# Is The US Open Cup Draw Really Random?

Yesterday US Soccer announced the 1st round draw for the Lamar Hunt U.S. Open Cup - a process that US Soccer says, “throughout the entire tournament will be determined by random selection.” Interestingly, clubs representing the NPSL and USASA were only awarded 2 home matches to 16 away matches, or one home match for each body. This means that out of 8 coin tosses in which the NPSL (or USASA) clubs were involved, only 1 flip ended in a favorable outcome (where ‘favorable outcome’ = hosting the match). As a function of the binomial probability distribution, there is approximately a 3.125% chance that 7 out of 8 flips would end in an unfavorable outcome.

The calculation assumes the following:

1. The number of trials or ‘flips’ is fixed. In this case, we will fix the number of flips at 8 to represent the 8 flips NPSL clubs would have been involved in. We will use to represent the number of trials.

2. There are only 2 possible outcomes which are equally weighted: hosting or travelling.

3. The probability of hosting is fixed. We will use p to represent the probability of hosting and will assign it a value of .5.

4. The flips must be independent. This condition is satisfied as each flip is a separate and unique event, independent of previous or successive flips.

Binomial Probability Distribution

When we input the data, the formula looks like this:

And thus we get a probability of 3.125% that only 1 NPSL team would be awarded hosting privileges out of 8 total possible hosting scenarios. Using the same equation, we can calculate the binomial probability of the outcomes for both NPSL and USASA clubs combined which is approximately 0.0018310546875 or .183%.

At 3% the result is highly unlikely, but I can give US Soccer the benefit of the doubt. At .183% the probability is just too small to blindly consider coincidence.

Now, many have already argued that the draw is fair the way it turned out as priority seems to have been given (mostly) to USL Pro and PDL clubs. The rationale is that these clubs generally have better facilities, better front offices, and more professional organizations as a whole - facts which at this point are hard to dispute (with some obvious exceptions). If this were the basis of awarding hosting rights, I would buy the draw. The issue is that US Soccer has stated that the draw was to be ‘determined by random selection’ - something that is shown above to have a highly unlikely probability.

Conspiracy theorists aside, maybe its time for US Soccer to live stream the draw live? This would at least introduce a little transparency into the process, and maybe even give a boost to tournament interest. What are you’re thoughts?