The NFL has a slotting system that is ever-so-slightly malleable, where a player who gets drafted one spot lower than another player occasionally gets a smidgeon of a better deal. And sometimes a quarterback gets an above-market deal. But position players and non-quarterback skill players are slotted, and despite the efforts of agents to break the slotting system when picked lower than the agent or player thinks he should be picked, the league mostly holds firm.
Andre Smith was an outstanding tackle at Alabama. The Cincinnati Bengals drafted him 6th in the draft last April. Smith and the Bengals can’t seem to agree on how much Smith should make, so I’ll help them out. It’s $8.83 million per year.
There are two unsigned first rounders left. I don’t care about Crabtree for a variety of reasons (#1: He’s from Texas Tech). The Bengals reportedly are offering Smith less than the #7 pick. They think they should pay what’s fair. Smith (and his agent Keels) thinks what’s fair is the long standing tradition of slotting first round picks.
I don’t know much about trend lines. Microsoft says that the best trend line is the one with an R-squared value closest to 1. So I showed the R-squared value (Format Trendline – Options) and tried all of the different kinds. Polynomial was the best one. I could get the R-squared closer to 1 if I increased the “Order”, but I stuck with the default because the line was prettier.
I wanted to show where Smith would end up on that line, but there doesn’t appear to be a way to do that automatically. First I went back into the Options to show the formula so I could compute Smith’s y value. Next, I created a new series that had #NA for every y value except for Smith, where I computed
A28 being where his x value is. Then I made his data marker orange and black.
In conclusion, Cincinnati should offer and Smith should accept $8.83 million per year for 5 or 6 years and let’s get on with playing football.
First — I enjoy this site, but the following line made me scratch my head: “I could get the R-squared closer to 1 if I increased the “Order”, but I stuck with the default because the line was prettier.”
A more accurate line of best fit was dropped because it didn’t look as ‘pretty’? I plotted the same data and a 5th order polynomial trendline, which increased the R^2 value from 0.9143 to 0.9336 (not a huge improvement).
http://dl.getdropbox.com/u/1606162/nfl_slotting_saketvora.jpg
This increased Smith’s estimated salary by 2% from $8.83m/year to $9.006M/year. This is a better reason to opt for the simpler trendline because the forecast doesn’t noticeably change for higher ordered polynomials.
I hate to nitpick here; let’s just promote best practices here.
For further analysis one could sub-segment into position type or try removing some of the weird outliers and recomputing trendlines that way.
thanks,
Saket
Frickin’ awesome post Dick.
Now let’s get on with playing some football!
If we’re talking best practices, let’s dispense with the polynomial fits. Poly fits are usually only good for cosmetic purposes, and not for predictions. Dick’s quadratic fit shows a minimum, with those late draftees on the right of the chart getting increasing contracts for being selected lower. Saket’s fifth order fit not only has the upturn for higher picks, it also has some other unexplained inflections, and the visual fit is not better than Dick’s.
I thought this looked like an inverse relationship (power law) or some kind of exponential decay. I hacked together some data that looked like that in the chart above, and saw that the usual standby fits (power, logarithmic, exponential) don’t provide a single fit for the whole data range, but this isn’t uncommon. Often phenomena can be described by piecewise fits, for example, two power law relationships, one for the high range and one for the low.
If the data were made readily available, as in a CSV file, we could try out fits more rigorously.
Jon Peltier, always the voice of reason! The moment I saw a quadratic fit, I thought – this can’t be right, because at some point the salary will increase with the rank… As an incorrigible data geek myself, I would love to get my hand on the data file and play with it, too! Looking at the shape of the curve, besides the 2 options mentioned already, some logistic / S-curve model could work.
Thanks for the comments. You can get my Excel sheet here: http://dl.getdropbox.com/u/1606162/nfl_draft.xls
Forgive the rough formatting, it was a quick and dirty investigation. The source of the numbers is the same as what was linked in the original article.
– Saket
Just because a higher order polynomial fit has a larger r-squared does not make it a better fit. First, it has to make sense. Does a 5th or a 6th order polynomial make business/engineering/scientific/logical sense? Very doubtful. One expects the contract amount to decrease the later one is picked in a draft, not fluctuate up and down as a high-order polynomial curve would. Given what I know of the trend I would think of a linear, an exponential, or a power fit.
Since there is an underlying reason to believe that QBs are paid differently than the other positions, one should exclude the 3 QBs from the analysis. If one were to plot the remaining data, two trends “jump out.” Positions 2 through 9 are almost in a straight line. Positions 9 through 32 seem to fit a power or an exponential curve.
For 2-9 a linear trendline as a r-squared of 99%. A power trendline for the 9-32 data has a r-squared of 97%.
Using the linear trendline, the 6th pick is worth 8.58 (annualized). The 10th pick is worth 4.95. Using the power trendline, the 10th pick is worth 4.97.
Well done, sir! ::applause::
I would say the above is almost certainly logarithmic. Removing pick 5 and 17 and making a scatter plot of ln(pick) vs ln(salary) produces a linear line with an r-swaured of around 94%.
if you aren’t already convinced that polynomial curve fitting is a bad idea, see http://en.wikipedia.org/wiki/Runge%27s_phenomenon
nflslotting.xls.zip
Where can I find information on which type of trendline to pick? You guys seem to have an idea just by looking at the data, but I don’t.
Dick,
Engineering school? Seriously though, I think it mostly comes with practice. As Tushar said, the type of fit has to make sense for the application. I had a professor who liked to say that with enough adjustable parameters (e.g. a higher-order polynomial fit), you could fit an elephant. His point was that any set of data could be made to look good with the right equation, but it may not make practical sense.
-Josh
Dick –
Over at Jon’s place:
http://peltiertech.com/WordPress/choosing-a-trendline-type/
http://peltiertech.com/WordPress/trendline-fitting-errors/
…mrt
While the ‘fit’ of the trend line can be argued down to the minutiae…bottom line is that the #6 Lardass should get ~$9mil based on relative data available. What is fascinating to me is that the data (pick versus slotting) does not take into effect the extraneous variables (when the picks signed, how long the hold out, amount of weed smoked, etc). Some picks sign right away. Others wait until the domino above them falls…the rest falling in line. After watching ‘Hardknocks’ on HBO, I wonder if the Lardass’ agent takes any of the quantitative data into account with his client. What would really pique my interest is the ‘right’ amount of days to play chicken against the franchise. In other words, there has to be a point of diminishing returns where too much stalling/posturing costs money (for both sides). Given the nature of the business, a good agent should get their client signed and into camp as soon as possible so that their growth accelerates to additional payday sooner on their next contract.
Good points SAR. Let met throw something else into the mix. I heard that the amount of an NFL player’s retirement is a function of how much he makes his first year. You leave a couple of hundred on the table now, it could cost you millions over your lifetime. I can’t find any confirmation of that though.
Watching Hardknocks, I get the feeling that the chick is really f*cking up the negotiations. Is that the way you see it?
From here:
http://blogs.nfl.com/2009/08/30/smith-ends-holdout-signs-deal-with-bengals/
“Andre Smith’s holdout is finally over, ending a month-long standoff with the Bengals. The team announced the sixth overall pick had signed shortly before he was to take the field for his first practice with the Bengals.
“Steve Wyche reports it’s a four-year, $26 million deal that includes $21 million guaranteed, according to a source with knowledge of the situation. The Bengals have an option to extend the contract after the 2010 season, which would make the deal a six-year, $42 million contract with $29.5 million guaranteed. Smith also has incentives that could increase the maximum value of a six-year deal to $50 million.”
Let’s see: $50M/6yr = $8.33M/yr
Not having Dick as his agent cost Smith $3M! :roll:
…mrt
And Smith broke his foot yesterday!