7 comments on “Do NFL teams actually use that draft pick chart when trading draft picks?”

Do NFL teams actually use that draft pick chart when trading draft picks?

The 2011 National Football League draft of players is tomorrow, and I was inspired by a really interesting post over on Mr. Honner’s blog regarding the NFL Draft Pick Trade Value chart and exponential decay. The gist is this: somewhere, sometime, someone came up with a chart that assigned a numerical value to every pick in the NFL Draft. I’ll let Mr. Honner describe the chart:

It turns out that football analysts have created a trade value chart that essentially standardizes the value of picks .  For example, a team holding the 7th overall pick, valued at1,500 points, might expect to receive the 21st pick (800 points) and the 26th pick (700 points) in return, were they to trade their pick.  This conventional valuation helps establish fair prices for trades, as it would in any commodities market.

I couldn’t have said it better.

Anyway, Mr. Honner established that the values of the draft picks decay exponentially (for some reason).

Courtesy of mrhonner.com

My questions were these: do NFL teams actually adhere to this chart? And how can we tell? And is there anything this data aggregation can tell us about horse-trading NFL draft picks?

Here’s a link to every draft day trade involving pick-swapping since 1992.

So let’s start putting together for use in a classroom.


NFL Trade Value Chart

Picks trade history

Guiding questions.

  • Do NFL teams follow the chart as accepted value for draft picks?
  • Does this chart relate at all to what happens on the field?
  • Why is there such a quick exponential drop in draft pick value?
  • Do teams that trade for higher picks tend to get better value or teams that trade for lower picks?

Suggested activities

  • First off, finding the exponential decay function that fits the chart could be interesting. Mr. Honner’s thankfully done that for us.
  • Class discussion: how can we tell if teams are following that chart?
  • Lotta data aggregation and manipulation. Excel to the rescue?

Potential Solution

A couple caveats before we begin:

  • The trading data do not show any additional players that were involved in the picks swap. For instance, teams often trade a draft pick for picks + a player. That is not reflected in the data.
  • Oftentimes teams trade future years’ picks. It’s tough to assign a value to that since that particular pick is in flux. For instance, if I trade a 2011 pick for a 2012 first-round pick, I don’t know immediately where that 2012 first-round pick will land. So I threw out all trades involving future picks.

Now onto some solution.

Here’s a terrible-looking spreadsheet I threw together attempting to aggregate the total pick value of both sides of a trade. The team that traded the higher pick is on the left. I called them the “Higher pick trader picks“. I’m not very creative. Conversely, the info on the right is the “Lower pick trader picks.” Each row represents a different trade.

The total value of the team’s picks that traded away the higher pick is listed in the green column. The total value of the other teams’ picks are listed in the purple column. (note: you’ll have to check it out in full-screen or download the document if you really want to see the spreadsheet in its full glory).

If we make a scatterplot of all the trades we can visually see if NFL teams basically follow this trade chart value. If the linear slope is one, then that’s a perfect trading match. That’s what I’ve done here.

Surprisingly, that’s a pretty good fit, meaning for the most part teams roughly adhere to the trade value chart. The slope is nearly one (0.972). A couple of things jump out at me.

Overall, a slope of 0.972 – or, less than one – suggests that the team that trades away the higher pick is getting the better value (this might be a good place to spot and let students ponder as to why this is), presumably in the form of multiple picks.

That said, for the extremely high-value pick trades (where the value of the traded picks exceed 2000), according to the draft chart, the teams that trade away their valuable, high picks are getting less value. Of the 5 trades that involve higher than 2000 points, 4 of them gave the advantage to the team trading away their lower picks. This is due to the extreme top-heaviness of the trade chart. To wit, according to the chart, the #1 overall pick is worth three times the #16 overall pick.

We could also plot the best-fit line as the horizontal axis as a really good visual of the alleged benefit of trading away higher picks in favor of more lower picks.

If we accept the trade chart as true values, then according to history, we have two suggestions for NFL General Managers:

1) In general trade away your higher picks for multiple lower picks.

2) However, DO trade up for extremely high picks (top 5).

You’re welcome, NFL GMs. Make the check out to Emergent Math. And be sure to give Mr. Honner a cut too.

1 comment on “‘What is it your students really do well?’ What “The Three Amigos” can teach us about Project Based Learning”

‘What is it your students really do well?’ What “The Three Amigos” can teach us about Project Based Learning

What is it your students really do well?

For those that aren’t intimately familiar with the classic ¡The Three Amigos!, as I am, this scene takes place as the villainous (and infamous) El Guapo and his henchmen are riding horseback to destroy the village of Santa Poco. Outmanned and outgunned, the people of Santa Poco are presumably defenseless against El Guapo’s legion. Lucky Day (played by Steve Martin) and the other two amigos arrive at the village to warn them.

What a great model of Project Based Learning (PBL). Join me as we glean a plethora of PBL truths from ¡The Three Amigos!.


Lucky Day: El Guapo is on his way.

Create an Exciting Entry Event.

A typical terrible Entry Document from one of my classes.

In this case, the entry document is a simple statement of fact: El Guapo is on his way. That’s all it took to develop a motivation in the people of Santa Poco. More than that: it creates an impending deadline of action. Recently, Julia gave a great webinar on creating an exciting entry event. What could be more exciting than the impending destruction of your town? Personally, too often my entry events were form letters from fake corporations which outlined exactly what the students would be doing and exactly what the students would be learning. In fact, I just ended up calling them “Entry Documents” because that’s all they were: documents that I typed up. Is it fair to ask students to develop interesting, dynamic projects when I won’t develop an interesting, dynamic Entry Event?

Looking back, they often weren’t particularly motivating and were much to constraining. A good Entry Event sets up the scenario, promotes student questioning, and, above all, motivates.


Carmen: Someday the people of this village will have to face El Guapo. We might as well do it now!

Lucky Day: In a way, all of us have an El Guapo to face someday. For some, shyness might be their El Guapo. For others, a lack of education might be their El Guapo. For us, El Guapo is a big dangerous guy who wants to kill us. But as sure as my name is Lucky Day, the people Santa Poco can conquer their own personal El Guapo who also happens to be the actual El Guapo.

Externalize the enemy.

In a traditional classroom, this is often done exclusively in the form of a summative assessment, such as a test, at the end of a unit. Even if you’re able to get away from a solely test-based-assessment, is the primary motivation of students’ in your class a good grade? The rubric? In a Project Based Learning unit, students are expected to overcome an obstacle en route to learning core content knowledge.

One arrow in the quiver of PBL is to “externalize the enemy.” Athletic coaches do a great job of this: it’s in their job description. The “enemy” is the other team. In one week, this enemy is going to come to the field of play and we must develop a strategy to compete. In Three Amigos it’s El Guapo. Even better, Lucky Day (played by Steve Martin) goes on to list several potential El Guapos.

Have you created an El Guapo in your class? Who or what is the externalized enemy? Is it a panel of experts? Or a fellow teacher? Or yourself? While it doesn’t have to be an entirely adversarial creation, an external enemy can motivate students to triumph over a foe.


Man: We want to defend ourselves, but how?

Ned Nederlender: By using the skills and talents of the people of Santa Poco.

…This is not a town of weaklings! You can turn your skills against El Guapo!

…Now, what is it that this town really does well?

[Long pause. Lots of “Hmmmm”s.]

Mama Sanchez: We can sew!

Students develop a strategy problem-solve the Entry Event.

The Three Amigos did not prescribe the methodology of the people of Santa Poco to overcome El Guapo. Rather, they asked the people themselves what they were good at. And even though you would attribute an ability to sew with defeating a squadron of vicious banditos, the Three Amigos helped facilitate the people’s talents to win the day (sorry: spoiler alert!).

It is up to the teacher/facilitator to get students to use their talents, passions, and expertise to overcome the problem put forth in the Entry Event. When’s the last time you asked your students “what is it that this class really does well? Too often, I would prescribe the final product of a project, hemming my students in to the limitation of my own creativity: You must write an article that describes…, you must give a presentation that demonstrates…, etc.

Instead, I should have asked students to develop their own methods and products to solve the Entry Event I gave them. This certainly would have required loosening the reigns a bit – a prerequisite for any PBL facilitator – and I may not have initially gotten the products I was envisioning, but I’m willing to bet the products I did get would be of better quality and more meaningful to my students. I’m sure initially, the Three Amigos would have preferred the townspeople all be skilled marksmen with a cache of invasion-repelling weaponry, but in the end, they utilized their skills – and developed some new ones – en route to success.

Using some of the key tenants of Project Based Learning, the people of Santa Poco, with their unique skills and abilities, were able to problem-solve their way through their exciting Entry Event. Why not let your students do the same?

2 comments on “The Dallas Mavericks are 2-16 in playoff games officiated by Danny Crawford. Is this statistically significant?”

The Dallas Mavericks are 2-16 in playoff games officiated by Danny Crawford. Is this statistically significant?


This shocked me.

The Mavs have a 2-16 record in playoff games officiated by Crawford, including 16 losses in the last 17 games. Dallas is 48-41 in the rest of their playoff games during the ownership tenure of Mark Cuban, who has been fined millions of dollars in the last 11 years for publicly complaining about officiating.

First of all, is that right? That A) the Dallas Mavericks perform so poorly in Crawford-officiated games, and B) Crawford is still being allowed to referee them? Really? Wow.

And there’s this, which might even be more damming: The Mavs are 4-14 against the Vegas spread. ESPN provides a nice chart of the individual games.

I specifically remember those 2006 Finals games against Miami. By many accounts, those were two of the worst officiated games in NBA history, in which Heat guard Dwyane Wade got what seemed to be every favorable foul call. It pretty much ushered in the era of NBA ref scrutiny.

This has to be tested for statistical significance.

Guiding Questions

  • Really?
  • Is this just coincidence or is there something else going on here?
  • Does Crawford have a vendetta against the Mavericks for some reason?
  • Does Crawford have a suspicious record with any other team?
  • Is there a potential way, other than referee malfeasance, that we could explain away this alleged disparity?
  • Maybe the Mavericks are just playoff chokers?

Suggested activities

  • Obviously if this were a statistics course you could look at statistical significance, which we’ll do in a minute.
  • If students are really up for it, they could delve into the games themselves and look for disparities in “referee stuff” like fouls, technicals, travelling, etc. We’re not going to do that in a minute.
  • Homework: students watch tonight’s Mavs-Trailblazers game closely and look for anything fishy from Crawford (although, this might serve as its own lesson in confirmation bias).

Potential Solution

Let’s start with our null hypothesis:

H(o): Danny Crawford is NOT biased against the Mavericks. The Mavericks’ playoffs woes in games he’s officiated is due to random chance.

I suppose first we have to figure out what the Mavericks’ Crawford-officiated games “should be.” The Mavericks are 48-41 in playoff games not officiated by Crawford, good for a winning percentage of 54%. Although, if you’re like me, you believe more in random chance for sporting events, and the “true percentage” is probably pretty much 50% over the course of a decade. But that could be a fun debate point in your class.

We also need to decide on a significance/confidence level α, usually 0.05 or 0.01.

So what is the probability of a team that “should” win 50% of its games (debatable) ending up winning just 2 of 18 games at random? Or rather, that this team should lose 16 (or more) of 18 games by random chance?

A P-Test would could look like this,

Probability of 16 losses + Probability of 17 losses + Probability of 18 losses =



So no matter what confidence level we choose, this is, again, pretty damning. If we assign a 50% of the Mavericks winning (less than for their other playoff winning percentage) there is only a six hundredths of a percent chance of this being total flukiness.

Before we go nuts, though, let’s look back at that chart. Now, if you’re not familiar with Vegas lines, the negative sign in front of the “DAL Line” column indicates the Mavericks were favored that game. You’ll note that Dallas was only favored/expected to win 8 of those 18 games, and Vegas is usually pretty dead-on about these sorts of things. If we use that as a “true winning percentage” the Mavericks would only be expected to win a mere 44% (a losing percentage of 56%) of their games, not 50%. Let’s recalculate.

Slightly less suspicious, but still grievously suspicious. It’s well below our 5% or even 1% confidence level.

Still, before I would get Ralph Nader involved, I would ask students, investigators, etc. to look for specific evidence pattern within the games themselves (as 82games.com has done for one specific game). The original ESPN article that led to this investigation suggested Dallas had more fouls and less free throws in Crawford-officiated games than others. A next step would be to look at the beneficiaries of the suspect officiating, i.e. Dallas’ opponents for these games. Did they get an inordinate amount of free throws? Did they tend to overperform, just as Dallas underperformed in these games. Now that we have the statistical basis to be suspicious, we can start the investigation in full.

Couldn’t this work as a real nice Project Based Learning Unit for statistics? The Entry Event could be the ESPN article, or Game 5 of the 2006 NBA Finals. The summative event could be that students could present their findings, host a panel or debate, or write a letter to their congressperson. Or Ralph Nader.

2 comments on “Can someone help me improve this problem? (U-Haul rental rates ; systems of linear functions)”

Can someone help me improve this problem? (U-Haul rental rates ; systems of linear functions)

So the Emergent Math family moved houses this weekend (editor’s note: they didn’t actually move the houses, they moved the furniture inside the houses). We were given basically three different options for U-Haul rentals of increasing size and increasing price. This led me to believe that a nice systems problem could be constructed from this.

I still feel that way, but it sort of got away from me. I think the idea of deciding whichtruck to rent + various mileage costs is pretty decent. But then things sort of spiraled out of my control and I ended up with a convoluted problem that was actually kind of tedious.

So I’m asking my faithful readership to help me out. I’ve split the problem up into two pieces – as I probably would have in a classroom setting. Help me make this problem better!

Basic gist of the problem:

Moving houses (ed. note: again, just the furniture – the author was not living in a double-wide). Three different U-Haul options of increasing square footage (733, 865, and 1015 cubic feet) with three different up-front costs for the U-Haul ($19.95, $29.95, and $39.95, respectively). Also, mileage costs $0.79 per mile – hence thenice linear functionality of the problem. Determine which U-Haul I should rent.

Documents (Part 1 and 2) below.

Best improvement to the problem gets a free oven mitt!