# Averages and Frequencies in NFL Scoring

### The Holidays Bring Out the Best in People

“I don’t want something I need. I want something I want: Something pretty.”
— Mia

### Some Words, Maybe Some Sentences and Paragraphs

I’m writing this section on Christmas, because what else am I going to do on Christmas? — spend time with family?

Anyway, I just received a Harry Potter wand as a gift. With that wand I’ve magically created some free time, which I’m using to write this piece, which is a holiday gift to you. Lucky you.

It’s been a while since I wrote an actual honest-to-goodness way-too-long I-have-no-idea-how-this-piece-is-going-to-turn-out Labyrinthian.

It’s also been too long since I mentioned Nate Silver and/or Nassim Nicholas Taleb just for the hell of it, so I figured that, since its the holidays, I’d kill two turtledoves with one well-thrown rock-like partridge in a pear tree.

I still have no idea what this piece is about, but neither do you, so at least we’re on the same page.

### This Is About Average — and That Was a Pun

In The Signal and the Noise, Silver has a chapter entitled, “How to Drown in Three Feet of Water.” It’s in part about the danger of averages.

How can averages be dangerous? As Silver points out, it’s possible for a statistician to drown in a river that’s only three feet deep on average.

Averages provide the illusion that subjects under consideration are smoother than they really are. Averages offer the semblance of homogeneity where heterogeneity exists. Averages (when applied poorly) make mountains into well-sized hills.

A person with six fingers on one hand and four fingers on the other still has an average of five fingers per hand. Warren Buffett (~\$75 billion) and his four lowest-paid employees on average have individual net worths of about \$15 billion per person — even though that figure in no way is representative of any of the people in the sample.

And an NFL wide receiver can average 12 fantasy points per game (PPG) even if he has performances of only no more than six and no fewer than 12 points in any game.

### Context is More Important Than Text

Averages — especially raw averages — can hide context. Here’s a screenshot from our Trends tool:

Here we have six quarterbacks averaging 18.9-19.9 DraftKings PPG. If we looked only at their average PPG, we would assume that these QBs are roughly equivalent. They’re not.

That average doesn’t take into account two important factors:

1. Market valuation
2. Standard deviation

By “market valuation,” I mean both site-based pricing and tournament ownership — how platforms value NFL players and how DFS players respond to those valuations in the open market of guaranteed prize pools.

Our proprietary Plus/Minus metric takes into account salary-based production expectations. Within the 18.9-19.9 PPG cohort Dak Prescott is a strong overperformer, and Cam Newton is a relative underperformer. Dak and Cam have almost identical production, but Dak has significantly outproduced his expectations. The context of our Plus/Minus metric reveals the extent to which, though comparable as producers, Dak is clearly superior to Cam as a DFS asset.

And it’s a happy coincidence that Dak, while providing the most site-based value, also provides the most GPP value as the lowest-owned QB of the cohort. If we compare Dak to Ben Roethlisberger, we see that, even though Dak trails Ben in raw PPG, he still provides more GPP value because of his substantially higher Plus/Minus and lower ownership. In those regards — but certainly not in other regards — Dak has been the better GPP play of the two.

### PPG and Plus/Minus

In the best of scenarios, PPG and Plus/Minus are collectively leveraged. If, for instance, a QB has a high PPG but low Plus/Minus (or vice versa) then he has limited utility. If, however, a QB has a high PPG and Plus/Minus in a particular situation, then he pretty much holds the key to the secret garden of DFS.

Roethlisberger at home:

Like Hagrid, Roethlisberger is a keeper of the keys.

### Way Too Many People Die While I’m Writing These Pieces

It’s now Christmas evening, and I just saw on Twitter that George Michael died. Prince died earlier this year while I was writing a Labyrinthian. And now half of Wham!

This is just another reminder of what Taleb highlighted in The Black Swan: Sometimes turkeys die when they least expect it.

### Frequency, Consistency, Etc.

In addition to ignoring market valuation, a focus on averages tends to obscure “standard deviation,” by which I mean that when we pay attention to averages we can risk ignoring the larger range of outcomes.

Within our Player Models, we have metrics that measure Consistency as well as the frequency with which players submit upside or dud performances. In determining Consistency, we calculate how often players reach their salary-based expectations.

In some ways, Consistency is more important than PPG. For cash games, what we tend to care about is not necessarily how many points a player scores but how much/often we can depend on him to score enough points to reach the cash line. In this scenario, volatility is not a virtue.

### Position-Specific Consistency

Even Consistency — the contextual metric for PPG and Plus/Minus — deserves context.

Here are the core FantasyLabs metrics for the top-five DK players in seasonal PPG at each position:

As you see, among elite NFL players DK Consistency varies greatly depending on position.

RBs are highly consistent, while pass catchers are less so, all of which makes sense: RBs are easier to project. Their per-game opportunities are more reliable. WRs and TEs in comparison are more volatile. Their targets are more dependent on context.

And on the topic of volatility . . .

### Another Random Section

Much of what Taleb talks about in The Black Swan can be boiled down to the concept of volatility. When people focus on the averages, they overlook the possibility or impact of volatility.

Averages can hide the Black Swan-ness of isolated data points within a larger sample. Averages can camouflage outliers, making Shakespeare into nothing but a collection of plays averaging about 22,600 words per text.

Averages hide the extremes.

At FantasyLabs we think of upside and dud performances in terms of (relative) extremes. If a player has a 60 percent Upside Rating, that means in half of his games (over a specified period of time) he has exceeded his salary-based expectations by at least one-half of a standard deviation. For Dud Rating, we look for performances that fell short of expectations by half a standard deviation.

For cash games a high Consistency is desirable. For GPPs, Consistency is fine but high and frequent volatility is better.

### Tavon Revisited

Earlier this year, I wrote about how GPP upside lies on the periphery, a fact that explains how Tavon Austin could be a player with GPP-winning potential despite being perhaps the NFL’s worst ‘real No. 1 WR’ in 2015 and scoring fewer DK PPG than the punchline that is Rueben Randle (11.73 vs. 11.59).

He was priced down on DK for much of the year and largely ignored in GPPs . . .

. . . but, despite finishing as the WR43 with 11.59 PPG, Tavon scored 10 touchdowns on the season and had four games in which he more than doubled his salary-based point expectation.

Most people — or the ‘average person’ — would see that Tavon finished WR43 in PPG and assume that he had been a boom-or-bust WR3/4. That’s bullshit. He was a WR1 . . . 25 percent of the time.

### Tyreek Hill Explained

As I’m writing this, the Christmas evening Broncos-Chiefs game is ending. What a surprise! — Hill scored another TD!

When a guy scores 11 TDs in 15 games, his production isn’t entirely fluky. He might be on the extreme end of his range of outcomes — especially if he has only 76 targets, 21 rushes, and 52 returns — but he’s almost certainly a talented player.

And Hill’s not just talented. He’s volatile: This guy’s a wide receiver who has no receptions on eight targets over the last two games  . . . and he’s still scored a TD in each game.

With certain players — especially versatile players whose teams are committed to giving them touches in high-leverage situations — the question isn’t, “How many points does he average?” The question is, “How frequently does he score enough points to make an outsized difference?”

How often can he be a Black Swan?

### An Email

I’m lucky enough on occasion to exchange emails with Shawn Siegele, the RotoViz writer who pioneered the Zero RB strategy. Here’s an email I sent him on Aug. 22 (I’ve edited so that it’s tighter. [I’ve redacted about 50 F-bombs.]):

Hey Shawn,

I hope that you’re doing well.

I’m doing research on Tyreek. Some of my research here might make its way into a Labs article, but since you’re a fan of the Chiefs and also agile pass catchers who go overlooked I thought this stuff might interest you.

As an athlete, he seems like he’s at least De’Anthony Thomas‘ equal on the basis of their pro day performances. He’s faster, bigger, more agile, and more explosive.

His college production at Western Alabama sucked in his final season, but 1) he scored touchdowns four different ways (receiving, rushing, and punt and kick returning), and 2) we shouldn’t expect much considering that he joined the team as the season was starting.

As a junior, in his first year at Oklahoma State, he was a great change-of-pace and third-down back who also had three return touchdowns. If he had stayed at OK St., he probably would’ve been a 1,000-yard player. Maybe even a 10-TD player. [Note: His 815-yard campaign in 2014 was impressive on its own considering that he was in his year of Division I competition.]

As a sophomore at Garden City Community College he was good enough to get a scholarship to OK St. He was the team’s leading rusher and second-leading receiver. In 10 games, he had 110 rushes for 638 yards and five TDs and 35 receptions for 557 yards and six TDs.

As a freshman at Garden City, he played in 11 games. He had just over 1,100 scrimmage yards and scored eight TDs (including a return TD). As a receiving RB, he was outstanding, catching 35 passes for 713 yards and five TDs, good for 22.6 and 27.8 percent of the team’s receiving yards and TDs. [Note: Those receiving percentages are unholy for RBs. They put him in the class of David Johnson, Giovani Bernard, and Brian Westbrook as a collegiate receiving RB — and that’s comparing his freshman season to their best seasons.]

Hill has done little in the preseason, the Chiefs offense probably isn’t a great place for him to try to get a lot of touches, and his best production was at CC. But there’s a chance that he could basically be DAT v.2.0, right?

Let me know if you have any thoughts.

Thanks,
Matt

To which Shawn responded with the following excerpted thoughts:

1. Completely agree.
2. As a player, he’s definitely interesting, and I think he’s going to play a pretty big role right away.
3. There are touches available in that gadget role as there really isn’t a No. 2 at WR.
4. The Chiefs seem to really love him. He appears to be playing well ahead of DAT.
5. He’s basically your Braxton Miller arbitrage guy. [Note: You know Shawn’s OGRV when he busts out the word “arbitrage.”]
6. I wouldn’t be surprised at all if he finishes with more production than Albert Wilson and Chris Conley.
7. Hope all is well. I always get pretty excited when I read a FantasyLabs article and it references Battlestar. Gaius Baltar FTW.

Tyreek Le Freak is absolutely the kind of player you can spot in advance if you’re looking for what’s possible in an upside scenario and not what’s likely on average in all scenarios.

### Putting a Bow on It

Let’s put a bow on this.

Oops, wrong box. You weren’t supposed to see that.

This piece is entitled, “Averages and Frequencies in NFL Scoring.” I’m not sure if that’s the best name for this article, but in it I’ve talked about averages, frequencies, and NFL scoring.

I also mentioned Silver, NNT, HP, BSG, RV, our Trends tools, and a dead musician.

I think we’re done here.

———

The Labyrinthian: 2016, 94

This is the 94th installment of The Labyrinthian, a series dedicated to exploring random fields of knowledge in order to give you unordinary theoretical, philosophical, strategic, and/or often rambling guidance on daily fantasy sports. Consult the introductory piece to the series for further explanation. Previous installments of The Labyrinthian can be accessed via my author page.

### The Holidays Bring Out the Best in People

“I don’t want something I need. I want something I want: Something pretty.”
— Mia

### Some Words, Maybe Some Sentences and Paragraphs

I’m writing this section on Christmas, because what else am I going to do on Christmas? — spend time with family?

Anyway, I just received a Harry Potter wand as a gift. With that wand I’ve magically created some free time, which I’m using to write this piece, which is a holiday gift to you. Lucky you.

It’s been a while since I wrote an actual honest-to-goodness way-too-long I-have-no-idea-how-this-piece-is-going-to-turn-out Labyrinthian.

It’s also been too long since I mentioned Nate Silver and/or Nassim Nicholas Taleb just for the hell of it, so I figured that, since its the holidays, I’d kill two turtledoves with one well-thrown rock-like partridge in a pear tree.

I still have no idea what this piece is about, but neither do you, so at least we’re on the same page.

### This Is About Average — and That Was a Pun

In The Signal and the Noise, Silver has a chapter entitled, “How to Drown in Three Feet of Water.” It’s in part about the danger of averages.

How can averages be dangerous? As Silver points out, it’s possible for a statistician to drown in a river that’s only three feet deep on average.

Averages provide the illusion that subjects under consideration are smoother than they really are. Averages offer the semblance of homogeneity where heterogeneity exists. Averages (when applied poorly) make mountains into well-sized hills.

A person with six fingers on one hand and four fingers on the other still has an average of five fingers per hand. Warren Buffett (~\$75 billion) and his four lowest-paid employees on average have individual net worths of about \$15 billion per person — even though that figure in no way is representative of any of the people in the sample.

And an NFL wide receiver can average 12 fantasy points per game (PPG) even if he has performances of only no more than six and no fewer than 12 points in any game.

### Context is More Important Than Text

Averages — especially raw averages — can hide context. Here’s a screenshot from our Trends tool:

Here we have six quarterbacks averaging 18.9-19.9 DraftKings PPG. If we looked only at their average PPG, we would assume that these QBs are roughly equivalent. They’re not.

That average doesn’t take into account two important factors:

1. Market valuation
2. Standard deviation

By “market valuation,” I mean both site-based pricing and tournament ownership — how platforms value NFL players and how DFS players respond to those valuations in the open market of guaranteed prize pools.

Our proprietary Plus/Minus metric takes into account salary-based production expectations. Within the 18.9-19.9 PPG cohort Dak Prescott is a strong overperformer, and Cam Newton is a relative underperformer. Dak and Cam have almost identical production, but Dak has significantly outproduced his expectations. The context of our Plus/Minus metric reveals the extent to which, though comparable as producers, Dak is clearly superior to Cam as a DFS asset.

And it’s a happy coincidence that Dak, while providing the most site-based value, also provides the most GPP value as the lowest-owned QB of the cohort. If we compare Dak to Ben Roethlisberger, we see that, even though Dak trails Ben in raw PPG, he still provides more GPP value because of his substantially higher Plus/Minus and lower ownership. In those regards — but certainly not in other regards — Dak has been the better GPP play of the two.

### PPG and Plus/Minus

In the best of scenarios, PPG and Plus/Minus are collectively leveraged. If, for instance, a QB has a high PPG but low Plus/Minus (or vice versa) then he has limited utility. If, however, a QB has a high PPG and Plus/Minus in a particular situation, then he pretty much holds the key to the secret garden of DFS.

Roethlisberger at home:

Like Hagrid, Roethlisberger is a keeper of the keys.

### Way Too Many People Die While I’m Writing These Pieces

It’s now Christmas evening, and I just saw on Twitter that George Michael died. Prince died earlier this year while I was writing a Labyrinthian. And now half of Wham!

This is just another reminder of what Taleb highlighted in The Black Swan: Sometimes turkeys die when they least expect it.

### Frequency, Consistency, Etc.

In addition to ignoring market valuation, a focus on averages tends to obscure “standard deviation,” by which I mean that when we pay attention to averages we can risk ignoring the larger range of outcomes.

Within our Player Models, we have metrics that measure Consistency as well as the frequency with which players submit upside or dud performances. In determining Consistency, we calculate how often players reach their salary-based expectations.

In some ways, Consistency is more important than PPG. For cash games, what we tend to care about is not necessarily how many points a player scores but how much/often we can depend on him to score enough points to reach the cash line. In this scenario, volatility is not a virtue.

### Position-Specific Consistency

Even Consistency — the contextual metric for PPG and Plus/Minus — deserves context.

Here are the core FantasyLabs metrics for the top-five DK players in seasonal PPG at each position:

As you see, among elite NFL players DK Consistency varies greatly depending on position.

RBs are highly consistent, while pass catchers are less so, all of which makes sense: RBs are easier to project. Their per-game opportunities are more reliable. WRs and TEs in comparison are more volatile. Their targets are more dependent on context.

And on the topic of volatility . . .

### Another Random Section

Much of what Taleb talks about in The Black Swan can be boiled down to the concept of volatility. When people focus on the averages, they overlook the possibility or impact of volatility.

Averages can hide the Black Swan-ness of isolated data points within a larger sample. Averages can camouflage outliers, making Shakespeare into nothing but a collection of plays averaging about 22,600 words per text.

Averages hide the extremes.

At FantasyLabs we think of upside and dud performances in terms of (relative) extremes. If a player has a 60 percent Upside Rating, that means in half of his games (over a specified period of time) he has exceeded his salary-based expectations by at least one-half of a standard deviation. For Dud Rating, we look for performances that fell short of expectations by half a standard deviation.

For cash games a high Consistency is desirable. For GPPs, Consistency is fine but high and frequent volatility is better.

### Tavon Revisited

Earlier this year, I wrote about how GPP upside lies on the periphery, a fact that explains how Tavon Austin could be a player with GPP-winning potential despite being perhaps the NFL’s worst ‘real No. 1 WR’ in 2015 and scoring fewer DK PPG than the punchline that is Rueben Randle (11.73 vs. 11.59).

He was priced down on DK for much of the year and largely ignored in GPPs . . .

. . . but, despite finishing as the WR43 with 11.59 PPG, Tavon scored 10 touchdowns on the season and had four games in which he more than doubled his salary-based point expectation.

Most people — or the ‘average person’ — would see that Tavon finished WR43 in PPG and assume that he had been a boom-or-bust WR3/4. That’s bullshit. He was a WR1 . . . 25 percent of the time.

### Tyreek Hill Explained

As I’m writing this, the Christmas evening Broncos-Chiefs game is ending. What a surprise! — Hill scored another TD!

When a guy scores 11 TDs in 15 games, his production isn’t entirely fluky. He might be on the extreme end of his range of outcomes — especially if he has only 76 targets, 21 rushes, and 52 returns — but he’s almost certainly a talented player.

And Hill’s not just talented. He’s volatile: This guy’s a wide receiver who has no receptions on eight targets over the last two games  . . . and he’s still scored a TD in each game.

With certain players — especially versatile players whose teams are committed to giving them touches in high-leverage situations — the question isn’t, “How many points does he average?” The question is, “How frequently does he score enough points to make an outsized difference?”

How often can he be a Black Swan?

### An Email

I’m lucky enough on occasion to exchange emails with Shawn Siegele, the RotoViz writer who pioneered the Zero RB strategy. Here’s an email I sent him on Aug. 22 (I’ve edited so that it’s tighter. [I’ve redacted about 50 F-bombs.]):

Hey Shawn,

I hope that you’re doing well.

I’m doing research on Tyreek. Some of my research here might make its way into a Labs article, but since you’re a fan of the Chiefs and also agile pass catchers who go overlooked I thought this stuff might interest you.

As an athlete, he seems like he’s at least De’Anthony Thomas‘ equal on the basis of their pro day performances. He’s faster, bigger, more agile, and more explosive.

His college production at Western Alabama sucked in his final season, but 1) he scored touchdowns four different ways (receiving, rushing, and punt and kick returning), and 2) we shouldn’t expect much considering that he joined the team as the season was starting.

As a junior, in his first year at Oklahoma State, he was a great change-of-pace and third-down back who also had three return touchdowns. If he had stayed at OK St., he probably would’ve been a 1,000-yard player. Maybe even a 10-TD player. [Note: His 815-yard campaign in 2014 was impressive on its own considering that he was in his year of Division I competition.]

As a sophomore at Garden City Community College he was good enough to get a scholarship to OK St. He was the team’s leading rusher and second-leading receiver. In 10 games, he had 110 rushes for 638 yards and five TDs and 35 receptions for 557 yards and six TDs.

As a freshman at Garden City, he played in 11 games. He had just over 1,100 scrimmage yards and scored eight TDs (including a return TD). As a receiving RB, he was outstanding, catching 35 passes for 713 yards and five TDs, good for 22.6 and 27.8 percent of the team’s receiving yards and TDs. [Note: Those receiving percentages are unholy for RBs. They put him in the class of David Johnson, Giovani Bernard, and Brian Westbrook as a collegiate receiving RB — and that’s comparing his freshman season to their best seasons.]

Hill has done little in the preseason, the Chiefs offense probably isn’t a great place for him to try to get a lot of touches, and his best production was at CC. But there’s a chance that he could basically be DAT v.2.0, right?

Let me know if you have any thoughts.

Thanks,
Matt

To which Shawn responded with the following excerpted thoughts:

1. Completely agree.
2. As a player, he’s definitely interesting, and I think he’s going to play a pretty big role right away.
3. There are touches available in that gadget role as there really isn’t a No. 2 at WR.
4. The Chiefs seem to really love him. He appears to be playing well ahead of DAT.
5. He’s basically your Braxton Miller arbitrage guy. [Note: You know Shawn’s OGRV when he busts out the word “arbitrage.”]
6. I wouldn’t be surprised at all if he finishes with more production than Albert Wilson and Chris Conley.
7. Hope all is well. I always get pretty excited when I read a FantasyLabs article and it references Battlestar. Gaius Baltar FTW.

Tyreek Le Freak is absolutely the kind of player you can spot in advance if you’re looking for what’s possible in an upside scenario and not what’s likely on average in all scenarios.

### Putting a Bow on It

Let’s put a bow on this.

Oops, wrong box. You weren’t supposed to see that.

This piece is entitled, “Averages and Frequencies in NFL Scoring.” I’m not sure if that’s the best name for this article, but in it I’ve talked about averages, frequencies, and NFL scoring.

I also mentioned Silver, NNT, HP, BSG, RV, our Trends tools, and a dead musician.

I think we’re done here.

———

The Labyrinthian: 2016, 94

This is the 94th installment of The Labyrinthian, a series dedicated to exploring random fields of knowledge in order to give you unordinary theoretical, philosophical, strategic, and/or often rambling guidance on daily fantasy sports. Consult the introductory piece to the series for further explanation. Previous installments of The Labyrinthian can be accessed via my author page.