A little Logic and Math for the draft

A cautionary primer on the NFL draft

For the last several years I have used the various draft analysts pre-draft predictions as subject matter in my Critical Thinking and Math Logic classes. Unless the 1st or 2nd picks were announced early, the analysts have done little better than random at placing the correct pick with the correct team in the correct slot. In the slightly easier task of guessing roughly when a player would be selected, they do a bit better in the first and second rounds and then fall apart completely. In other words, it is nearly impossible to make accurate predictions after the first few picks.

Here are a few of the difficulties.

1) Very noisy data. What teams actually think of players and what positions they most want to fill is generally difficult to judge. Further, teams are actively lying.

2) Availability bias. Our opinions are biased by what we know. In low information environments we place too much weight on what we have seen - players from our favorite schools - and discount the vast areas about which we know little or nothing.

3) Weighting. When we hear that a player should go 15-20 or something, this idea colors our thinking. Our opinion of that player will shift towards the 15-20 slot when, without that information, we might have placed them much higher or lower.

4) Confirmation bias. If we like a player for the above reasons, we will tend to remember information that confirms our ideas and forget or discount information that contradicts our ideas. Because we are susceptible to 2 and 3 above, 4 becomes particularly troublesome.

Add to this the permutations prevented by the draft. If we assume that 50 players could conceivable be chosen in the first round - then the possible permutations are 32!/32!(50-32)! This is a very, very large number of possibilities.

Through the magic of Hypergeometric distribution, this works out to be something like a 64% chance to pick one player correctly, 40% chance to pick two players correctly, 25% chance to pick three players and 16% chance to pick four. If you arer curious, there is a 5.5 x10^-14 chance to get all 32, that is what you might call unlikely.

In other words random guessing by a monkey, let's name him Cleveland Browns, should produce one or two correct picks much of the time, three correct occasionally, and rarely more than that. If you pick four correct picks, that is a clear demonstration you are better than our test monkey Mr. Browns.

Now the 2013 draft results looked like this -

Mike Maycock got 6 correct picks - a clearly non-random outcome, but considering the first two picks of Fisher then Joeckel seemed telegraphed, we might count him with four correct picks, still better than Mr. Browns.

Walter Football only got four correct, which is meaningful but not great. Most others like Bucky Brooks etc. did less than four. In other words, predicting actual players to actual teams is really difficult.

However, the relative value of players is usually pretty close. So a player predicted to be in the top five rarely falls too far, and players rated to be in the mid first rarely show up in the second.

Just a cautionary note as we all get very excited by all the possibilities - of which it turns out there are a lot.

And by the way, after the first round, no one does better than Mr Browns.

Hypergeometric progression for those who might be interested.

P(X=k) = (K/k)(N-K/n-k)/(N/n)

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