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# How the NHL Draft Lottery odds are totally screwing the Philadelphia Flyers

It’s probably not a vast NHL conspiracy against the Flyers, but hey ... we can never be too sure.

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We all know that the NHL is specifically rigged against our team, the Flyers. But now, we have definitive proof. A huge thanks to Micah @IneffectiveMath for bringing this issue to my attention.

Let’s talk about the math of the NHL Draft Lottery, which will be held on April 29. There’s a nice explanation of how it works on hockeyviz.com, but I’ll cover the important points. If you don’t care about math, feel free to skip to the end of this piece, or even share it without reading. Just make sure you’re mad about it.

You may recall that last year, the Maple Leafs had a 20% chance to win the first overall pick, followed by the Oilers’ 13.50% chance, the Canucks’ 11.5% chance, etc. This year, due to the addition of the Vegas Golden Knights, the NHL has to modify some things about their lottery odds.

According to expansion draft rules, Vegas gets the same odds as the third-worst team, which is Arizona this year. So, Vegas has an 11.5% chance of winning the draft lottery.

But that’s added in with the rest of the teams, so the probabilities now sum to 111.5%. As we know, having 111.5% of anything is only mathematically possible if it’s the amount of effort that a player puts into a hockey game.

So we must divide every team’s probability by 111.5% to rescale things, which slightly hurts every team’s chances across the board.

### Rescaled NHL Draft Lottery odds to accommodate Las Vegas

NHL Rank Team P(1st Pick) Rescaled
NHL Rank Team P(1st Pick) Rescaled
30 Avalanche 20% 17.94%
29 Canucks 13.50% 12.11%
28 Coyotes 11.50% 10.31%
N/A Golden Knights 11.50% 10.31%
27 Devils 9.50% 8.52%
26 Sabres 8.50% 7.62%
25 Red Wings 7.50% 6.73%
24 Stars 6.50% 5.83%
23 Panthers 6% 5.38%
22 Kings 5% 4.48%
21 Hurricanes 3.50% 3.14%
20 Jets 3% 2.69%
19 Flyers 2.50% 2.24%
18 Lightning 2% 1.79%
17 Islanders 1% 0.90%
Total 111.50% 100.00%

Now, the NHL has a problem, because they don’t just randomize the draft lottery by putting the probabilities into a computer program. They like to televise it, after all.

Here’s a detailed explanation of the process from 2015, but the gist is pretty simple: They draw 4 numbered balls from a lottery machine that holds 14 balls in total. There are 1,001 possible combinations of balls — they’re picking 4 out of 14 balls without replacement, or 14 choose 4. In the past, 1,000 of those combinations were allocated randomly to teams, and the last one was discarded.

Using 2016 as an example, the last place Maple Leafs had a 20% chance of winning, which amounted to 200 winning combinations. If the Flyers finished 19th during the 2015-16 season, they would’ve had a 2.5% chance, or 25 combinations. But they were busy being in the playoffs, and I was busy watching them play hockey instead of writing articles like this one.

So the NHL has to give each team their share of winning ball combinations based on the new probabilities that include Vegas. But these rescaled probabilities present a challenge if you want to use the same lottery system, because you can’t have fractions of balls. Therefore, the probability percentages have to be rounded to the nearest tenth, because 0.10% of 1000 combinations = one whole combination.

The Flyers’ chances go from 2.242% to 2.2%, which implies 22 winning combinations in total. This seems unimportant because many other teams are slightly hurt by rounding as well, but the Flyers lose 0.042%, which is the most out of any team. Still, everything that’s been calculated so far is very reasonable.

But now this starts to get interesting (relatively speaking). Rounding hurts more than it helps in terms of team probabilities, and the new rounded probabilities sum to 99.8%. That’s 99.8% x 1,000 = 998 ball combinations for the lottery process that have been accounted for.

There are two left that need to be allocated to teams or tossed aside. What happens to those combinations?

There are a couple of ways to intuitively deal with this issue. You could give the extra combinations to the worst teams, this year’s Avalanche and Canucks. Maybe even give both combinations to the Avs because of how uniquely awful they were.

Alternatively, you could give the extras to the teams that are penalized most by rounding their win probability. That would be the Flyers and Hurricanes. Remember that giving an extra combination to a team is equivalent to giving them a .10% higher chance of landing the first overall pick.

### How rounding impacts the NHL Draft Lottery odds

NHL Rank Team P(1st Pick, Rescaled) Rounded Rounding Effect
NHL Rank Team P(1st Pick, Rescaled) Rounded Rounding Effect
19 Flyers 2.24% 2.20% -0.04%
21 Hurricanes 3.14% 3.10% -0.04%
30 Avalanche 17.94% 17.90% -0.04%
24 Stars 5.83% 5.80% -0.03%
25 Red Wings 6.73% 6.70% -0.03%
26 Sabres 7.62% 7.60% -0.02%
27 Devils 8.52% 8.50% -0.02%
28 Coyotes 10.31% 10.30% -0.01%
28 Golden Knights 10.31% 10.30% -0.01%
29 Canucks 12.11% 12.10% -0.01%
17 Islanders 0.90% 0.90% 0.00%
18 Lightning 1.79% 1.80% 0.01%
20 Jets 2.69% 2.70% 0.01%
22 Kings 4.48% 4.50% 0.02%
23 Panthers 5.38% 5.40% 0.02%
Total 100.00% 99.80% -0.20%

As it turns out, we already have an answer from the NHL on how they’ll handle this.

Look at the table below and compare the rounded probabilities we just calculated to the actual probabilities listed in this article. They look the same, right?

But there are two teams with differences: the Hurricanes and the Avalanche. Their probabilities are .10% higher than we expected. That means one extra combination each, so now all 1,000 combinations are accounted for.

### The actual 2017 NHL Draft Lottery odds

NHL Rank Team P(1st Pick, Rescaled) Rounded Actual Rounding Effect Total Effect
NHL Rank Team P(1st Pick, Rescaled) Rounded Actual Rounding Effect Total Effect
19 Flyers 2.24% 2.20% 2.20% -0.04% -0.04%
21 Hurricanes 3.14% 3.10% 3.20% -0.04% 0.06%
30 Avalanche 17.94% 17.90% 18.00% -0.04% 0.06%
24 Stars 5.83% 5.80% 5.80% -0.03% -0.03%
25 Red Wings 6.73% 6.70% 6.70% -0.03% -0.03%
26 Sabres 7.62% 7.60% 7.60% -0.02% -0.02%
27 Devils 8.52% 8.50% 8.50% -0.02% -0.02%
28 Coyotes 10.31% 10.30% 10.30% -0.01% -0.01%
28 Golden Knights 10.31% 10.30% 10.30% -0.01% -0.01%
29 Canucks 12.11% 12.10% 12.10% -0.01% -0.01%
17 Islanders 0.90% 0.90% 0.90% 0.00% 0.00%
18 Lightning 1.79% 1.80% 1.80% 0.01% 0.01%
20 Jets 2.69% 2.70% 2.70% 0.01% 0.01%
22 Kings 4.48% 4.50% 4.50% 0.02% 0.02%
23 Panthers 5.38% 5.40% 5.40% 0.02% 0.02%
Total 100.00% 99.80% 100.00% -0.20% 0.00%

But why did the Canes and Avs get the extra combinations? I don’t have the answer to this question, I’m seriously asking.

Could it be random? Sure, but I have an easier time believing there’s a systematic and highly-effective NHL conspiracy against the Flyers. I mean, the NHL has two extra combinations to allocate and they’re given to the teams right below the Flyers in terms of being unfairly penalized due to rounding.

A potential 0.10% difference in probabilities isn’t huge, but it isn’t nothing, and we have no explanation for this discrepancy.

This isn’t some secretive rigging operation that I happened to witness. Every article I’ve linked to is freely available on NHL.com. The evidence is clear, and the math doesn’t lie. So what’s the deal? Where’s the Flyers’ extra combination?

Maybe it’s a typo. Either way: your move, NHL.

***

By the way, long-time reader, first-time writer. Feel free to ask me questions on Twitter and/or check out some of my less conspiracy-based work at Hockey Graphs.