"Dissecting QB Value In Fantasy Football -- The Zero QB Theorem"

[Axe Elf]

Well, I will leave it alone at this point too. You see, I axually do care for my students and hope they don't get sucked in to this idea that you can win 8 games without starting a QB, but if they aren't bright enough to see what's wrong with this "Theorem" even after it's been rather thoroughly debunked, then I guess they will get what they deserve.

 

On to more useful lessons...

[keggerz]

Well, I will leave it alone at this point too. You see, I axually do care for my students and hope they don't get sucked in to this idea that you can win 8 games without starting a QB, but if they aren't bright enough to see what's wrong with this "Theorem" even after it's been rather thoroughly debunked, then I guess they will get what they deserve.

 

On to more useful lessons...

 

And if you think the point of this is to try and win 8 games without a QB then you completely missed the point so it is better that you move along. Never once does the article advocate playing without a QB...No it advocates waiting on QB because you don't need big points from the position to have a successful team.

[Tford]

I like the outside the box thinking here but there are a couple statistical flaws here. Nothing to do with the data itself, but straight math no-nos. Some points I took away from this.

 

 

1) In statistics, you cannot apply any mathematically derived solution of a subset onto a whole set and keep it valid. The qualifier that causes it to be a subset in the first place contains assumptions or data characteristics that are not inherit to every piece of data in the whole set.

 

In this case, the extrapolation of win % without a QB within the "win" subset cannot be applied to the "total games" whole set. Other factors caused the win subset to be a win in the first place. Things like good games from your other players and/or a bad game from your opponent. Those factors are not always present in the other data subset "losses". Therefore any derived number from the wins subset, can't apply to the other games, it can only by compared to a similar derivation to the whole set. In order for your win % extrapolation to hold true, every game would have to involve good games from your other players or a bad game from your opponent. We already know this not to be true.

 

 

2) I like where you were going with the Average wins for a team with a top-3 QB. I think that analysis is much more relevant. Since we know that in every league with an even amount of teams and a 13 games fantasy regular season, the mean win average must be 6.5, determining the true mean of the top QB subset and comparing that true mean to the whole set true mean of 6.5 will hold much more relevance if we assume that fantasy regular season follow a normal distribution (most things do).

 

That said, three things prevent your analysis from sticking.

 

- In order to compared mean to mean, you need to know what the standard deviation of both the set and subset is to determine whether the null hypothesis is true (subset mean = true mean or rather, subset mean is not significantly different than true mean). In this case, you are trying to prove just that. If the subset mean is the same as the set mean, then a top QB should not provide any statistical advantage. However, simply stating that your calculated subset mean is 6.6 is only half the answer. You need to use standard deviation to determine how far away from the mean is normal. A normal distribution of 6.5 mean and 0.1 standard deviation is drastically different from the same mean and 1.5 standard deviation. You reference CV (coefficient of variation) in your article later on. In this case, a lower CV might prove the null hypothesis false whereas a higher CV might prove the null hypothesis true.

 

- In order to complete that, you need a much larger sample set on the order of 1000s of leagues. You need to eliminate bias from the data set as much as you can. Did the top 3 QB owner tend to draft WR heavy? Did he always lead out RB? Was it the same guy in multiple leagues? You need the answer to all of these questions and any question like it to be sometimes, not usually or seldom. If you cannot say that, then your sample set is not randomized enough to be considered a whole set.

 

- Top 3 QB seems to be an arbitrary number. Using your SOFA classic league, the pick difference between QB3 and QB4 drafted was 7, 7, 7, 5, 2, 1 and 2 going back to 2006. What makes the QB3 selecting team so markedly different from the QB4 selecting team? In addition, sometimes the QB3 was selected as high as round 1 and others it was selected as low as round 5. A round cutoff would have more appropriate since I would argue that the guy who took Drew Brees at QB3 (5.06) in 2007 (whoever drafted for the The Huddle oddly enough) or the guy who took Aaron Rodgers at QB3 (4.12) in 2009, got much better value than the guy who took Drew Brees at QB3 (1.11) in 2012. You go on to speak about VBD in your article but QB3 in round 4-5 is markedly different than VBD in round 1-2. I would argue that lumping those teams into the same data subset isn't as valid as lumping all round 1-2 QB drafting teams together and seeing what analysis that holds.

 

3) Your analysis involving CV and miss rate is spot on and is very relevant in my opinion. It highlights the disparity between what RB1/WR1 you can draft in round 1-2 versus waiting a round because you drafted QB versus the disparity (smaller) of the QBs were you to wait. I don't know if Olympic miss rate is relevant simply because a top 3 QB drafted will likely be started for his fantasy team every week he is healthy. That said, major points were not made off of Olympic MR so it doesn't really matter.

 

4) Finally, and I only bring this up because I am an engineer and I am a nerd, theorems are statements that are proven factual time and time again through multiple proofs and derivations from other theorems and accepted fact. Theory, in a statistical sense, is a hypothesis that has been rigorously tested and being proven true through repeated mathematical test. It is not a law as it may not have yet been tested under specific conditions which may test its validity.

 

What you have is a hypothesis. A proposed explanation for a result, behavior or phenomenon that can be tested to prove/disprove validity.

 

 

 

All in all, good read.

[keggerz]

I like the outside the box thinking here but there are a couple statistical flaws here. Nothing to do with the data itself, but straight math no-nos. Some points I took away from this.

 

 

1) In statistics, you cannot apply any mathematically derived solution of a subset onto a whole set and keep it valid. The qualifier that causes it to be a subset in the first place contains assumptions or data characteristics that are not inherit to every piece of data in the whole set.

 

In this case, the extrapolation of win % without a QB within the "win" subset cannot be applied to the "total games" whole set. Other factors caused the win subset to be a win in the first place. Things like good games from your other players and/or a bad game from your opponent. Those factors are not always present in the other data subset "losses". Therefore any derived number from the wins subset, can't apply to the other games, it can only by compared to a similar derivation to the whole set. In order for your win % extrapolation to hold true, every game would have to involve good games from your other players or a bad game from your opponent. We already know this not to be true.

 

 

2) I like where you were going with the Average wins for a team with a top-3 QB. I think that analysis is much more relevant. Since we know that in every league with an even amount of teams and a 13 games fantasy regular season, the mean win average must be 6.5, determining the true mean of the top QB subset and comparing that true mean to the whole set true mean of 6.5 will hold much more relevance if we assume that fantasy regular season follow a normal distribution (most things do).

 

That said, three things prevent your analysis from sticking.

 

- In order to compared mean to mean, you need to know what the standard deviation of both the set and subset is to determine whether the null hypothesis is true (subset mean = true mean or rather, subset mean is not significantly different than true mean). In this case, you are trying to prove just that. If the subset mean is the same as the set mean, then a top QB should not provide any statistical advantage. However, simply stating that your calculated subset mean is 6.6 is only half the answer. You need to use standard deviation to determine how far away from the mean is normal. A normal distribution of 6.5 mean and 0.1 standard deviation is drastically different from the same mean and 1.5 standard deviation. You reference CV (coefficient of variation) in your article later on. In this case, a lower CV might prove the null hypothesis false whereas a higher CV might prove the null hypothesis true.

 

- In order to complete that, you need a much larger sample set on the order of 1000s of leagues. You need to eliminate bias from the data set as much as you can. Did the top 3 QB owner tend to draft WR heavy? Did he always lead out RB? Was it the same guy in multiple leagues? You need the answer to all of these questions and any question like it to be sometimes, not usually or seldom. If you cannot say that, then your sample set is not randomized enough to be considered a whole set.

 

- Top 3 QB seems to be an arbitrary number. Using your SOFA classic league, the pick difference between QB3 and QB4 drafted was 7, 7, 7, 5, 2, 1 and 2 going back to 2006. What makes the QB3 selecting team so markedly different from the QB4 selecting team? In addition, sometimes the QB3 was selected as high as round 1 and others it was selected as low as round 5. A round cutoff would have more appropriate since I would argue that the guy who took Drew Brees at QB3 (5.06) in 2007 (whoever drafted for the The Huddle oddly enough) or the guy who took Aaron Rodgers at QB3 (4.12) in 2009, got much better value than the guy who took Drew Brees at QB3 (1.11) in 2012. You go on to speak about VBD in your article but QB3 in round 4-5 is markedly different than VBD in round 1-2. I would argue that lumping those teams into the same data subset isn't as valid as lumping all round 1-2 QB drafting teams together and seeing what analysis that holds.

 

3) Your analysis involving CV and miss rate is spot on and is very relevant in my opinion. It highlights the disparity between what RB1/WR1 you can draft in round 1-2 versus waiting a round because you drafted QB versus the disparity (smaller) of the QBs were you to wait. I don't know if Olympic miss rate is relevant simply because a top 3 QB drafted will likely be started for his fantasy team every week he is healthy. That said, major points were not made off of Olympic MR so it doesn't really matter.

 

4) Finally, and I only bring this up because I am an engineer and I am a nerd, theorems are statements that are proven factual time and time again through multiple proofs and derivations from other theorems and accepted fact. Theory, in a statistical sense, is a hypothesis that has been rigorously tested and being proven true through repeated mathematical test. It is not a law as it may not have yet been tested under specific conditions which may test its validity.

 

What you have is a hypothesis. A proposed explanation for a result, behavior or phenomenon that can be tested to prove/disprove validity.

 

 

 

All in all, good read.

 

TJ, I appreciate the feedback and lesson...had I known you were so versed I would have consulted with you.

 

As to #1: While I can't apply the 61% to the set I can say that 61% did win their games and I can use the point differential as a frame of reference.

 

So I have a Zero QB Hypothesis (that's to many characters for twitter )

Edited July 19, 2013 by keggerz

[Axe Elf]

His first point is what Fleming and I were trying to say, in layman's terms.

[Grogansghost]

Lots of interesting stuff so far - but this data presumes every team keeps the QB they drafted. What about trades?

 

 

Just kidding Keggerz - I really enjoyed the article and ensuing discussion.

[chiroacademy]

OK here are the stats from the winner of my league last year: He picked Cam Newton in Rd 2. That was the 6th QB off the board. His record was 8 wins and 5 losses. Without his QB he goes 5 wins and 8 losses and misses the playoffs. He still wins 62%of the games that he originally won. I don't know if that is good or bad but he doesn't make the playoffs w/o a QB. If he does make the playoffs he wins the first rd and loses in the second rd of the playoffs to me and I win the league.

 

If we exchange Cam Newton for Locker He goes 7 wins and 6 losses

 

If he makes the playoffs he stills wins rd 1 and loses rd 2

 

If we exchange Cam with Palmer her goes 7 and 6 and same results in the playoffs

 

I

Edited July 19, 2013 by chiroacademy

[keggerz]

OK here are the stats from the winner of my league last year: He picked Cam Newton in Rd 2. That was the 6th QB off the board. His record was 8 wins and 5 losses. Without his QB he goes 5 wins and 8 losses and misses the playoffs. He still wins 62%of the games that he originally won. I don't know if that is good or bad but he doesn't make the playoffs w/o a QB. If he does make the playoffs he wins the first rd and loses in the second rd of the playoffs to me and I win the league.

 

If we exchange Cam Newton for Locker He goes 7 wins and 6 losses

 

If he makes the playoffs he stills wins rd 1 and loses rd 2

 

If we exchange Cam with Palmer her goes 7 and 6 and same results in the playoffs

 

I

 

The article doesn't advocate playing without a QB, "it doesn't advocate playing without a quarterback. Quite the contrary, what it helps to illustrate is that your quarterback doesn't heed to do all that much to put you in a position to win double digit games."

 

I'm not sure why you picked Locker when he missed multiple games. Realistically a team will plug a QB that plays in.

[keggerz]

I like the outside the box thinking here but there are a couple statistical flaws here. Nothing to do with the data itself, but straight math no-nos. Some points I took away from this.

 

 

1) In statistics, you cannot apply any mathematically derived solution of a subset onto a whole set and keep it valid. The qualifier that causes it to be a subset in the first place contains assumptions or data characteristics that are not inherit to every piece of data in the whole set.

 

In this case, the extrapolation of win % without a QB within the "win" subset cannot be applied to the "total games" whole set. Other factors caused the win subset to be a win in the first place. Things like good games from your other players and/or a bad game from your opponent. Those factors are not always present in the other data subset "losses". Therefore any derived number from the wins subset, can't apply to the other games, it can only by compared to a similar derivation to the whole set. In order for your win % extrapolation to hold true, every game would have to involve good games from your other players or a bad game from your opponent. We already know this not to be true.

 

 

I thought about this a bit more and I have tweaked the part that talked about extrapolating the wins. I still stand by saying that 61% of team that won still won because they did, those are hard numbers...So I changed it to put a 61% win % in perspective saying that it would equate to 7.9 wins. I also added what the win % was for the top-3 ADP quarterbacks (50.4%) but the 6.6 wins for the top-3 wasn't an extrapolation, that was a hard number from the beginning.

 

My intent wasn't to deceive anyone and from the start the only reason I wanted to show hard number wins was because it would be easier for people to relate to those numbers. I still feel the point stands that good teams win the majority of the time...in spite of QBs not because of them.

 

Oh, and if Taco Bell can call what they serve meat then I'm still calling this a Theorem

Edited July 19, 2013 by keggerz

[chiroacademy]

I picked Locker because he was mentioned earlier and the games he was hurt didn't come into play. If I replace Cam with a 15 point QB every week he still ends up 7 and 6. Cam had 2 big games that won it for him in those weeks. Other than those 2 games, his QB was a complete non-factor. But Cam also had 2 weeks of 30 plus points that he still lost in those weeks.

 

I still buy into the strategy of picking up a QB in a late round. There is more to a team than the QB.

 

The Team who drafted Aaron Rodgers finished 8th at 4-8-1

The Team with Drew Brees finished 9th at 4-9

The Team with Tom Brady finished 7th at 6-7

[chiroacademy]

I don't care what you call it. Your info is very well thought out and useful. Good work. I think you are trying to hard to validate your findings. Either people use it or they don't. All of the banter is distracting. Bottom line - picking a top tier QB is not the end all. The gap between a top tier and a later round QB can be more than made up by drafting a stronger RB, WR and TE core and thus you are more likely to win.

[chiroacademy]

The article doesn't advocate playing without a QB, "it doesn't advocate playing without a quarterback. Quite the contrary, what it helps to illustrate is that your quarterback doesn't heed to do all that much to put you in a position to win double digit games."

 

I'm not sure why you picked Locker when he missed multiple games. Realistically a team will plug a QB that plays in.

 

 

I didn't think you were suggesting to play without a QB. I was providing my stats.

[keggerz]

I didn't think you were suggesting to play without a QB. I was providing my stats.

 

I wasn't but some seem to intimate that I am.

[Big Country]

So, I'll stick with my normal hypothesis that I apply to most drafts, and I believe your mR and pR numbers support these basic ideas.

 

 

1. I am much more confident in my ability to find a QB that can contribute meaningful numbers to my team in the later rounds than I am in finding the RB or WR that will contribute meaningful points.

 

2. I am much more confident in my ability to find a top ten WR outside of the first two rounds than I am in my ability to find a top ten RB in those same rounds.

 

 

Now, this does not mean I am always drafting an RB first or that I am never taking a QB in the first 4 rounds, as there are many other factors that come into play such as lineup/scoring rules and which players are actually available when my pick comes up, but, all else being equal, these are two of my basic tenets that I believe your mR and pR support.

[Caveman_Nick]

Correct

 

 

Nevermind my PM. This answers my question.

 

Strong teams win by a lot of points. Take away any one player and they probably still win most weeks. If you took the same teams over the same time frame and eliminated a player that was drafted at roughly the same ADP as their starting QB*, which would probably be on average the team's RB2, I think you would find the winning percentage stays about the same as well.

 

* take the top 12 QBs drafted and average their ADP. Find the top 12 RB2's and average their ADP. Compare. It could be WR1, but probably not. Definitely not RB1. Doubtful it would be TE1. RB2 is probably the best comparison.

[Bring Back Pat!!!]

Great work Keg. I fully understand what you're showing. And the comparisons and questions about other positions are irrelevant and worthless. This is an examination of the QB position only. As the NFL has become more and more of a passing league there has been a sanction of fantasy players who believe you must get a top QB to win. Hell, one expert took Rodgers #1 overall in the Index league! But the more and more it becomes a passing league, the more quality QBs are out there. Fantasy football is often about position scarcity and some people don't understand that.

 

In most leagues teams only start 1 QB, so debating and analyzing the numbers as to where to draft the starting QB is a valid project. The data shows (whether or not the analysis is 100% accurate from a stats class point of view, I'm not sure) that waiting on your starting QB and filling the roster at all the other positions can be a winning strategy. To me, it makes sense. QBs are easier to predict since generally each team only has 1 starter. But many teams have RBBC and others also have more than one starter-worthy WR (ATL, and DEN for example).

[keggerz]

Great work Keg. I fully understand what you're showing. And the comparisons and questions about other positions are irrelevant and worthless. This is an examination of the QB position only. As the NFL has become more and more of a passing league there has been a sanction of fantasy players who believe you must get a top QB to win. Hell, one expert took Rodgers #1 overall in the Index league! But the more and more it becomes a passing league, the more quality QBs are out there. Fantasy football is often about position scarcity and some people don't understand that.

 

In most leagues teams only start 1 QB, so debating and analyzing the numbers as to where to draft the starting QB is a valid project. The data shows (whether or not the analysis is 100% accurate from a stats class point of view, I'm not sure) that waiting on your starting QB and filling the roster at all the other positions can be a winning strategy. To me, it makes sense. QBs are easier to predict since generally each team only has 1 starter. But many teams have RBBC and others also have more than one starter-worthy WR (ATL, and DEN for example).

 

Thanks, Dave.

[darin3]

Great work Keg. I fully understand what you're showing. And the comparisons and questions about other positions are irrelevant and worthless. This is an examination of the QB position only. As the NFL has become more and more of a passing league there has been a sanction of fantasy players who believe you must get a top QB to win. Hell, one expert took Rodgers #1 overall in the Index league! But the more and more it becomes a passing league, the more quality QBs are out there. Fantasy football is often about position scarcity and some people don't understand that.

 

In most leagues teams only start 1 QB, so debating and analyzing the numbers as to where to draft the starting QB is a valid project. The data shows (whether or not the analysis is 100% accurate from a stats class point of view, I'm not sure) that waiting on your starting QB and filling the roster at all the other positions can be a winning strategy. To me, it makes sense. QBs are easier to predict since generally each team only has 1 starter. But many teams have RBBC and others also have more than one starter-worthy WR (ATL, and DEN for example).

 

 

Good post - another couple things to consider: one, the anomaly of the rookie (or very young) QB that's no longer "throw to the lions". RG3, Luck... heck, even Tannehill and Weeden showed flashes last year. There may not be as many rookie QBs this season that have those kinds of impacts (heck, I'd go so far as to say only one has any shot). But the preponderance of the rookie making early splashes (as opposed to not completely crapping the bed) makes for an even deeper talent pool in redraft formats.

 

And secondly, to a small degree, would be the growing popularity of the running QB formations. That gives the QB just another means of putting up points. Even if it's just 20-30 rushing yards every game... heck, that's 2-3 points per game.

[flemingd]

This theorem tells us nothing by itself. Keg, you yourself have said it's not intended to encourage starting no QB, so what's it supposed to tell us? That we can retain 61% of wins we already won doesn't excite me. I want to win more games, not less. I want to win some of the games I originally lost. I want to avoid losing games. This isn't telling me how to do that, let alone proving why.

 

Since QB's are the highest scorer, it stands to reason we'd see even more positive results under a Zero RB theorum. Since the margin of victory is the same, a lower scoring position should result in an even better win retention.

 

I don't mean to be insulting with my tone, more tongue in cheek, but seriously, where's the beef?

 

I'll give you an example of where I thought this would be going:

 

The Top 3 QB's averaged N points in the leagues used in the data set.

The Replacement Value of QB (average of QB13-QB15) is N1 in the leagues used in the data set.

 

Using my homer league, N = 26.9, N1 = 21.4, and the raw data Keg provided, we can see that of the 704 losses, the Replacement Value QB only accounted for 46 of them, or 6.5%. What are the numbers N and N1 in this data set?

 

So now tell me the Replacement Value at RB. If I draft Rodgers in the 1st I know I'll win 6.5% more games than getting Big Ben in the 8th. But what's my opportunity cost? How big a price will I pay going from Lynch to Matthews? From Calvin to Shorts? Because this is the ENTIRE POINT behind waiting on a QB - you only lose X at QB, but Y at the other position.

[keggerz]

This theorem tells us nothing by itself. Keg, you yourself have said it's not intended to encourage starting no QB, so what's it supposed to tell us? That we can retain 61% of wins we already won doesn't excite me. I want to win more games, not less. I want to win some of the games I originally lost. I want to avoid losing games. This isn't telling me how to do that, let alone proving why.

 

Since QB's are the highest scorer, it stands to reason we'd see even more positive results under a Zero RB theorum. Since the margin of victory is the same, a lower scoring position should result in an even better win retention.

 

I don't mean to be insulting with my tone, more tongue in cheek, but seriously, where's the beef?

 

I'll give you an example of where I thought this would be going:

 

The Top 3 QB's averaged N points in the leagues used in the data set.

The Replacement Value of QB (average of QB13-QB15) is N1 in the leagues used in the data set.

 

Using my homer league, N = 26.9, N1 = 21.4, and the raw data Keg provided, we can see that of the 704 losses, the Replacement Value QB only accounted for 46 of them, or 6.5%. What are the numbers N and N1 in this data set?

 

So now tell me the Replacement Value at RB. If I draft Rodgers in the 1st I know I'll win 6.5% more games than getting Big Ben in the 8th. But what's my opportunity cost? How big a price will I pay going from Lynch to Matthews? From Calvin to Shorts? Because this is the ENTIRE POINT behind waiting on a QB - you only lose X at QB, but Y at the other position.

 

In simple terms it tells you that the majority of wins are by a large point differential. The second half of the article was to show how the value among the positions related. I still think that those value metrics are valid and viable and quite honestly think they were the most important part of the article.

 

If the article isn't giving you what you want I apologize for that, but in my eyes it does a good job showing that QB value is below RB/WR & TE.

[irish]

In simple terms it tells you that the majority of wins are by a large point differential. The second half of the article was to show how the value among the positions related. I still think that those value metrics are valid and viable and quite honestly think they were the most important part of the article.

 

If the article isn't giving you what you want I apologize for that, but in my eyes it does a good job showing that QB value is below RB/WR & TE.

 

 

It's simply because we start less of them in most leagues and the difference between the #1 QB and say #10/#12 isn't nearly as bad as waiting on RB, WR or TE and seeing the more severe drop-off in statistical output at those positions.

[bostonsoxandy]

I'll have to dig in with some fresh eyes tomorrow if I get the chance (hopefully). I like what my semi-conscious brain post Saturday night is reading right now -- looks like some great work keg.

[delfamdelfam]

http://www.fantasysharks.com/artman2/publish/Statistically_Speaking_Why_drafting_a_QB_in_the_Top_of_the_Draft_is_a_Wise_Move.htm

[Jaboz]

Thank you for this piece. I've always had the opinion that QBs are overvalued, but never had any solid data to back that up. In the past I've foolishly argued with friends in my main league about the merit of drafting a QB in the 1st.. until I realized that, much like in poker, I should be happy when my opponents make poor decisions. I'm afraid though, with the depth at the position this year, that they may start waiting (there's usually 4-5 QBs off the board by the mid 3rd round) and end up drafting the more important positions - but we'll see.

 

It was pretty interesting to see how TE's stacked up as far as the CV, considering the position generally has the same number starters with respect to QB. That, to me, is yet another major indicator of the general lack of value that QB has to offer. And that isn't even touching on other adverse factors to QB value, like PPR. Articles like this, are why I've been coming back to the huddle. Thanks again!

[keggerz]

Thank you for this piece. I've always had the opinion that QBs are overvalued, but never had any solid data to back that up. In the past I've foolishly argued with friends in my main league about the merit of drafting a QB in the 1st.. until I realized that, much like in poker, I should be happy when my opponents make poor decisions. I'm afraid though, with the depth at the position this year, that they may start waiting (there's usually 4-5 QBs off the board by the mid 3rd round) and end up drafting the more important positions - but we'll see.

 

It was pretty interesting to see how TE's stacked up as far as the CV, considering the position generally has the same number starters with respect to QB. That, to me, is yet another major indicator of the general lack of value that QB has to offer. And that isn't even touching on other adverse factors to QB value, like PPR. Articles like this, are why I've been coming back to the huddle. Thanks again!

 

You're welcome and glad you enjoyed the article. Good luck in your league(s) this year