FF501: Prorated Average Value Theory (PAVT)

08/13/2005 12:46 PM -  Robert Cobb

Contributed By: Robert Cobb

This article discusses a common-sense method for valuing fantasy football players.  If you’ve read through all of the material in the FantasyFootball.com University Series up to this point, you are well-prepared for a discussion on how to place value on players.  If you need a bit of background before we get started, I suggest reviewing Player Value and Rank & the Cheat Sheet in FF404: Average Draft Position.  Now that you understand what player value is and why it is important to establish how much more valuable one player is than another, let’s take a look at one of the best ways to establish good player values.

What is it?
The Prorated Average Value Theory (PAVT) is a method of quantifying the value of players by merging current player rankings with proven averages for fantasy points scored.  It adheres to the criteria essential for any good cheat sheet:

1. The league scoring system is taken into consideration
2. Players are assigned a value and not just a ranking
3. Players are listed together regardless of their position
   (QBs are compared to RBs, etc.)

The difference between PAVT and other approaches like Real Value is that it uses average rankings instead of projected statistics.  PAVT accepts the fact that it is impossible to guess every fumble, catch, and yard gained.  Besides, it is not always raw statistics that make us favor one player over another.  I may not be able to use statistics to justify my belief that Plaxico Burress will be a bust as the #1 WR in New York, but I know where I want him on my cheat sheet relative to the other WRs.  PAVT allows me to focus on where players belong in relation to each other and then uses statistical trends to tell me how valuable the players I have prioritized are.

PAVT output is based on the idea that a player’s value is equivalent to how many more fantasy points he is expected to score than others.  This is a fine definition of value, but it needs to be balanced with an understanding that a player’s value on draft day is defined more by where he is drafted.  We can’t ignore this simple fact and blindly follow a cheat sheet lest we draft players when we could have waited or we miss out on players because the league perception of their value is skewed.  I’ll touch on this more later, but let’s first discuss how PAVT can be used to create solid player values.

Concept 1: The number of fantasy points scored each year changes very little

Within each league, approximately the same number of fantasy points is scored each year, and those points are awarded consistently to the same positions.  From year-to-year, the fantasy points scored by the top RB, indeed the 2^nd, 3^rd, and all of the rest of the RBs are almost the same.  When we acknowledge this fact, we are free to concentrate on who will be the 1^st, 2^nd, and 3^rd RB while letting the points fall where they may.  Under this approach, trying to forecast future statistics serves only as an exercise to help rank players in the right order.  It is no longer useful to fudge projections up or down to suit our preferred rankings.  Under PAVT, projections can be a justification for our rankings, but they are never the sole means to the end.

When determining the number of fantasy points scored, it is important to use your league scoring system because we need to know which players/positions are most important in your league. This is one way in which a PAVT cheat sheet is customized to your particular drafting situation.

But, are past-year statistics really consistent enough that we can conclude players in future years will follow the same pattern?  Because NFL rules change and defenses adjust, it is important to average the past few years to account for any trends.  Let’s take a look at RBs over a recent 3 year period:

The top 3 RBs over the past three years:

Year	Rank	Player	Fantasy Points
2002	1	Holmes, Priest	371
2003	1	Holmes, Priest	371
2004	1	Alexander, Shaun	300
Average for #1 RB			347
2002	2	William, Ricky	314
2003	2	Tomlinson, Ladainian	339
2004	2	Barber, Tiki	296
Average for #2 RB			316
2002	3	Tomlinson, Ladainian	305
2003	3	Green, Ahman	335
2004	3	Tomlinson, Ladainian	282
Average for #3 RB			307

The important thing to note is that, even though 2003 was a huge year for RBs, there is no overlap from one ranked player to the next.  A more comprehensive and revealing analysis is to look at the top 50 RB fantasy points scored for each of the past three years.

The graph above charts one line for each year analyzed.  Mapping the average number of points scored by players ranked 1 through 50 illustrates how we can reliably expect the same number of points to be scored every year.  Regardless of whether or not the points are exactly the same each year, we can see that the relative value of one player to the next is very consistent (note the similarity of the curves).

Past performance is the single most important factor when forecasting future production.  In fact, projection-based cheat sheets for the coming year forecast a conservative number of fantasy points proportional to the points that players ranked in those slots historically score.  The 2005 RB projections from three popular web sites are as follows:

Rank	Site	Fantasy Points
1	Site A	301
1	Site B	318
1	Site C	306
Average for #1 RB		308
2	Site A	282
2	Site B	303
2	Site C	302
Average for #2 RB		296
3	Site A	273
3	Site B	283
3	Site C	276
Average for #3 RB		277

The web sites have all forecasted slightly lower output that is inline with historical averages.  What else would we expect the prognosticators to work from?  The projected statistics must be based primarily on past performance.  So, what is the point in laboring over these statistics if they never change?  PAVT and projection-based approaches are both dependent on past-year statistics, but it is the players and not the statistics that change from year to year, so let’s just worry about figuring out which players are going to earn these points!

Concept 2: When averaged together, rankings reveal their own player values

After determining how many fantasy points players score on average, it is time to rank players and derive an expectation of their future performance.  This is something that almost every fantasy owner does in the preseason.  Ranking players is a matter of considering their past performance and their current situation (injuries, personnel changes, strength of schedule, etc.).

Early work on the Average Value Theory (AVT), the predecessor to PAVT, held that the #1 ranked RB should be assigned the average number of points scored by the #1 RB over the past few years.  In the example above, this would be 347 points.  The problem with this approach is that there is rarely a consensus on who the #1, #2, #3, etc. player is going to be.  The fact that a consensus does not exist tells us something important about the player… we should not be giving him credit for all of the fantasy points averaged over the past few years.  If the average rank of a player is 1.5, we should understand that there is no clear-cut #1.  This is great information because it will fine tune our expectations for the player by taking advantage of average rankings and not forcing players into ranking slots.  Perhaps there is no obvious #3 RB this year or maybe there are two TEs expected to finish second with no clear #1.  That is fine and it is expected; however, these revelations can only be recognized if we use average rankings to prorate fantasy points across the rankings.

PAVT demands only that we rank players against others at the same position.  Applying the points yielded by your scoring system will help create an overall list that ranks players regardless of position.  Let’s say Tomlinson, Alexander, and Holmes are the top ranked players for the upcoming year.  Their average ranks are 1.5, 2.25, and 3.75 respectively.  Under the old AVT approach, this would equate to a one-to-one mapping between the #1, 2, and 3 RBs and the average points scored by the #1, 2, and 3 ranked RBs over the past few years.

AVT
Rank	Player	Fantasy Points
1	Tomlinson, Ladainian	347
2	Alexander, Shaun	316
3	Holmes, Priest	307

Note that Holmes was awarded the full amount of points (307) averaged by RB #3 over the past few years even though his actual ranking is 3.75.  By prorating the points across the average ranking, PAVT assigns players only those points that they deserve:

PAVT
Rank	Player	Fantasy Points	Calculation
1.5	Tomlinson, L	332	316 + (347 – 316) * .50 = 332
2.25	Alexander, S	314	307 + (316 – 307) * .75 = 314
3.75	Holmes, P	291	286 + (307 – 286) * .25 = 291

With a ranking of 3.75, Holmes receives 100% of the #4 RB points (286) plus 25% of the difference between the #3 and #4 RB points.  This is a fairly basic example, but it illustrates how future expectations based on rankings can be used to align players with fantasy point projections taken from historical averages.

Concept 3: Players at different positions can be compared to each other by factoring in their league demand

The final step needed to produce a PAVT cheat sheet is often referred to as “applying a baseline” and is commonly used in player valuation schemes.  Players at different positions must be “leveled” against one another in an effort to create a listing of the best overall players regardless of position.  This is a mandatory draft preparation step because you must know which positions present the best available bargain with each pick.  The most common approach for combining players into a single list is to subtract the number of points expected for the worst starter at each position from each player at the position.  So, in a 12 team league that starts 2 RBs, the points expected by the 24^th RB are subtracted from every RB.  Deciding on a baseline to use is a common topic of debate.  A few more baseline options are discussed here.

As you may surmise, the baseline is the Achilles heel of all player valuation schemes because people tend to abuse it to impart knowledge of their league drafting style or their own drafting strategy.  If QBs are not listed in the PAVT cheat sheet in the exact order someone expects them to be drafted, they will often adjust the QB baseline to artificially inflate the value of all QBs.  Drafters know that a player’s value is defined on draft day by where they are drafted, so they try to turn their cheat sheet into a drafting order by using whatever baseline serves their purpose.  Player value schemes like PAVT and Real Value are not designed to be a drafting strategy; rather, they are intended to make sure each draft pick achieves the most “bang for your buck”.  Trying to tweak a PAVT cheat sheet to mirror an expected draft order destroys its purpose.  The raw player values are important to understand and can be taken advantage of if the drafter knows how to combine them with drafting tendencies.

Drafting with a PAVT cheat sheet
As mentioned earlier, player value schemes like PAVT do not specify the order in which players should be drafted. They can, however, be used during a draft to determine if a player justifies his draft pick.  The goal is to draft a player whose PAVT value is in-line with the other players drafted near the pick.  Draft a player with a lower PAVT value than those around him, and you will have overpaid.  A player picked with a higher PAVT value than those around him is considered a bargain. The most effective use of PAVT is to combine it with drafting tendencies and a real-time analysis of what is going on in the draft.  Average Draft Position (ADP) is helpful for determining where players are typically being drafted, but determining how much more or less a player is worth than their original PAVT value during the draft is dependent upon factors such as everyone else’s roster status, their estimation of player values, remaining strength at each position, bye week implications, back-up needs, etc.  A great drafter knows these variables must be reevaluated after each pick.

Fortunately, the drafting tools available at FantasyFootball.com are designed to make creating and using a PAVT cheat sheet easy. Draft Planner uses its database of statistics and daily ranking updates to perform all of the calculations needed to generate PAVT values.  You can then import this cheat sheet into your draft day companion, Draft Predictor.  Draft Predictor combines the PAVT player values with drafting tendencies to predict who your opponents are going to draft.  The tools clearly separate the process of generating player values (Draft Planner) and maximizing value during the draft (Draft Predictor).  Using these tools should eliminate the temptation to fudge baselines or projections in order to justify your rankings.  Raising the value of a particular position using a baseline adjustment has the side-effect of causing teams to draft a second player at the position earlier than normal.  Draft Predictor priority settings allow fine-tuning of each position depth so that the raw PAVT values are never compromised.

You will find plenty of opinions regarding which method of valuing players produces the best results.  If you are looking for a common-sense approach that lets you focus on preseason research and not worry about projecting every last statistic for the upcoming year, PAVT may be right for you.

PAVT was created by Robert Cobb in 2004.  It is based on the AVT work of Wade Iuele and Christopher Annunziata in 2002.