That First Shot

A few weeks ago Pawpaw observed that in CDFA best-three-of-five contests, the winner of the first match went on to win 62% of the time. How much of that is skill and how much is blind-luck?

First, let's start with the premise that it is all blind-luck. Or, posed another way, there is no measurable difference between contestants and the winner is chosen by noise or random variation in technique. Then, any deviation from the predicted outcome will be a measure of difference between contestants or an artifact of small-numbers.

In a binary contest with five digits, there are 32 sets of outcomes (2^5). Pawpaw already told us we had already run one contest since we "know" who the winner of the first contest is. That means we have 16 possible outcomes (2^4).

Here are the sixteen outcomes. If both shooters are equally skilled then each outcome is equally likely.

But then you point out, "Joe, the contest stops once one of the contestants wins three. Many will not go the entire five rounds."

Geaux Tigers! colors.

With winners shown. We can verify the brute force method by computing the odds for the winner of the first match-up winning the next two matches in straight sets.

Since the odds (if both are equal) is 50% for any given match, then winning two in sequence is 50%-time-50% or 25%. We would expect to see 4-of-16 in the table shown above with shooter #1 winning in three straight...and that is what we see.

So, based on this brute-force analysis, even if both shooters are identical, the winner of the first match has a 9-in-16 chance of winning the best 3-of-5 contest. 9/16 = 56% which is less than 62% but not HUGELY less.

Seeding

Seeding can make results look more or less random. The NCAA basketball tournament seeds weak-to-strong which tends to favor the "predicted" outcomes.

Seeding contestants of like-strength favors an element of random-chance. A relatively weak or new contestant can make a deep run in a tournament and an experienced, skilled contestant can get bounced in the first round.

The conclusion I would draw from this analysis is that the CFDA does a fantastic job "seeding" if their goal is to reward new shooters and to keep the contests fun.