Player Values with Range of Outcomes and the Importance of Upside

Updated: July 4th 2021

The term “range of outcomes” is probably familiar to many of those who play games of chance.  We do not always know precise outcomes for certain situations, fantasy football being one of those situations.  Player statistical output arises from an array of random forces which we can’t control or necessarily predict.  Fantasy gamers may arrive at valuable estimates, however, when looking at a range of possibilities.  This article utilizes basic probability mathematics to help the reader answer questions relating to player values with a range of potential outcomes, referred to as expected player values.  The article is more theoretical than data-driven so do not get too caught up in the specific numbers used.  Try to think more about the methodology and how it can be used to answer your own fantasy questions.

Expected Player Values

Before we look at the unknown, let’s examine how player values are calculated in fantasy football.  This article will use the familiar value based drafting (VBD) method as a start in determining fantasy expected player values (note there are a number of similar methodologies for determining player values).  Player values (V) are calculated as the difference between points scored (P) and the baseline points of a replacement level player (BL).  The replacement level point level is typically taken as something similar to the next best player available after all fantasy starters for a league. For example, the 13th best QB in a 12 team 1QB league would be the baseline scorer, but this may also vary according to method and application.  We will use average points per game (PPG) as our points in this article for simplicity.  The player value equation then is simply:

V = P – BL

Let’s say a player scores 14 PPG and the baseline replacement player scores 12 PPG, the player’s value is equal to 2 PPG.   We should also note a player’s value has a floor of zero (no negative values).  A player who scores at or below the replacement level has zero value according to this method.

Now what happens if we add a bit of the unknown and don’t know what a player will score but do have an idea of possible outcomes?  We may still estimate the player’s value if a suitable set range of scoring possibilities is available.  Our expected player value (E(V)) is:

E(V) = E (P – BL)

The replacement level scorer tends to remain relatively stable from year to year and whatever variation which happens is the same for each league and position group so we assume a constant baseline for the purposes of this article.  We can then present our expected value equation in the following form:

 E(V) = sum (Prob(i) x (P(i) – BL))    for all i where Prob is the probability of a player averaging a certain point total.

For example, let’s say there is a 50% chance a player scores 14 PPG and a 50% chance the player scores 16 PPG with the same 12 PPG baseline scoring used previously.  The player’s expected value would simply be:

E(V) = 0.5 (14 – 12) + 0.5 (16 – 12) = 3 PPG

Now that the methodology has been presented, we may answer a basic fantasy football related question.

Example Problem: How Much is Upside Worth?

This is a question which garnered much interest last year, maybe most famously in Scott Barret’s Upside Wins Championships.  To answer this question, the article compares players with wider range of outcomes (more upside and downside) against those with narrower range of scoring possibilities (less upside and downside).

The article assumes a simplified discrete approximation of the normal distribution going forward for fantasy points per game on various mean levels with the same 12 PPG replacement level scorer.  The “Example Probability Distribution” graph below displays a player with a mean of 14 PPG and 10% chances of scoring 10 or 18 PPG, 20% chances of 12 or 16 PPG, and a 40% chance of scoring 14 PPG.  Our expected value for this player would thus be:

E(V) = 0 + 0.2 (12 – 12) + 0.4 (14 – 12) + 0.2 (16 – 12) + 0.1 (18 – 12) = 2.2 PPG

Note the 10 PPG component of the equation gets no value because it is below replacement level (remember no negative values).

We can then extend the concept to examine groups of scoring ranges and associated expected values as seen in the chart below.  The three boxes have 11, 14, and 18 PPG mean scores.  The Narrow range of the 11 PPG box spans from 9 PPG to 13 PPG while the Broad range shows a distribution from 5 PPG to 17 PPG as possibilities for example.


Expected Values for Sample Scoring Ranges

There are a number of key observations and implications which may be drawn from the data.  The importance of upside is readily apparent when looking at the first box with a mean scoring of 11 PPG.  The Narrow range of outcomes produces almost no expected value while the Broad range produces nine times the amount.  There is an intuitive explanation for this.  So much of a lower-tier player’s scoring distribution is at or below replacement level that they only produce value when they produce at the upper end of the distribution.  That makes the player with the wider range of outcomes far more valuable in this case even though the projected stats are equal.

Contrast the 11PPG mean players with the 18 PPG high end scorers in the 3rd box.  The 18 PPG mean scorer produces the same expected value no matter if the scoring distribution is in the Narrow range or Broad Range.  Again this makes intuitive sense.  The upper-tier player is practically always a fantasy producer scoring valuable points, even at the lower levels of production.  That means he doesn’t suffer from the same issues of the lower-tier player at the lower levels of the distribution and thus doesn’t have the big parts of fantasy irrelevance in the distribution.  There is another concept called “risk-aversion” in which people generally prefer the less risky option.  This might actually cause individuals to select the Narrow range player (less risky) over the Broad range scorer among the upper-tier players given there is no expected value difference.  An individual with similar projections between Tyreek Hill and DeAndre Hopkins, for example, might prefer Hopkins if they view him as a less risky option.  The conservation may change when we are talking about big tournaments and other fantasy structures weighted heavily to a very small percentage of the top teams.

The key conclusion from the previous discussion is that upside matters but it matters a lot more for those at the lower-end of the fantasy spectrum.  The importance of upside fades as we move to the higher-level fantasy assets. 

Bio:  Bernard Faller has degrees in engineering and economics.  He currently lives in Las Vegas and enjoys athletics, poker, and fantasy football in his free time.  Send your questions and comments (both good and bad) on Twitter @BernardFaller1.


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Rethinking League Settings

Updated: April 17th 2018

A person recently asked me about auction values for some available players (all running backs and wide receivers) in his upcoming RSO free agent auction.  After looking over his team, I noticed he had a big need for tight end and quarterback and so asked him if he had any questions about QB and TE values.  His response essentially was “Who cares?  They are tight ends and quarterbacks so I will just take what is left over”.  Is that really how we want our leagues set up?  This issue is common in many leagues.  You can look at the big disparity in franchise tag values between positions or notice how late in rookie drafts tight ends and quarterbacks typically start going off the board to understand the issue.

With many leagues yet to begin, now is a good time to review league settings before startup auctions begin, particularly scoring and starting position requirements.  This article gives you a few ideas about how to address the big value differences between positions in your leagues.

Player Scoring

Let us do a quick review of player scoring among positions before we proceed.  I used data from the last four NFL seasons (2014-2017) to compute averages for player scoring on a Points Per Game (PPG) basis among the primary position groups in a fairly typical Points Per Reception (PPR) setting with quarterbacks scoring 4points per touchdown pass, -2 points per interception, and 1 point per 20 passing yards.  Figure 1 displays the results from which we can derive a few key insights to keep in mind going forward.  First, all position groups follow a similar pattern where the difference between player scoring tends to lessen as we get further down the ranks.  Second, quarterbacks generally score more as a group than other positions for most typically used scoring settings.  This becomes more important for those incorporating an RSO Open Flex (Superflex) spot.  Third, tight ends are drastically outscored by running backs and wide receivers.  This means a tight end will almost never be a good choice for your flex option.  Next, we examine what this means for player value.

Figure 1.  Average Player Scoring among Position Groups

Player Values Issues

Our next step is computing player values using our player scoring from above.  The question becomes what is player value?  In this context we define value as the difference between a starter’s PPG and the first league bench player for each position.  For example, say that the RB10 scores 15 PPG in a 10 team, start 2 running backs league and the RB21 scores 10 PPG.  The RB10 would have a value of 5 PPG.  A person may calculate each starter’s value using this methodology and examine the total values associated with each position group and relative to the other groups.

My baseline setting for this exercise is a typical 12 team league starting 1 QB, 2 RBs, 3 WRs, and 1 TE using the scoring rules stated earlier.  Note that changing from a 3 WR league to a 2 WR plus 1 flex spot does not materially affect player values as wide receivers typically outscore running backs and tight ends over the flex spot range in a PPR league.  Figure 2 shows the values corresponding with our typical league using the averaged player scoring data detailed previously.

Figure 2.  Average Values among Position Groups in Baseline League

The above chart brings into sharp focus the big value differences between QBs/TEs and RBs/WRs.  The quarterback position, for example, holds only about 1/4th the total value of running backs and 1/5th that of wide receivers while the top quarterback averages about half the value of the top running back.  The average starter value of quarterbacks and tight ends are also significantly below that of running backs and tight ends.  Another issue involves the value concentration for the top quarterbacks and tight ends.  The top-6 quarterbacks and tight ends hold approximately 5/6th and 4/5th, respectively, of the total value at each position.  Many leagues use deeper starting requirements with more flex spots where the value differences between positions become even more pronounced.

Solutions to Value Issues between Positions

Thankfully there is no shortage of ways addressing the issues stated above.  Changing starting requirements, the number of teams, or scoring rules can have big impacts on player values.  RSO offers multiple scoring and roster options which provide plenty of flexibility to suit your league tastes.  Let’s examine one example of league settings which help balance our player values, a modified version of our baseline 12 team league adding another QB/Superflex and tight end spot with quarterbacks scoring 6points per touchdown pass and -3 points per interception plus giving tight ends 1.5 PPR scoring.  Looking at figure 3 below, the effect on league values is dramatic and presents some pleasing traits when compared to our baseline league.  Total player value is far more balanced between positions with the average starting player holding similar values among all positions.  The top players at each position also approach values far closer to one another.

Figure 3.  Average Values among Position Groups in a 2QB/2TE League

The modified league provides just one example address valuation differences and should not be thought of as a “be all” to every league.  There are countless league size, scoring variations, and starting lineup changes which can affect player valuations in positive ways.

2QB vs Superflex

I have used 2QB and Superflex leagues somewhat interchangeably in the above valuation analysis but there are differences you need to be aware of in your leagues.  The quarterback position is somewhat unique for fantasy purposes in that all NFL teams essentially play one quarterback each week barring the occasional injury or benching.  Each week there are at most 32 realistic starting options available, and as little as 26 in some bye weeks, for starting QB spots on RSO teams.  This means that, generally, some teams will likely be left without a viable quarterback for their second quarterback spot during bye weeks.  Taking a zero at the highest scoring position is extremely difficult to overcome in a given week which makes quarterbacks far more valuable in a 2QB league.  Backup quarterbacks also become roster considerations in 2QB leagues given the importance of fielding a QB.  A superflex league gives a team the ability to place another skill position player in play which is very appealing in many circumstances.  Superflex leagues also offer more strategic flexibility in how you construct your roster through trades, free agency auctions, and the rookie draft.

There is an argument that 2QB leagues should create an active trade market as competitive teams in need of quarterbacks are forced to look at other teams’ rosters for replacements.  Every league is different, but in my experience trade markets tend to freeze up for quarterbacks in deeper 2QB leagues due to the scarcity of starting options available.  The type of quarterback who should be part of an active trade market , veterans on expiring contracts, are not typically held by uncompetitive teams and competitive teams rarely want to depart with QB depth.  Nobody wants to give up quality starters on long-term deals.


There is no right or wrong way to set up your league but league settings will have big consequences on player values.  If you are bored of having quarterbacks and tight ends holding little value, consider starting your new league by adding an additional starting slot for each and/or changing other settings to bump up the value.  The result is a more challenging league which truly rewards good players no matter the position.

Bio:  Bernard Faller has degrees in engineering and economics.  He currently lives in Las Vegas and enjoys athletics, poker, and fantasy football in his free time.  Send your questions and comments (both good and bad) on Twitter @BernardFaller1.

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