The statistics of small numbers and the very limited number of goals in a hockey game lead to NHL games being very random. All it takes is one more chance goal to put the Capitals way ahead of the Knights' average. More mathematically speaking, since the sample size of scoring events per game is so low (~4 for hockey and ~100 for basketball), the spread of scores is much broader in hockey games, and it's harder for real differences in ability to manifest above the randomly expected noise. So the underdog Capitals have a much greater chance of winning based only on the points/goals statistics than the underdog Cavaliers.

Biased coins

I loved Michael's analogy of the biased coins, so I'll expand on it a bit to show that the answer doesn't really depend as much as you'd think on how behind each underdog is in points per game. Note in this model we're assuming there are a limited number of scoring opportunities in a game, and the chance either team scores is represented by their relative "point per game" statistic.

As it stands, the Capitals are outscored by about $4.5 \%$ while Cavaliers are outscored by $8 \%$ . Let's make life even harder for the Capitals and say the Knights averaged 3.37 points per game. That would make the Capitals outscored by the exact same $8 \%$ that the Cavaliers get outscored by.

Bringing in the biased coin: You have an unfair coin that has an $8 \%$ higher chance of coming up tails than heads. So $P(\textrm{heads}) = 0.48$ and $P(\textrm{tails}) = 0.52$ . In which scenario would you rather bet on heads, the underdog result? Best of 5 flips of the coin, or best of 100 flips?

Of course you'd rather bet on best of 5 flips. Intuitively we could expect to beat the odds a couple times, but not over many many events.

Distributions

Here's the expected distribution for the number of heads flipped out of 5 for our biased coin (it's the Binomial Distribution ): The odds of heads winning here is about $46 \%$ .

Now the distribution of expected heads out of 100 flips: The odds of heads winning here is about $30 \%$ .

For 1000 flips, the chance of heads coming up ahead is less than $10 \%$ .

When would the Stanley Cup be a sure thing?

Because of the low number of scoring events per game, hockey games are determined a lot more by randomness than by skill differences. Vox had a fun Youtube video about this last year ( Vox video ).

How much higher performing would a hockey team need to be (in this one metric, points per game) to make a hockey game as predictable as the Cavaliers Warriors game? Well, if we use the biased coin model above with an $8 \%$ advantage to model a basketball game, 100 scoring events means the underdog will only win about $30 \%$ of the time. With only 5 scoring events, the advantage would need to be $56 \%$ to have the same underdog win rate, like if the Knights outscored the Capitals 4.5 points per game to 3.1.

Of course, this is a super simplistic view of both games. There is a lot more to it than points per games, including most notably each team's defensive performance. But the point that the low sample size of scoring events in hockey makes the game a bit less predictable based on prior performance remains.

$\frac{109}{101}\approx 1.0792$ so the Cavaliers get outscored by about 8%. $\frac{3.26}{3.12}\approx 1.0449$ so the Capitals only get outscored by about 4.5%. Knowing nothing about the distributions of scores (and how ties are broken in hockey), I figure the Capitals have a better chance.

It's like you have a coin that's biased against heads, say, only 40% chance of coming up heads. Your friend wants to bet even money that you'll get tails. You know you have to play your friend at least once. How many times do you want to keep flipping? If you play it just a few times, you've got a decent chance of coming out ahead, even though it's less than 50% of that happening. If you play a hundred times, you're a sure bet to lose your money. That's how casinos reliably make their money.

The ratio 3.12/3.26 is closer to 1 than 101/109. Therefore the Capitals is more competitive against its rival than Cleveland is to the Warriors. LET`S GO WARRIORS! 😁

Just think about this critically. The point differential between WSH and LVK is much closer than that of GSW and LeBron's Cavalier's. The chance of Washington winning is hugher considering how even both NHL teams are point wise.

This method of course looks at the numbers and doesn't consider factors such as LeBron James's immense skill and the simple fact that Ovechkin will never win a Stanley Cup.

I cheated; as a hockey fan, I already knew the answer. Mauboussin’s Skill-Luck Continuum, based on statistics, explains that hockey introduces more randomness into game results. In hockey language, it’s called “Puck Luck”. Basketball has far less randomness. Read & watch this article & video for the explanation: https://www.vox.com/videos/2017/6/5/15740632/luck-skill-sports

😁👍

Assume all the teams score follow a normal dist N(u, $sigma$ ) ; NBA team always scores above 60 points per game

• by normal dist properties

3s is about equal to 101 - 60 for cavaliers; and 3s is about equal to 3.12 for capitals

s = 13.67 for cavaliers; s = 1.04 for capitals

Then Pr[ Z > (109-101)/13.67 = 0.585] < Pr[ Z > (3.26-3.12)/1.04 = 0.1346]

So Capitals has higher chance than Cavaliers

I went strictly by the percentage difference in scoring...

I find (most of?) the solutions offered here unsatifactory, mainly because they bring in assumptions that were not stated in the problem description (such as assumptions about distributions). Maybe it was not a good problem.

My reasoning was as follows. Considering an average of 3.12 and the fact that all scores are natural numbers, it is clear that this team must have played games with final scores of 4 or more. Similarly, a team with an average of 3.26 must have played games with final scores of 3 or less. Thus, the undrdog here has a fair opportunity to win. For a team with an avrage of 101, for all we know, all their games could end with 101 points. Similarly for an average of 109. Hence, the underdog would have no chance to win.

On the other hand, if the average ot 109 was achieved by 99% of their games ending with 100 points and 1% of them with 1000 points (I know little about basketball :-), then the underdog has a 99% chance of winning. So, without further assumptions, the problem does not seem solvable.

Hochey team have to go throughout shoter adversity, 109/101 = 1.079 = 8% Cavs outscored range. 3.26/3.12= 1.045= 4% Capitals outscored range. This mean they have a better chance to win.

Warriors score 8% more (on average) than Cavs, even when in basketball there are 3 point goals, Cavs would need 3 more triples on average to win over Warrios. On the other hand, Knights score 4% more (on average) than Capitals and provided the fact that both score about 3 goals per game, the Capitals just need 1 goal on average to win over the Knights. Even if we assume that it is "more difficult" to score on hockey, for the overall result of the match, one goal weights more on a hockey game than a goal on a basketball game.

☢️ Too silly solution for the philosophical minds... ☢️ My solution is a really very simple.

As we know the Las Vegas nights and the Golden state Warriors have the better odds to win the Championship in their respective sport.

We can use simply the unitary method Basketball----corresponds to-----Hockey 109-----corresponds to------3.26 101-----corresponds to------3.021

Hence we can see 3.021 is less than 3.12

Hence the probability of winning of Washington capitals is more than the Cleveland Cavaliers.

So Washington capitals are more likely to win their respective Championship.

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