Does the NHL's "loser point" help weaker teams?

Back when I calculated that it took 73 NHL games for skill to catch up with luck in the standings, I was surprised it was so high. That's almost a whole season. In MLB, it was less than half a season, and in the NBA, Tango found it was only 14 games, less than one-fifth of the full schedule.

Seventy-three games seemed like that was a lot of luck. Why so much? As it turns out, it was an anomaly -- the NHL was just having an era where differences in team talent were small. Now, it's back under 40 games.

But I didn't know that at the time, so I had a different explanation: it must be the extra point the NHL started giving out for overtime losses. The "loser point," I reasoned, was reducing the importance of team talent, by giving the worse teams more of a chance to catch up to the better teams.

My line of thinking was something like this: 

1. Loser points go disproportionately to worse teams. For team-seasons, there's a correlation of around .4 between negative goal differential (a proxy for team quality) and OTL. So, the loser point helps the worse teams gain ground on the better teams.

2. Adding loser points adds more randomness. When you lose by one goal, whether that goal comes early in the game, or after the third period, is largely a matter of random chance. That adds "when the goals were" luck to the "how many goals there were" luck, which should help mix up the standings more. In fact, as I write this, the Los Angeles Kings have two more wins and three fewer losses than the Chicago Blackhawks. But, because Chicago has five OTL to the Kings' one, they're actually tied in the standings.

But ... now I realize that argument is wrong. And, the conclusion is wrong. It turns out the loser point actually does NOT help competitive balance in the NHL. 

So, what's the flaw in my old argument? 

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I think the answer is: the loser point does affect how compressed the standings get in terms of actual points, but it doesn't have much effect on the *order* of teams. The bottom teams wind up still at the bottom, but (for instance) instead of having only half as many points as the top teams, they have two-thirds as many points.

Here's one way to see that. 

Suppose there's no loser point, so the winner always gets two points and the loser always gets none (even if it was an overtime or shootout loss). 

Now, make a change so the losing team gets a point, but *every time*. In that case, the difference between any two teams gets cut in half, in terms of points -- but the order of teams stays exactly the same. 

The old way, if you won W games, your point total was 2W. Now, it's W+82. Either way, the order of standings stays the same -- it's just that the differences between teams are cut in half, numerically.

It's still true that the "loser point" goes disproportionately to the worse teams -- the 50-32 team gets only 32 loser points, while the 32-50 team gets 50 of them. But that doesn't matter, because those points are never enough to catch up to any other team. 

If you ran the luck vs. skill numbers for the new system compared to the old system, it would work out exactly the same.

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In real life, of course, the losing team doesn't get a point every time: only when it loses in overtime. Last season, that happened in about 11.6 percent of games, league-wide, or about 23.3 percent of losses.

If the loser point happened in *exactly* 23.3 percent of losses, for every team, with no variation, the situation would be the same as before -- the standings would get compressed, but the order wouldn't change. It would be as if, every loss, the loser got an extra 0.233 points. No team could pass any other team, since for every two points it was behind, it only gets 0.233 points to catch up. 

But: what if you assume that it's completely random which losses become overtime losses?  Now, the order can change. A 40-42 team can catch up to a 41-41 team if its losses had randomly included two more overtime losses than its rival. The chance of that happening is helped by the fact that the 40-42 team has one extra loss to try to randomly convert. It needs two random points to catch up, but it starts with a positive expectation of an 0.233 point head start.

If losses became overtime losses in a random way, then, yes, the OTL would make luck more important, and my argument would be correct. But they don't. It turns out that better teams turn losses into OTL much more frequently than worse teams, on a loss-for-loss basis.

Which makes sense. Worse teams' losses are more likely to be blowouts, which means they're less likely to be close losses. That means fewer one-goal losses, proportionately. 

In other words: 

(a) bad teams have more losses, but 
(b) those losses are less likely to result in an OTL. 

Those two forces work in opposite directions. Which is stronger?

Let's run the numbers from last year to find out.

If we just gave two points for a win, and zero for a loss, we'd have: 

SD(observed)=16.47
SD(luck)    = 9.06
SD(talent)  =13.76

But in real life, which includes the OTL, the numbers are

SD(observed)=15.44
SD(luck)    = 8.48
SD(talent)  =12.90

Converting so we can compare luck to talent:

35.5 games until talent=luck (no OTL point)
35.4 games until talent=luck (with OTL point)

It turns out, the two factors almost exactly cancel out! Bad teams have more chances for an OTL point because they lose more -- but those losses are less likely to be OTL almost in exact proportion.

And that's why I was wrong -- why the OTL point doesn't increase competitive balance, or make the standings less predictable. It just makes the NHL *look* more competitive, by making the point differences smaller.