Howdy Field Gulls, it's been a while! I hope you've enjoyed yourself while I took a brief hiatus to work on other personal projects. The last time I wrote, I predicted a sound 34-24 Seahawks victory. Wrong as I was, I continue to happily listen to Queen.

Luckily for my dearth of writing, post Super Bowl football coverage tends to slow down. Free agency is fun, but what interests me more is the NFL Draft.

In previous years, I enjoyed perusing mock drafts to familiarize myself with prospects and learn more about the draft process through thoughtful articles. If you haven't had the chance, I would recommend reading Davis Hsu's articles on Ted Thompson's draft tendencies here.

Reading articles like Davis' always make me dream of the ideal draft day for the Seahawks. So it is with great curiosity that I ask, what's your ideal draft scenario? (And be reasonable...)

Thought it out? Mine would be to trade down from the first round and select Joel Bitonio, and then draft a defensive pass rusher. Why trade down? If you read Davis' article you would note how successful trading down has helped make Green Bay (and others). That history alone is enough to convince me that trading down is ideal, but considering how deep this draft is, trading down would net even more talent than typical drafts.

#### The Question

If trading down sounds good to you too, then the next logical question I would ask is this: how likely are the Seahawks to trade down?

When I thought about this question yesterday, the answer seemed pretty simple to find. All I needed to do was look through past trades, determine how many were for 32 (moving down), and do some division from the number of trades.

Using Pro Sports Transaction's draft trade history tool, I was able to look through the past five years of trades with a focus on pick 32. Of all the trades that took place, none included pick 32. In fact, you have to go back to 2006 to even find a trade that involves the 32^{nd} pick. That year, the Steelers traded up from the 32^{nd} spot, not down. I kept looking through previous years and I gave up before I found team that had traded down from 32.

Given that no team has traded down from 32 in the last five years (and longer), it would be easy to say that the probability of the Seahawks trading down this year is 0. After all, if there have been no trades for the 32^{nd} pick in recent years, then it would stand to reason that the pick has undesirable attributes. For example, it's a first rounder, but in name only. Perhaps picks surrounding the 32^{nd} are filled by teams who wouldn't want to trade with the (likely) Super Bowl winner. There are plenty of reasons why the 32^{nd} pick consistently stays put, but I don't think this 0 probability is quite accurate.

*At this point, I won't mind if you skip down to the results section. I'll try to explain the methodology well, but it might not work.

#### The Methodology

Instead, to calculate the probability of the 32^{nd} pick being traded (down), we have to think about the draft picks as on-off switches. Instead of trying to calculate the probability of trading the 32^{nd} pick with some complex combinatorics set-up (more on that later), we simply look at each pick and tag it as "traded" or "not traded."

It looks like this:

Once we've created that binary chart, we can add more detail. We add things like who started with the pick and who ended with the pick. So for example, when the Seahawks traded down with the Eagles in 2012 (from 12 to 15, and some other draft compensation), we would code both those picks as "traded" or in the chart above as a 1.

Because it takes two to tango, most trades will switch two picks into the traded category. If we were just looking at the first round, and the Seahawks-Eagles trade was the only trade, then we could say that the probability of trading the 12^{th} or the 15^{th} was about 6.25% (2/32, or 1/16) for future drafts. For when a player is traded for a pick, like Roy Williams for the Cowboy's first rounder in 2009, we'll only count one spot as being traded. Similarly, multiple transactions can lead to an odd number of spots landing in the traded category. For example, the Eagles traded down twice in one draft. They went from 17 to 19 to 21. In the end, that would count as three traded picks, not four. After we've tallied the number of spots defined as traded, we can then simply divide the number of traded spots that we want by the number of total spots. Because we're looking at five years and we're focusing on the first 45 picks, we'll end up with 225 total trade spots.

That's the basic gist of how we're going to define probability for this problem. Those reading closely might notice that the above methodology would still yield a 0% probability for the 32^{nd} pick because the pick was still never traded. To address that problem, what we'll do is cut the draft up into buckets, or as I'll call them (because I'm the fancy writer) talent plateaus.

A talent plateau is simply a collection of picks that would reflect similar value based on the talent usually available. Because the difference between pick 31, pick 32 and pick 33 are all minimal. It stands to reason that when one of those picks are traded, the determination the trading partner is making is relatively random. That is, when a team wants to trade up from say, 40, whether they end up trying to trade for 31, 32, or 33 is fairly random based on which players are still available. In other words, the fact that the 32nd pick hasn't been traded in the past, doesn't mean that it's impossible. It may just be due to chance that it wasn't selected in its talent plateau by a team looking to trade up a few spots.

Speaking of talent plateaus, the first talent plateau contains the first five picks. These are the guys who have some combination of on-field production, outrageous talent, and positional value. Some aspects, like elite talent, are weighted more than others, but the gap between the first few picks isn't enormous.

The drop off to the next plateau is pretty large, however. These players have some concerns: competition level, production, talent. Whatever the case, these players aren't quite as risk free as the first plateau. I'm defining this plateau as the 6^{th} to 15^{th} pick.

The next plateau is the 16^{th} pick to the 25^{th} pick and from there it's the 26^{th} to 35^{th} and the 36^{th} to the 45^{th}. I stopped after that, because at that point, there's really very little chance that the Seahawks (or any other team) would trade down (I haven't seen it happen yet or anything close).

Once we've created these plateaus, we can determine how often a trade occurs between them and the relative frequencies and percentages.

Below is the chart of frequencies. First, recall that each trade eats up two spots (unless the trade was for a player) so to find the number of trades between rounds simply divide each bracket number by two.

To read the chart, start with your first plateau, then follow a colored line to another plateau to find the frequency of trades between them. In the case of the first plateau, there were two traded spots (or one trade) within the plateau. That's when Cleveland moved down to pick 4 from pick 3 and it's represented by the vertical line that does not extend to any other plateau. There were 6 trade spots between the first plateau and the second. Lastly, there were also two traded spots (again, one trade) between the first plateau and the third. Each plateau will only have lines of the same color, so the green lines represent when the first plateau trades down.

Because we're interested in the 32^{nd} pick, we're only interested in the 4^{th} plateau trading with itself, or with the fifth plateau (the purple lines). In the last five years, we have 18 spots being exchanged. Because we're looking at 225 drafts spots in total (45 spots x 5 years), we simply divide 18 by 225. That comes out to 8% exactly.

#### The Result

So are we there? Have we figured out the Seahawks probability of successfully trading down?

Sorry, but not quite. While using talent plateaus are helpful, the method we used is still a bit simplistic and flawed. It's not bad, but it's not great either.

This whole article has been operating under the assumption that previous experiences can be generalized to predict future outcomes. That is, the past history of the draft can help us predict the outcomes this year or in the future. Problem is, with small sample sizes and the partially subjective nature of drafting, prediction through induction becomes a tough sell (for more see: The Problem of Induction).

Really, to get to the answer we want, the combinatorics I mentioned earlier probably represent a better 'true' probability. The problem is, when we use combinatoric methods to derive the probability we end up dividing a smaller infinity by a larger infinity. There are just simply too many ways that picks can be traded to determine a complete sample space.

Not only that, but we have to look at some subjective scales too. Like, how likely are the Texans to want to trade up given their needs? What about Washington? Looking at the teams immediately after the Seahawks, the Atlanta Falcons stand out as the most likely to trade up (especially given their history). However, the depth of the draft, and the relative weaknesses of their team, make a trade with Atlanta seem unlikely.

Considering that the plateaus we created earlier include some picks that wouldn't work for trading down (the picks before 32), and no team drafting at 32 has traded down in recent history, I'd say that 8% earlier, skews a bit high. If we take a subjective Bayesian approach, we can integrate all the different forms of evidence to converge on a probability. And after evaluating the evidence, **I'd say the Seahawk's chances of trading down are about 2%**. Or about 2% higher than Hamdeen Sabahi's chances in the Egyptian presidential race. Hey-ooh! Egyptian electoral humor for yah!

Of course, when a Teddy Bridgewater drops to 32 and the Browns want him more than anything, I'll be wrong. Until then, I'll just keep hoping Seattle drafts Joel Bitonio.

Take it easy, Field Gulls.

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