# Is Trading Down a “Free Lunch”?

While it seems like many people are coming around to the idea that the Eagles should trade down, I figured I’d provide an exercise that illustrates why trading down (but not too far!) is the best option.

First, remember that I previously posted the historical success rates for picks 1-5, 6-10, and 11-15, finding very little difference in the odds (though there are definitely positional differences).  That itself is pretty good evidence for trading down if there is not a single high-quality prospect at a position of great need.

Now let’s play a probability game that will get us to the same place, albeit with a different route.

Suppose I placed three \$1 bills and one \$20 bill in a hat and asked you and three of your friends to take turns picking one bill (blindly).  The goal, of course, is to select the \$20 bill.  Would you want to choose 1st, 2nd, 3rd, or 4th?

The answer might be obvious for those of you familiar with probabilities, but I’m going to run through the math anyway:

1st Choice: 1 out of 4 chance; 25%

2nd Choice: 75% chance the \$20 is still there, 1 of 3 chance you select it (75/3) or 25%

3rd Choice: 50% chance the \$20 is still there, 1 of 2 chance you select it (50/2) or 25%

4th Choice: 25% chance the \$20 is still there, if it is you get it, so 25%

So which turn would you want?  It doesn’t matter!  Your odds of getting the \$20 are the same, regardless of whether you choose 1st, 2nd, 3rd, or 4th.

However, I’m betting there’s almost nobody that (prior to reading) chose to pick 4th.

Why is that?

I don’t know, and it could be the result of a number of factors. Perhaps you all actually did choose to pick 4th and I’m way off base, but I really doubt that.  Maybe there is some “participation premium” by which having the opportunity to actually “pick” a bill is assigned a slightly higher value than just receiving whatever is left over.  Maybe we can get really existential and say that there’s something inside all of us that prefers to have some “control” (i.e. getting a choice of bills), even when it’s not real.

Regardless, the odds remain the same, and the reasoning doesn’t matter to us.

Applying it to the Draft

Obviously, the above game is not a perfect representation of the NFL draft.  There are multiple “\$20s” in every draft, as well as a much wider selection of values in general.  Also, teams are not picking blind, they know which prospect they are selecting (which would ruin the game above).

However, in particular cases (this draft being one), I think the \$20 game is a useful metaphor.  In the game, we know the values but are choosing blindly.  In the draft, we know who we are choosing but don’t know the true values.  While on the surface it’s a bit different, in reality the outcomes remain similar.

So at pick #4, let’s say the Eagles are choosing between Eric Fisher, Dee Milliner, Star Lotulelei, and Dion Jordan.

Which one is the “elite” player?  Is there more than one?  Are there none?  I’m sure everyone has an opinion, but how sure are you?  They’ve all received very similar scouting grades and ratings (when looking at a multiple sources).

Note: I’m ignoring positional differences here because all four of those players would fill a need for the Eagles.

I would argue that, while they are all likely to be good players, I have NO IDEA who will be the “best”.  I could take a guess and write a very compelling essay for why “my guy” is so clearly better than everyone else.  Or I can just admit that projecting player success is an INCREDIBLY hard thing to do and impossible to do perfectly.  In fact, the professional scouts have already tried to do that, and came up with VERY SIMILAR SCORES.

This is a similar point to the one I made in “The Bad GM Theory” post, and one I’ve likely made several times before that.  Let other teams pay a premium for “false control”.  In a draft with so many prospects grouped so closely together, let’s just admit that we don’t know, with any certainty, which is best.

Look back at the \$20 game and pretend you have the first pick.  Do you take that pick? or do you trade it to the guy picking 4th, who is willing to give you \$2 as payment for switching?

Trade down a few picks, take whatever compensation is available, and let someone else “choose first”.  Our odds of success will be the same, and we’ll pick up and extra pick or two in the process.

Please note that this only holds because we are looking at a tightly packed group of prospects.  Also, you might be saying, this is no different from the normal case for trading down, one that has been made many times before.

Let me finish by clearing that up.  The normal case for trading down is that “we want more picks” and “we’ll still get a good player”.  What I’m saying here is that our odds of getting the BEST PLAYER are no different at #4 than at #7 or #8.  So we can pick up those extra picks and NOT LOSE ANYTHING.

This year, at least, trading down does indeed offer a “free lunch”, and why would you ever turn that down?