounding positions, which
reduce a QB’s effectiveness. However,
QB error remains under 2 FPG, which means QB’s are not moving wildly on your
VBD board. If you take this positional discrepancy
into account, you should be able to compensate during the draft. When the 2002 stats are final, we will be
able to determine if QB error is steadily increasing, or merely fluctuating. A benefit of AVT is that the formula takes
into account new data after each season, thereby making the AV calculations
more complete. The question then becomes, “Is 5%, 6% or even 11% an
acceptable margin of error?” To
determine that, we looked at the 2001 projections from fourteen (14) Fantasy
Football sources and performed the same margin of error analysis. We ignored the actual player names and
compared what these experts projected for 2001 seasons to the actual results,
using the same method as above. The best of the group were:
The worst of the group were:
To illustrate the effect of
wildly overvaluing one position over another, we calculated a VBD list using
the worst set of projections, ESPN.com.
Here is ESPN’s Top 20 VBD list:
They must really subscribe to
the Stud-RB Theory! Fifteen RB’s in the
top 20 positions. Would you draft off
of this list? Using AVT to calculate VBD for
the 2001 season, you would have obtained this Top 20 list:
It is always possible for players at a position to explode, and wreck the curve. However, AVT postulates that, more than likely, the distribution of FP will follow previous years’ distributions. This helps you limit the subjectivity of | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
