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.


More Analysis by Bernard Faller

RSO Mock Contract Draft

Updated: March 20th 2021

One of the items I wanted to accomplish this offseason was hosting a mock draft utilizing RSO contracts.  The mock presents a unique type of draft where drafters selected RSO contracts for available players, in effect a full league mock dispersal draft.  This unique style offers difficult choices as each selection must not only take into account the total value of a contract but also the opportunity costs of potentially missing out on another player a GM valued.  Below the reader may find all team mock drafts along with brief analysis of some picks.

The Draft Structure

10 teams selected 15 contracts with assumed starting requirements of 1QB/1 Superflex/2RB/2WR/1TE/2 Flex, PPR scoring, and a $180 milion salary cap.  Average contract data came from RSO auctions in 2020 prior to the start of the season with one year taken away from average contracts in order to examine typical contracts which might be available to RSO GMs.  Naturally, this mock excludes some players whose contracts averaged one year in length last year (examples include James Robinson and Drew Brees).  No rookie contracts were included.   No consideration to extensions or franchise tags was given so that only the contracts themselves were assigned value.

The Top 40

A look at the top forty contracts selected seems like a good spot to start with the average salary in millions shown above.  The first four players form the core of many teams and team salary cap restraints typically do not present much of an obstacle through four contracts.  GMs simply select the best values as they see fit.

Maybe the most notable part of this mock was the lack of wide receivers chosen at the top.  The first wide receiver taken was with the 17th contract and just four wide receivers were chosen through the first 30 picks while even four tight ends were selected in the top-31 picks.  The depth of wide receiver can be seen with quality starters taken throughout the draft (and some not drafted at all).

Six quarterbacks and four running backs composed the first round.  The value of quarterbacks in shallow superflex leagues like this mock remains a mystery to many.  This group of GMs paid a premium in terms of pick value locking up the top group of passers.  I typically don’t like the value of top quarterbacks given the relatively small marginal point spread between passers when compared to other positions.   The value of middle tier QBs tends to be excellent and one may usually assemble a nice batch of low-cost options for weekly matchup plays.  The reader will see application of the strategy below in my team mock.

Interesting Contracts not Drafted

The number of teams and salary cap made drafting every potential relevant player unrealistic.  Drew Lock ($9M/2 yrs), Teddy Bridgewater ($8M/1 yr), Melvin Gordon($17M/1 yr),  Chris Carson($13M/1yr), Zach Ertz($13M/1 yr), Evan Engram($11M/1 yr), Julio Jones($26M/2 yrs), Juju Smith-Schuster ($24M/2 yrs), and Amari Cooper($22M/2 yrs) represent a sample of contracts not drafted in this mock.  Julio and Cooper seem especially egregious misses when looking at rosters afterwards.

Teams 1 and 2

Both of our first two GMs took similar, fairly common team-building approaches for superflex leagues, paying up at quarterback in terms of draft capital and foregoing tight ends until later.

Best Values:  The room generally loved Josh Allen’s contract finding it well worth the first pick at his relatively low cost and Diontae Johnson should provide tremendous value in PPR leagues.  Team 2 locked up Justin Jefferson for 2 years at a significant discount from market price after one of the best rookie seasons ever from a wide receiver.

Questionable Picks:  I don’t think any of team 1’s picks are necessarily troublesome.  I question if the GM would consolidate marginal starters, late round tight ends, etc. into an every-week starter like Julio or add running back depth like Gordon if they had the choice again (similarly for team 2 with players like Brown and Samuel).  Hindsight is always easier when you know how cap allocations turn out.

Hurts’ contract is interesting as simultaneously price cheap and draft pick expensive in this exercise.  He’s definitely underpriced compared to what the contract will go for later this year and his range of outcomes includes a QB1 finish.  On the other hand, he was among the worse quarterbacks in the league during his time as a starter and part of his range of outcomes includes not being the starter for all or a portion of the year.  The team gave up the chance at a premium player for a massive question mark.

Teams 3 and 4

I drafted team 3 so will examine it a little more.  The big difference from other squads is that I did not pick a QB until the 5th round where every other team had their first QB by the 3rd and all but one picked a QB by the 2nd round.  My team also concentrated on locking up the core players on multi-year contracts more than some others.  The pick of Taylor raised some eyebrows but really shouldn’t.  The fantasy RB6 from 2020 and FantasyPros’ consensus dynasty RB4 priced as the RB14 for 2 years seems a nice foundation piece.  I grabbed Kittle in the 3rd as the last of the big three tight ends.  McLaurin, Fuller, and Aiyuk produced top-20 WR per game fantasy years last season.  Taysom Hill is the super arbitrage version of Jalen Hurts picked far later in this mock.

Team 4 landed Herbert to start on a cheap deal allowing a very balanced roster highlighted by a tremendous receiving group.

Best Values:  Robby Anderson was a fantasy star early last season.  Carolina actively tried to upgrade QB this offseason and Curtis Samuel may be gone in free agency.  Mark Andrews is a nice grab that late in the mock.  There’s some volatility with Lamar Jackson and a low volume passing offense but he is one of the few tight ends with significant workloads.

Questionable Picks:  Team 3 has no questionable picks.  I will not allow it.  The concern for team 4 is going out of the mock with Winston as the only other quarterback after Herbert.  The contract is nice but he is not a starting quarterback at this point with only a few potential landing spots left.

Teams 5 and 6

Both GMs paid handsomely for a couple of elite players plus took a wait and see approach to tight end.

Best Values:  Second-year running backs Akers and Dobbins will be popular players especially with these discount contracts.  I also like the Smith/Goedert combo at tight end for cheap.

Questionable Picks:  It was a very nice mock for team 5 with no real issues, maybe a little consolidation to upgrade the RB2 spot could be argued.  The stars and scrubs approach took a toll at the end for team 6 who failed to grab a viable tight end due to cap constraints.  Grabbing Knox with Goedert (who went one pick after) on the board at just a little higher salary had to be a gut punch.

Teams 7 and 8

Both teams utilized a diverse drafting strategy grabbing one of every position by round 5 and taking their 2nd QB by round 7.  Team 8 really went for players on the cheap after the first couple of picks providing a lot of cap flexibility later on when most other teams were trying to save dollars.

Best Values:  Diggs’ contract sits at the WR20 price, enough said.  The $4M contract of Gibson is almost guaranteed to provide outstanding value if just for a year.

Questionable Picks:  Despite a jump in real life play, Mayfield was just the QB26 in per game fantasy scoring last season.  I see no reason to jump on the 11th highest quarterback contract this early in the mock.  Team 8 used most of the big cap surplus to get Sutton, Godwin, and Kupp later on in the draft.  All are fine players but this seems like a bit of a let-down considering the other high salary players available.

Teams 9 and 10

Team 9 took a very flat salary structure across most of the picks avoiding expensive picks early where team 10 paid up for his early picks.

Best Values:  I will simply quote Team 9’s GM. “Swift one of my top 5 RBs going forward. Easy decision here. Was surprised he was still available.”  Metcalf is one of the top fantasy wide receivers for many with lots of room to provide value on this contract.

Questionable Picks:  Using more than $30M combined on Tua, Jones, and Goff seems like overkill for marginal superflex quarterbacks and a glaring chance to upgrade other positions.  Paying Fournette $17M presents quite a risk for a running back limited in the passing game without a team.

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.

More Analysis by Bernard Faller

RSO Staff Picks 2020: Week 9

Updated: November 8th 2020

Stephen’s Picks

Matt’s Picks

Kyle’s Picks

More Analysis by Stephen Wendell

IDPs 101: How to Build Your 2020 DL Core

Updated: April 23rd 2020

He uses statistics as a drunken man uses lamp posts – for support rather than for illumination.
Andrew Lang, Scottish Novelist

Its Draft Week folks!!!  Talk about couldn’t have come any sooner too.  My fantasy circles were particularly chatty this weekend.  It got me thinking – aside from how grateful I was to have a temporary distraction from the daily stresses of the Coronavirus, I couldn’t help but wonder how we all got here.  I’m speaking in regards to my friends becoming the Dynasty nuts they are today.  It really was not too long ago I was drafting with owners who would try their best to select all Bucs’ players, or they based their decisions on whether or not someone played in the SEC.  Of course, now it seems like every owner keeps a finger on the pulse of the league year round.  We’ve got guys arguing about snap counts and average completed air yards in mid-April.  It’s beautiful!

Throughout this evolution, I have noticed a trend amongst our fantasy community as a whole.  We are all perfectly capable of taking a stance on a player & backing it up with numbers.  Whereas, we Saints’ homers used to proclaim Cam Jordan the best DE in the league simply out of Who Dat loyalty, we now back up our boasts with data (i.e., Jordan’s 40 sacks the last 3 seasons are the most of any DE in that time frame).  However, the problem is most owners are only interested in pursuing the numbers when it’s time to argue about their favorite players or the biggest names.  There is so much unrealized insight out there.  My hope is that this article can act as a springboard for reshaping your relationship with statistics, and ultimately regaining the edge you had back when your competitors were drafting Kevin Faulk in the 4th round because he went to their high school.

Take a look at some of these names:

Landon Collins – recorded 5 Ints and 4 Sacks in 2016.  He has since logged 2 Ints and 1 sack in 42 games.

Geno Atkins – 9+ sacks in 4 straight seasons. He finished with half that number last year.

J.J. Watt – only managed 4 sacks in the 8 games he played in 2019

Khalil Mack – failed to reach double digit sacks for the 1st time in 5 years.

We see this kind of stuff every season.  Big names will eventually let you down at every position, and IDPs are especially volatile.  I understand the frustration.  You signed the best IDPs in the game and it didn’t work out.  What more could you possibly do?

For starters, you must step off that carousel.  Chasing today’s biggest names will rarely yield tomorrow’s best results.  I challenge you all to try this instead.  Forget the names altogether and focus on the odds.  Therein lies my goal.  To provide RSO readers with actionable odds they can use in building their Defensive Line core this offseason.

I approached this challenge from 3 different perspectives.  The 1st – Based off the last 10 years, what are the odds of success for DL rookies in Years 1, 2 and 3?

I categorized these rookies into 3 subgroups: Top 10 Selections, 1st Rounders 11-32, and 2nd Rounders.  I determined success by the scale with which most of my RSO leagues score IDP production (1 point per Tkl, 0.5 per Assist, 2.5 points per Half-Sack, 7 points per FF or FR), along with an arbitrary target of 80 points.  Here’s what I found.

Top 10 Picks 11-32 2nd Round
Year 1 40.0% 13.2% 7.7%
Year 2 46.7% 24.5% 14.6%
Year 3 40.0% 33.3% 17.0%
1 of 3+ 86.7% 42.2% 29.8%
2 of 3+ 66.7% 24.4% 10.6%
3 of 3 20.0% 8.9% 0.0%
0 of 3 33.3% 60.0% 63.8%

The Top 10 consist of 20 players: Ndamukong Suh, Gerald McCoy, Tyson Alualu, Marcell Dareus, Dion Jordan, Ezekiel Ansah, Barkevious Mingo, Jadeveon Clowney, Dante Fowler, Leonard Williams, Joey Bosa, DeForest Buckner, Myles Garrett, Solomon Thomas, and then 2019’s Draft Class – Nick Bosa, Quinnen Williams, Clelin Ferrell, Josh Allen and Ed Oliver – whom only qualify for Year 1 figures.  Of the 15 players that came before them, only Ezekiel Ansah, Joey Bosa and Myles Garrett (more on these 2 later) have attained our definition of fantasy relevance all 3 years.

The sample size for Picks 11-32 (53) and 2nd Rounders (52) are much bigger.  As you can see, the odds increase with each season.  Also, both subgroups experience a steep descent from its antecedent.  This table’s 2 biggest takeaways:  At 40%, the Top 10 picks are 3 times more likely to be relevant their rookie season than the 1st Rounders 11-32 are.  The same holds true with the 2 out of 3 or greater successful seasons stat.  The Top 10’s 66.7% is also nearly 3 times the success rate of the remainging 1st Rounders.  This is useful information, but I was not satisfied with stopping here.  This brings us to the 2nd method of inquisition.

Let’s simplify things.  The DL position is predicated on getting to the QB right?  Therefore, Sacks are a powerful metric for which we can base our research.  I gathered all the DEs/DTs that recorded 7.5+ sacks in the last 10 seasons.  I then documented which year in the player’s career the feat was achieved.  Below is an example from 2010.

Name Year 
John Abraham 11
Jason Babin 7
Charles Johnson 4
Justin Tuck 6
Osi Umenyiora 8
Jared Allen 7
Chris Clemons 7
Robert Mathis 8
James Hall 11
Trent Cole 6
Dwight Freeney 9
Ndamukong Suh 1
Carlos Dunlap 1
Raheem Brock 9
Cliff Avril 3
Chris Long 3
Justin Smith 10
Mario Williams 5
Ray Edwards 5
Israel Idonije 7
Julius Peppers 9

Here are the results tallied up from seasons 2010-2019.

Year of Career Total
1 13
2 20
3 30
4 31
5 32
6 21
7 22
8 21
9 20
10 14
11 10
12 2
13 1

Only 13 players reached the 7.5 benchmark in year 1, 3 of which occured in 2019 (Josh Allen, Nick Bosa, and Maxx Crosby).  In Year 2 we observed a rate similar to that of Years 6-9.  Then we reach our sweet spot in Years 3-5.  I was pleaseantly surprised with how clean of a trend we wound up with here.  It energized me.  I had to know what sort of results would emerge from combining the previous 2 research methods.

The 3rd Perspective – How did each player on the list above fare sackwise in Years 1, 2 and 3?  With 92 qualifying Defensive Lineman, we had a total of 50 1st/2nd Rounders.  Here are the players of note:

3 of 3
Top 10
3 of 3
Picks 11-32
2 of 3
Top 10
2 of 3
Picks 11-32
2 of 3
2nd Round
Ezekial Ansah Dwight Freeny Myles Garrett Cam Jordan Osi Umenyiora
Aaron Donald Joey Bosa Robert Quinn Calais Campbell
Khalil Mack J.J. Watt Frank Clark
Andre Carter Jason Pierre-Paul Jabaal Sheard
Julius Peppers John Abraham
Mario Williams
Ndamukong Suh


 Total 3 of 3 2 of 3 1 of 3 0 of 3 2 of 3 1 of 3
Top 10 16 1 7 6 2 50.0% 87.5%
21 2 5 7 7 33.3% 66.7%
2nd Round 13 0 4 5 4 30.8% 69.2%

Our sample size decreased significantly here, but we are still able to recognize the Top 10 picks’ irrefutable edge.  So what does it all mean Basil?

Let’s assume this is your league’s first year, and you are operating with a 30 man roster that starts 2 DL.  In this scenario, I would want to roll with 4 guys.

I would start by making an aggressive push to lock up a Top 10 selection in the Rookie Draft, which this year figures to be Washington’s Chase Young.  If I have to move some picks around to lock him up, so be it.  I’m then targeting players entering Years 3, 4, 5 in the Auction since that range has the best odds.  Myles Garrett or Joey Bosa are Priority 1, and  I am willing to spend as much as 10 mil a year for one of them.

After that we have a couple of solid options at DT in Chris Jones and DeForest Buckner.  DTs often enjoy discounts since sacks are harder to come by at that position, and this pair endured a combined 11 sack dropoff in 2019.  I would want to add one of them or Yannick Ngakoue, who is severly underated.  Fun fact.  Yannick is 1 of 2 players from our list, not drafted in the 1st 2 Rounds who recorded 7.5+ sacks in all 3 of his first seasons.  The other was Jared Allen.

Finally, I am targeting a potential breakout player that has shown glimpses and will be acquired on the cheap.  Guys like Sam Hubbard, Jonathan Allen, Derek Barnett, Shaq Lawson, Matt Ioannidis, and Marcus Davenport all fit the bill.

Finding success in RSO leagues is all about planning and execution.  Although I will respect and even fear your trio of Cam Jordan, Aaron Donald and Melvin Ingram some weeks, I know the odds are in my favor to finish the year with a top DL core.  I challenge you to take a similar apporach this season.

More Analysis by Grant Viviano

RSO Staff Picks: Week 13

Updated: November 28th 2019

Week 12 Results & Overall Standings

1. English – Week 12 11-3 // Overall 116-59-1

2. Papson – Week 12 10-4 //Overall 115-60-1

3. Wendell – Week 12 9-5 // Overall 109-66-1

Happy Thanksgiving to all of you GMs. We are especially thankful for your support and enthusiasm to our platform. Our CTO Kyle English retook the lead in the year long picks challenge by going on an island picking Seattle and the 49ers, both of whom dominated their opponents. Pappy had a decent week as well and my mediocre 9-5 has me seven games back of Kyle (it does not look good for me this year). Our picks for this week, including today’s Thanksgiving slate are below. Best of luck to all of you on the playoff bubble punching your ticket this week. Enjoy the games and the holiday weekend.

NFL Game Picks























More Analysis by Stephen Wendell

RSO Staff Picks: Week 8

Updated: October 26th 2017

Week 7 Results

1. Wendell – 12-3

2T. English 10-5

2T. Papson 10-5

Overall Standings

1. Wendell – 66-40

2. English – 65-41

3. Papson – 61-45

After 7 weeks at the top of the standings, Wendell has caught up with English. Led by his Raiders and Chargers correct predictions, Wendell goes 12-3 and wins the week and takes over first place on the year with a slim one game lead over English. And at 61-45, Papson is only five games out of first place. There will not be much ground made up this week however as the three of us only differ on two games with Kyle liking gunslinger Matt Moore tonight on the road in Baltimore and Wendell liking Derek  Carr and the Raiders on the road in Buffalo. It is a rare week that there is this much agreement amongst us, so we are either going to be really right or really wrong. Here are our picks for Week 8:

NFL Game Picks



















More Analysis by Stephen Wendell