# Dynasty, in Practice: Power Laws. (They're Not What They Sound Like.)

Examining the distribution of player performance and making another case for concentrating value.

In this week’s Dynasty, in Theory, I talked about the value of concentrating production into fewer roster spots. I looked at the question from a ceteris paribus standpoint. (Ceteris paribus just means “all else being equal”, but I figure if I say it in Latin it sounds more like I know what I’m talking about.)

That’s cool from an abstract conceptual standpoint, but not directly applicable to the real world. (Side note: the preceding sentence is pretty much the unofficial motto of “Dynasty, in Theory”.) The reason why it’s not directly applicable is because of the way production is distributed in the real world. So let’s talk about how production is distributed and why “all else being equal” isn’t necessarily the best framework from which to view concentration.

Also, since this is tangentially related to our dynasty value charts, let’s take a look at those while we’re at it and discuss using them as guidelines in determining trade value.

## Skewing the Distribution

Anyone who has taken a statistics course, (and perhaps most who have not), is going to be familiar with the phrase “normal distribution”. Or perhaps they’d recognize it better under its pseudonym, the “bell curve”, so named because they’re… ummm… curves that vaguely resemble bells.

Many aspects of life take on a bell curve shape when plotted out. Height, for instance, is normally distributed. Most people cluster very tightly around the average. The further from average you get, the fewer people you will find. The average American man is 5’10” tall, which means you’ll meet a lot of guys who are 5’8” or 6’0”, and very few guys who are 6’6” or 5’2”.

However, it’s not at all abnormal for distributions to take a different shape. In fact, there are rather a lot of different shapes a distribution can take. Some of them have relatively uninteresting names, such as the poisson distribution, which aimed for something awesome-sounding and overshot it by just one “s”.

For today, though, we’re going to concern ourselves with the intriguingly-named “power-law distribution”. Power-laws sound like some sort of mechanism by which to secure dynastic succession, but when talking about data, they really just mean something highly skewed, with a small number of very high values and a large number of relatively low values.

If that description sounds familiar, it’s because it should. Fantasy performances follow a power-law distribution. If you look, for instance, at the top running back seasons in history, you will find one season with over 400 points, seven seasons with 350-400 points, 27 seasons with 300-350 points, 97 seasons with 250-300 points, 225 seasons with 200-250 points, 532 seasons with 150-200 points, and 1057 seasons with 100-150 points.

As a result, going back to the two hypothetical teams proposed in this week’s Dynasty, in Theory, it should be several orders of magnitude harder to find a 25 ppg RB and a 5 ppg RB than it is to find a pair of 15 ppg RBs.

Let’s say we look at things based not on raw production, but on where that production ranks. Instead of comparing a pair of RBs who score 25/5 with a pair that score 15/15, let’s compare a team with the #1 and #24 running backs to one with the #12 and #13 running backs. Our good friend Mr. Power-Law tells us we should expect the former combo to outscore the latter. Is that what we see?

In 2014, in standard scoring, the #1/#24 combo did indeed outscore the #12/#13 combo… by a whopping 77 points! In fact, the #1 running back scored almost as many points as the #12 and #13 running backs all by himself, (304.1 to 348.2). You could have paired the #1 running back with the #73 running back— Juwan Thompson, a 4th-string back on the Denver Broncos— and the pair still would have scored more points than the #12/#13 combo.

Was 2014 an aberration? Not really. In 2013, the #1 and #58 running back would have outscored the #12 and #13. In 2012, the #1 and #61 backs would have carried the day. In 2011, it would have taken the #1 and #53 backs. In the most extreme example, in LaDainian Tomlinson’s record-setting 2006 season, he actually outscored the #12 and #13 backs all by himself by 55.4 fantasy points.

This is why “all else being equal” doesn’t really apply to real-world situations. A top fantasy performer and a scrub off the street will not perform as well as two solid fantasy options. Instead, the “stud and dud” combo will usually outscore the solid performers straight up. Which is just one more reason why teams should be chasing studs and concentrating value as much as possible.

## Power Laws and Value Charts

This power-law distribution is why I think value charts are so valuable. Simple ordinal rankings give no clue as to the scale of the differences. If you asked the average fantasy owner whether they’d rather have the #1 and #40 running backs or the #12 and #13 running backs, I’d wager the overwhelming majority would prefer the latter pair.

But take a moment to look at the values in the PPR Scoring, Balanced Approach chart from this week. In terms of combined EVoB and EVoS, the gap between the #1 dynasty receiver, (Julio Jones), and the #5 dynasty receiver, (Antonio Brown), is about as large as the gap between the #5 receiver and the #20 receiver, (Brandon Marshall). “Small” shifts of just one or two spots at the top of the chart are as meaningful as massive differences of 20 or 30 spots further down the board.

(As an aside: “combined EVoB / EVoS” is what is used to sort the chart, but it’s not always the most appropriate comparison of player value. If you compare just based on EVoB, then the gap between the #1 and #5 receivers is about as large as the gap between the #5 and #17/18 receivers. Still quite a substantial difference.)

This realization carries with it two philosophical implications. The first is just further reinforcing the importance of concentrating value and acquiring “studs”. The second is an interesting takeaway for how we should be spending our time and effort.

Part of submitting rankings is exposing them to questions and criticisms. Those questions and criticisms are a vital part of improving the product and making sure we're not missing anything. But I find that the majority of the questions I receive tend to focus on the bottom of my rankings. I’ll often get people asking why I have someone ranked 30th at his position instead of 50th, or 50th instead of 30th.

The simple— but unsatisfactory!— answer is that I don’t spend nearly as much time on the bottom of my rankings as I do on the top. I view that as a useful optimization. In one of my earliest articles for Footballguys, I wrote about how time was a limited resource and one of the key skills in fantasy football is being able to deploy it where it will do the most good.

The more complex— but equally unsatisfactory!— answer is that a 20-spot difference at the bottom of my rankings is barely any difference at all. Which isn’t to say that we shouldn’t still want to get it right, it’s to say that the guy ranked 50th might be as close to the guy ranked 30th as the guy ranked 5th is to the guy ranked 3rd. Ordinal rankings magnify differences at the bottom and minimize differences at the top, but these distortions are merely illusory.

## One Last Note on the Value Charts

There’s one last note I wanted to make about using the value charts as a trading tool, and I didn’t know where else to mention it, so I figured I’d place it here.

It’s nearly impossible to make a trade value chart that is universally applicable in dynasty, simply because the market varies so much from league to league. There is no position where this is more true than at quarterback. I feel comfortable that the values I’m assigning to the quarterbacks are accurate in terms of what kind of production they will provide over baseline and average starters. (If I were not, I would not be publishing them.)

This doesn’t mean that I feel those values are a perfect reflection of the quarterbacks’ trade value. You see, when comparing a quarterback and a running back who both give you 50 points over an average starter, we must also consider the opportunity cost of acquiring an average starter!

Here’s a simple illustration: let’s say that I’m well below replacement level at both quarterback and running back, and I want to upgrade both positions. I’m attempting to gain a 50 EVoS starter at one position and a perfectly average starter at the other. Whichever combination I get, (50 EVoS QB / 0 EVoS RB or 0 EVoS QB / 50 EVoS RB), will improve my team by the exact same amount. I should therefore be willing to pay exactly as much to acquire one combo as I would be to acquire the other.

If I can get the average starter at quarterback for a 3rd round pick, while the average starter at running back would cost a 1st round pick, then that impacts how much I’m willing to pay for the 50 EVoS starter at each position. Because my league devalues quarterbacks so much, I am not willing to pay as much to acquire as 50 EVoS quarterback as I am to acquire a 50 EVoS running back.

So just because I have Cam Newton over A.J. Green in my Balanced PPR value chart does not mean I would trade A.J. Green to acquire Cam Newton. It means if I played in a perfectly optimal league where everyone valued quarterbacks appropriately, I would make that trade. But I must also recognize that almost all leagues devalue quarterbacks to one degree or another, and incorporate that realization into my trade valuations.

There’s no one-size-fits-all solution to this problem. Nobody can know your league’s history and preferences except for you. So that would be a good place to start- take a look at what quarterbacks have typically cost in trade, and use that as a starting point.

There’s another useful trick you can do to ensure you aren’t going overboard on quarterbacks just because the chart says the value is there. When trading for a new quarterback, subtract from his value the value of the best quarterback currently on your roster. If the combined EVoB/EVoS of Cam Newton is 559.1, and your current best quarterback is Andy Dalton with a combined value of 102.6, then Newton is upgrading the position by 456.5 points- a value more on par with Emmanuel Sanders at receiver than A.J. Green.

The trick also works well at the tight end position, especially in leagues where you’re only going to be starting one. It’s less important at running back and wide receiver, though, given the higher rate of injuries and the ability to start multiple players every week. It’s less likely that you’re going to be forced to leave quality running backs or wide receivers on your bench than it is you’ll be forced to do so at quarterback or tight end.

In the end, though, this is just a helpful starting point. It’s important that you still mitigate the values with some consideration for the opportunity cost inherent at each position. At quarterback, it’s less compelling to pay a premium for a top-tier performer when mid-tier performers are often available so cheaply.