I think it is safe to say, that at one point or another, we have either heard, or uttered the saying, “I can beat you with one arm tied behind my back.”
That is the essence of the Zero QB Theorem, a theorem that isn’t nearly as complex as Fermet’s Theorem or even the Pythagorean Theorem.
Don’t worry; the Zero QB Theorem doesn’t require the use of geometry, calculus or any advanced mathematics – just simple addition and subtraction. Therefore, it’s safe to say that it won’t make history in mathematical circles, but it’s a game changer for the fantasy football community.
Zero QB Theorem – If you zero out the quarterback’s points on a winning fantasy team, they still win a majority of head-to-head matchups.
Below is an example from the 2012, SOFA Classic league hosted at MyFantasyLeague.com.
(KFFL) 156.78 – 16.28 = 140.50 > 131.36 (ROTOWIRE)
Perception Isn’t Reality
As I was mining the data for this research from three different leagues – SOFA Classic, SOFA IDP (both are expert leagues) and a random non-expert MFL league (Best Dam Fantasy League Period!) with six point passing TDs – my findings were shocking, even to me. That led me to create some polls at my blog (FullImpactFootball) to see what sort of perceptions people had regarding what a quarterback meant to a fantasy football team.
The questions were simple:
1. How many games do you win with a zero at QB?
2. On average, how many points do you lose by (with a zero at QB)?
3. How many wins/year do the top-3 QBs (ADP) average?
Since I was researching three different leagues, I wanted to see how that might influence people’s views, which is why I asked the same three questions for all three leagues. The polls substantiated how I thought people would perceive a quarterbacks value for their fantasy teams.
|How Many Games Do You Win With A Zero At QB?|
|SOFA Classic||SOFA IDP||BDFLP!|
Easy to see that people don’t hold out much hope for a team with a zero at the quarterback position to win many games. Adding up the percentages for wins from 0-1 to 4-5 you end up with 89.57% (SOFA Classic), 67.20% (SOFA IDP), and 97.37% (BDFLP!) of respondents voting for five or fewer wins.
|On Average, How Many Points Do You Lose By?|
|SOFA Classic||SOFA IDP||BDFLP!|
|Pts Lost By||%||Pts Lost By||%||Pts Lost By||%|
Not only do people think you won’t win many games by taking a zero at the quarterback position, but in SOFA Classic (42.37%), and BDFLP! (68.00%) many expect you to lose by more than 15.00 points. In SOFA IDP (24.54%) voters didn’t think that losses would be as much as in the other two leagues – likely due to the expanded rosters that are fielded in that league.
|How Many Wins/Year Do The Top-3 QBs (ADP) Average?|
|SOFA Classic||SOFA IDP||BDFLP!|
When it came to the top-3 quarterbacks – based on ADP rank – voters heaped on the wins. 51.35% (SOFA Classic), and 58.66% (BDFLP!) of voters felt that the top-3 QBs would log 8 or more wins. The 32.30% for 8 or more wins in SOFA IDP once again shows that people feel that the expanded rosters make the quarterback position slightly less important than in the other two leagues.
One of my favorite sayings is, perception is reality, but for this exercise, you’re about to find out the opposite is true.
I looked at seven years worth of fantasy matchups for each of the three leagues – a grand total of 1,805 matchups. My findings fly directly in the face of what the voters from the above polls thought. If ever you were going to have an open-mind, now would be the time.
The findings in the following tables are based on the Zero QB Theorem. The Win % column is the percentage of games that a team still won once their points at quarterback were zeroed out. The next column shows the average points a winning team lost by after their quarterback points were zeroed out.
|SOFA Classic||SOFA IDP||BDFLP!|
|Year||Win %||Pt Diff||Year||Win %||Pt Diff||Year||Win %||Pt Diff|
The total number of games won for all three leagues combined was 1,101 of the 1,805 matchups. That’s a combined win % of 61%. To put that in perspective, a 61% win % would extrapolate to 7.9 wins in a 13 week regular season. Putting the win % in contact for each league in the study, you would be looking at 8.2 wins (SOFA Classic), 8.4 wins (SOFA IDP), and 6.9 wins (BDFLP!) for each league.
Unbelievably, 61% win percent is more than what the top-3 ADP quarterbacks have averaged over the past seven years. Hard to believe, but the numbers speak for themselves.
How many teams in your league(s) won more than 61% of their games last year – with a quarterback?
|Average Wins By The Top-3 ADP Quarterbacks (including QB points scored)|
|SOFA Classic||SOFA IDP||BDFLP!||Combined|
|Year||Avg. Wins||Year||Avg. Wins||Year||Avg. Wins||Year||Avg. Wins|
There is a reason that people draft a top-3 ADP quarterback early – to gain an advantage over their competition. As the above chart illustrates, there is no advantage. Not when a top-3 ADP quarterback averaged a win % of 50.4%. Putting that in perspective, a 50.4% win % is the equivalent of just 6.6 wins in a 13-week season (note: the above chart is based on real world wins, not extrapolated wins). A 50.4% win % doesn’t equate to an advantage over the 61% noted above for the Zero QB Theorem quarterbacks. Instead, it’s safe to say the above chart shows that drafting a quarterback early is detrimental to the overall competitiveness of a fantasy team.
Looks like drafting a stud quarterback isn’t exactly all it’s cracked up to be. I was shocked too, so much so, that I decided to see how the top-3 ADP quarterbacks fared in the playoffs. The results as you’ll see, were even more shocking.
|Total Number Of Playoff Wins By A Top-3 ADP QB (including QB points scored)|
|SOFA Classic||SOFA IDP||BDFLP!||Combined|
Yes, what you are looking at is a sub-par playoff record (27-28, 49.1%) for the top-3 ADP quarterbacks over the past seven years. For clarification purposes, BDFLP! didn’t have playoffs in 2006, that year the top-3 ADP quarterbacks finished 2nd, 9th, and 11th.
While the Zero QB Theorem states that a winning fantasy team will win the majority of their games if you zero out their quarterback points, it doesn’t advocate playing without a quarterback. Quite the contrary, what it helps to illustrate is that your quarterback doesn’t need to do all that much to put you in a position to win double digit games. Don’t believe me? Then look at the following scatter plot.
Instead of zeroing out the quarterback points for the winning teams if I used an average of just 12 points/game, the win % would have climbed to 83.4%, good for an average of 10.8 wins.
Don’t get me wrong, you can’t just bypass the quarterback position, draft badly, and expect to win 10 plus games. No, what the research shows, is that a good team is a good team, and it isn’t defined by its quarterback play.
At this point, if you kept an open mind, it should be abundantly clear that quarterback value isn’t even close to what many perceive it to be. However, even with an open mind, I’m sure you are wondering…
After conducting my research, I wanted to bounce my findings off someone, so I turned to a friend, Jake Richmond – a very astute fantasy football player – to see what he thought of my findings. He said, “I can’t help asking…will this metric stand up to scrutiny?” he later added, “metrics only mean something in context, and right now there’s no context.”
Jake was right, my research needed context; I needed to show the why. Considering that quarterbacks are generally the highest scoring fantasy position, I had my work cut out for me.
When I looked at the five-year average scoring by position for the top-24, I found quarterbacks – 12 (50%) of them – dominated it. If you drill down even more, the numbers make quarterbacks look even more valuable. Based on the past five year’s averages, quarterbacks accounted for 58.3% of the top-12 overall scorers, and 80% of the top-5 overall scorers.
|Overall Rank||Positional Rank||Average Points||Overall Rank||Positional Rank||Average Points|
SOFA (Site Owners Fantasy Association) scoring is the scoring system
used for the above chart. You can find the complete five-year
positional scoring averages chart, by position, at my blog. In addition, all scoring numbers are based on a 16 week/15 game season.
Easy to see quarterbacks are the top dogs when it comes to points scored. However, if it were all about points, I wouldn’t have needed to do any research, or write this article, and you wouldn’t be here reading it. Instead, it’s about value, which isn’t as cut and dry for comparison’s sake.
Figuring out how to compare one position in fantasy football to another is no easy task. Sure, you could try to utilize VBD (Value Based Drafting), but I’m of the opinion that VBD is flawed. I’m not going to get into VBD beyond pointing out what I feel is its biggest flaw – baselines. With VBD you have to set baselines, and it doesn’t matter what method you use – average starter, worst starter, or top 100 – the point is, YOU are assigning a value to one player (zero baseline) at each position and then basing values off of those pre-set values. Think about it in these terms; is QB12 really worth the same as say RB24, WR36, TE12, K12 or D/ST12?
There is one principle to VBD that is spot on, and that is the fact that VBD isn’t about total points but the distribution of points among each position. All I had to do was find a better way to measure the distribution of points for each position, which is kind of like trying to find the Holy Grail of fantasy football.
Even though I feel that VBD is flawed, I figured it would be wise to look at the VBD values – using the last starter method – to see if anything jumped out at me. Since I already was of the mindset that QB value is overstated, I decided to see how quarterbacks compared to the kicker and D/ST positions. After all, those two positions are the least valuable of all fantasy football positions.
Just looking at VBD, you see that quarterback value is much greater than kicker, and D/ST value. At first blush, it might seem that this was a wasted exercise…it wasn’t.
|Rank||QB Points||QB VBD||Kicker Points||Kicker VBD||D/ST Points||D/ST VBD|
When looking at the above chart I noticed that the VBD value – while different – between each position looked close in value. That prompted me to run a new calculation – percent of VBD value to points scored (utilizing the five-year scoring chart) – generating a new percent that should be comparable across positions. That metric helps to frame what isn’t apparent just looking at VBD values. Instead of relying on a comparison based on the total point distribution among players at each position, it allows for a better apples to apples comparison. The reason this is needed is that scoring parameters, and starting requirements are not the same for all positions. Scoring parameters are why quarterbacks generally are the highest scoring position in fantasy football…do not get highest scoring confused with most important.
|Percent of VBD Value To Points Scored|
Analyzing the above chart, I saw that quarterback numbers now looked to be in line with D/ST numbers. The next step was to look at the average percent as it pertained to the starters at each position (note: in an effort to keep the chart orderly, I didn’t include the numbers for WR25-WR36. If you are interested in seeing them just request them from me via email.)
|Starter’s Average Percent of VBD To Points Scored|
At this point, I’d like to put this to rest, but I can’t. Because of my views regarding the shortcomings of VBD, I just can’t in good conscience put a bow on this. At a minimum, I am on to something.
After hours on end staring at my five-year positional scoring average chart (as well as other data), and trying a multitude of calculations to help prove what VBD affirmed in the above charts, I decided to take a break in order to clear my head…before pulling all my hair out.
That break turned out to be a twitter excursion. As I perused my timeline, I happened upon a tweet from JJ Zachariason (@LateRoundQB) about an article he wrote titled, “Understanding WR Volatility.” What happened next was odd…I clicked the link and read JJ’s article. What’s odd about that, is that I generally try to not read other people’s work when I am writing. I don’t want to be influenced by their views, etc. Yet, this time, for some inexplicable reason, I read, and thank the fantasy gods I did, because JJ – without even knowing – helped me find the Holy Grail – the Coefficient of Variation (CV).
Coefficient of Variation – “The normalized measure of dispersion of a probability distribution is called as coefficient of variation as often abbreviated as CV. In probability theory and statistics, it is also known as unitized risk or the variation coefficient. The CV is derived from the ratio of the standard deviation to the non-zero mean and the absolute value is taken for the mean to ensure it is always positive. It is sometimes expressed as a percentage, in which case the CV is multiplied by 100.”
In English, calculating the CV will assign a value to each position based on how it relates to the mean for points scored by that position. I could have just calculated the mean based on one criterion, but I decided that if I truly wanted to get a representation of how the value based on CV relates across positions that I should do so by calculating the mean in multiple ways.
The first mean calculation utilized the number of starters for each position (1QB, 2RB, 3WR, 1TE, 1K, and 1D/ST). The second mean was calculation utilized the total number of starters for each position, plus the first tier of backups. In other words, 24 QBs, 36 RBs, 48 WRs, 24 TEs, 24 Ks, and 24 D/STs are the numbers that comprised the second mean calculation. The final mean calculation utilized the average number of players at each position drafted in the SOFA Classic league over the past five years.
The results based on starters has the quarterback CV closest in value to D/ST, but even looking at the CV for starters plus first backup tier and drafted players, it is very apparent that QB CV value takes a back seat to RB, WR and TE.
|Mean based on starters (1)||Mean based on starters, plus 1st backup tier (2)||Mean based on drafted players (3)|
Now that we have a statistical basis for comparing the distribution of points scored position by position, you might think we can wrap this up. However, we can’t – not just yet. So far, all we know is, when compared to the RB, WR, and TE positions, no matter which mean calculation is used, the QB position has the smallest point distribution. That, in and of itself, goes a long way toward proving that QB is the least valuable among the big four positions, but it doesn’t put it completely to bed.
I decided that looking at ADP (average draft position) and seeing how ADP compared to end of season rankings could prove fruitful. In short, I found my bow.
I had bounced a ton of stuff off Jake, and at times, I think I probably almost made his head explode, but honestly, it was helping to keep mine from doing just that. Anyway, I was re-reading an email I had sent Jake when something I wrote jumped off the page at me, “if you “miss” on a QB”, that was it, my aha moment. Calculating a miss rate (mR) by position, based on ADP and end of season rankings is another piece of the context puzzle.
The following table shows the mR average, mR percent and an “Olympic” mR based on the past five years.
|Position||2008||2009||2010||2011||2012||Total||mR Average||mR Percent||“Olympic” mR|
The numbers in the above chart constitute the number of times a player, based on ADP data, was drafted to be a starter at their position, and failed to rank as a starter in the end of season rankings. So if the ADP QB6 finishes as QB15 in the end of season rankings that would constitute a miss. Note: The “Olympic” mR throws out the high and low score and was included to make sure that an outlier wasn’t severely impacting the averages.
The next step is to look at “replaceability” for each position. Doing so required a few different steps. One step would be to figure out the parameters for calculating a mR mean.
The parameters I came up with are; QB9-QB12, RB16-RB24, WR25-WR36, TE8-TE12, K8-K12, and D/ST8-D/ST12. Those parameters are derived from the average number of misses (see the highlighted mR Average column above) for each position. As an example, the quarterback position has a mR average of four, so the mR mean is calculated using the final four starting quarterback positions (QB9-QB12), if the mR number was three then the mR mean would have been calculated using QB10-QB12.
Based on the five-year scoring chart for QB9 (277.74), QB10 (272.41), QB11 (260.71) & QB12 (256.04) the mR mean is 266.73. That same process was used to calculate the mR mean for each position.
Following that, using the five-year scoring chart, I calculated the percent to mR mean for all non-starters for each position. Dividing the average by the mR mean created a percent to mR.
Those percents were then grouped into ranges. The number of instances within each range was then divided by the available supply of non-starters, leading to a positional replaceability percent (pR). Note that the second range includes all of range one, and range three includes both range one and range two. Below is an example to help better visualize the process.
That may have been a bit hard to follow, but I think it was important to walk-through the mathematical process that was utilized to get to the end result.
Keep in mind; the easier it is to replace something, the less value it has. That’s why the K and D/ST positions are afterthoughts for fantasy owners.
Now that we have the three pieces to our context puzzle, let’s put them together and see what it looks like.
|Position||CV (1)||CV (2)||CV (3)||mR||“Olympic” mR||pR (range 1)||pR (range 2)||pR (range 3)|
All three of the CV columns show that quarterback has by far the smallest differential in point distribution when compared to the running back, wide receiver, and tight end positions. The mR (miss rate) illustrates that the quarterback position is the easiest position from which to draft a starter. However, if you did end up whiffing on your quarterback, the pR (positional replaceability) metric shows that, outside of the kicker and D/ST positions, quarterback is by far the easiest position from which to find a replacement starter.
Put A Bow On It
So there you have it, a theorem with more than ample data to prove it’s true, along with two new metrics – mR (miss rate), pR (positional replaceability) – and CV (coefficient of variation), that helped to put positional value in context in order to support using the quarterback position for the Zero QB Theorem.
I know that for many, this theorem won’t be easy to accept, but the numbers don’t lie. What the numbers actually do, is prove and strengthen the stance of what people already on the “late-round quarterback” train thought.
Remember, there was once a time when drafting any player but a running back in round one was taboo. Times change, but some people just don’t like change and/or won’t accept change. If you have league mates that don’t like change, or are slow to accept it, use the Zero QB Theorem to beat them with one arm tied behind your back.
If you have any questions or comments surrounding the Zero QB Theorem, feel free to chime in here in our NFL Fantasy Football Forum. You can also follow me on twitter @SteveGalloNFL, and if you have any questions, feel free to email me at firstname.lastname@example.org.