Mindfreak: The odds of finding four starters in the draft

Brian Xanders and John Elway have both said they want to come away with four starters from the 2011 Draft.

It's certainly an ambitious goal, and one appreciates Xanders and Elway setting the bar so high without resorting to meaningless slogans.

But is it likely?

Earlier in the week, Dave Krieger took a shot at pointing out how difficult a task Xanders and Elway have in front of them.  His conclusion?

Optimism, naivete and, let's be honest, pure fantasy are always in unlimited supply around the NFL draft.

Kreiger based his conclusion on some decent evidence--namely, that Mike Shanahan and Josh McDaniels had limited draft success.

What do the numbers actually show us?  Is Krieger correct?

The probability of drafting four 3-year starters

The first thing we'll need to decide is how to define our starters.  For the purpose of this analysis, I'll assume Xanders and Elway aren't drafting players to start for one year, but rather an extended period.  Thus, I'll use 3-year starters as the benchmark.  It makes sense, given that the average NFL career is slightly longer than three years (so we are told).

Using a little dash of probability theory and twenty years of draft research provided by Tony Villiotti at Draftmetrics, we can determine the probability of Xanders and Elway succeeding.

Villiotti´s excellent research into the draft of every team shows the following percentage chances that a player drafted in the following positions will either become at least a 1-, 3-, or 5-year starter in the NFL:

Draft Positions 1-13 14-28 29-48 49-74 75-114 115-200 201+
Observations/Picks 260 300 400 520 800 1720 1235
1-year starter percentages 93.80% 88.70% 76.00% 63.70% 45.90% 30.00% 16.10%
3-year starter percentages 74.60% 60.70% 55.00% 39.80% 23.60% 14.10% 7.40%
5-year starter percentages 53.50% 42.70% 35.30% 23.70% 14.60% 7.20% 4.00%

Using this base data, we can apply the laws of probability to determine the likelihood that the Broncos will have any number of draft picks from this draft start for a 3-year period.  The math required for such calculations isn't difficult.  So that you get the hang of it, I'll provide an easy example.

Let's say we wanted to determine the probability of the Broncos' first four draft picks starting for at least one year.  We would multiply the success rate of the first draft pick by those of the second, third, and fourth choices.  The calculation would be as follows:

0.938 X 0.760 X 0.760 X 0.637 = 0.3451 = 34.51%

So there is just better than a 1/3 chance that we'll see these four draft picks starting at least one year in Denver.

What about 3-year starters in a seven-pick draft?  The calculations become much more complex because the combinations of hitting on at least four draft picks out of seven is large, and because the probability of success changes with each draft pick.  Nevertheless, the data--after seven rounds of calculations and probability tree diagrams-- is as follows:

3-Year Starters  %
Probability (7 Starters) 0.01%
Probability (6 Starters) .39%
Probability (5 Starters) 4.09%
Probability (4 Starters) 20.37%
Probability (3 Starters) 53.03%
Probability (2 Starters) 84.24%
Probability (1 Starter) 97.88%
Probability (0 Starters) 100%

The Broncos' probabilty of drafting four starters (3-year starters) from this draft is just over 20%.  While this means that there is a chance, 80% of the time, it's going to be silver and black and eyepatches.

As Krieger correctly surmised, Xanders and Elway have their work cut out for them.  Let's hope Xanders is a draft savant in sheep's clothing.   

Does the fact that both men are driving the Broncos' shiny new draft car out of the driveway for the first time make you more optimistic?

On the positive side, the Broncos stand a great chance of getting at least two starters from this draft (league average), and slightly greater than a coin flip's chance of plucking three starters.  It's virtually a lock that they will find at least one starter (even if they have to use some confirmation bias to do so!).

Other Probability Questions

Using the same data and the same probability calculations, we can calculate the answers to many other draft-related probability questions.  I'll list a few of them here:

Question: What's the probability that the Broncos will hit on all seven of their picks?

Answer:  Extremely low under every scenario--well below 1%.  

Question: What's the probability that the Broncos find at least one 5-year starter in this draft?

Answer: 87.72%.  They actually stand a 53% chance of getting two 5-year starters as well.

Question:  What's the probability one of these draft picks makes the All-Pro Team at least once in their career?  Or three times?

Answer: There's a 40.53% chance that one of the draft picks makes the All-Pro Team Once.  There's a 12.41% chance at least one of them makes three All-Pros.

Question:  What about the Pro Bowl?  

Answer: There's a 65.02% chance one of these draft picks plays in at least one Pro Bowl.  There's a 32.94% chance at least one of them plays in three Pro Bowls.

Question: What's the most interesting fact you've found from these calculations?

Answer: In a competition of extremes, the Broncos have a greater chance of busting on all seven of their draft picks than they do hitting on all seven.  

Question: Do you get your jollies off drawing probability trees?

Answer: Does Al Davis like to make believe he's a pirate?

I’m glad we had this talk.  Now, vaya con Dios, Brah.

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