We have all heard it before: “my team looks like they’re going to win (or lose) every game in the season!” As well as being a notorious goal to achieve in popular NHL-franchise video games. An 82-0-0 regular season record is a fantasy scenario for every hockey fan, though we all acknowledge that it is a physical (and nearly statistical) impossibility.
If you’ve ever wondered what the odds are of a team getting an 82-0-0 record, let me show you some mathematical proof of concept:
Odds of a team winning may increase or decrease depending on injuries, fatigue, streaks, opponents, and a million other intangibles, which is one of the reasons that Vegas odds makers have their hands full on a daily basis. For example, imagine that the Washington Capitals are on a 3-game winning streak, but they’ve lost Braden Holtby to injury in a pre-game practice, lowering their odds of winning. In addition to Holtby’s injury, Alexander Ovechkin has been producing at a 2.00 points-per-game ratio, but he is historically more likely to score more than 2 against their upcoming opponent, improving the Capitals’ odds of winning.
For this thought experiment, let’s imagine that there are three outcomes, each of which are equally likely: win, loss, and overtime loss. This puts the likelihood of each event at 33.3 (repeating) percent. Ignoring all other factors (called variables), the odds of an event for which a probability exists repeating itself is a multiplication of those odds. In plain English, a two-game winning streak (assuming that the odds stay the same) as a function is the probability of winning times the probability of winning, or 33.3 percent squared (which is 11.1 percent).
For every additional game added onto the winning streak, the power of the function increases by one; in essence, a 10-game winning streak is one third to the power of 10. Since we are working with fractions, the numerator (top number) and denominator (bottom number) is multiplied by each subsequent numerator and denominator. We have already assumed that the odds do not change from game to game, so the numerator will always be one and the denominator will always be three. As more and more games are added, the fraction gets smaller and smaller, but never (really) approaching zero: this is called an asymptote, if you were to put it in a Cartesian plane, it would look like a quarter-pipe, with a tall right side and a curve that approaches the horizontal axis but never touches.
The million-dollar question, though, is: under this scenario, what are the exact odds of winning 82 consecutive games? Since we are dealing with a very small number, using scientific notation, the odds are 7.456 x 10 ^ -38. If you were to write this number out, it would look like this: 0.00000000000000000000000000000000000007456 percent. To put it into perspective, an electron’s mass is approximately 9.109 x 10 ^ -31 kg, ten billion times larger of a number than the odds of winning 82 consecutive games.
Real statistics, though, are slightly more forgiving, with teams bumping into the occasional “gimme” games bringing the odds of winning above 50 percent, making the odds astronomically higher (in the order of 10 ^ -23, assuming equal odds of winning and losing), though still considerably small. Elite teams with approximately 70 percent chance of winning on a nightly basis have a 1.986 x 10 ^ -11 percent chance of getting the perfect season. That is, of course, assuming that the odds from game to game remain unchanged. As the hockey season progresses, the odds of a team getting a perfect season would be a dynamic function that incorporates each game individually with all the variables attached, making for a very messy and ugly equation (that, for your own sanity, I recommend not trying at home).
As a note of encouragement, the odds are identical if you are looking at them from a losing perspective, meaning that if we ever see an 82 in any column, the team in question is either incredibly talented, extremely lucky, insanely unlucky, or exceptionally awful.