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Fun with Numbers: How Not to Project Playoff Probabilities

The top story on the Toronto Star's website today was the ominous-sounding "Leafs chances of getting to playoffs? 1.7%." This 1.7% figure comes from, which runs Monte Carlo simulations of the NHL season to determine how many times the Leafs will make the playoffs. And according to Dave Feschuk, who authored the column, that makes sense. After all:

"You don't need to think too much to know the Leafs are abysmal. They're 29th in the 30-team league standings. They're 125-1 Las Vegas long shots to win the Stanley Cup, the second-longest odds on the board behind the 150-1 Islanders."

Sounds about right so far? Let's look at the Leafs and the Islanders a little more closely:

Team Cup Odds Playoff Odds
Odds of Winning the Cup
if they make the Playoffs
New York Islanders 0.67% (1/150) 43% 1.6%
Toronto Maple Leafs 0.8% (1/125) 1.7% 47.1%

The odds of each team making the playoffs comes from, while the odds of winning the cup comes from the Vegas lines that Feschuk mentions.

Think about that for a moment. Professional gamblers think the Leafs have the second-lowest odds to win the cup. But if we assume the 1.7% figure from Sportsclubstats is correct, then if the Leafs were somehow able to squeak in to the last playoff spot this season, they would be the favorite to win the Stanley Cup. By a wide margin. They'd have a 90% chance of beating Pittsburgh in a 7-game series. So they're both the worst team in the league...and by far the best.

What Sportsclubstats and Feschuk are both missing in their analysis is a little thing that I spend way too much time yammering on about called "regression to the mean." For example, when the Leafs had a seven-game winless streak to start the season, I found that past teams that started out similarly had made the playoffs 29% of the time. But Sportsclubstats had their playoff odds at just 8.2% that day. However bad these seven-game losers were, Sportsclubstats thinks they're way, way worse.

Sportsclubstats may use a sophisticated algorithm to look at strength-of-schedule, but when it determines a team's expected winning percentage, it does nothing more than look at goals for and against. But as Jonathan Willis pointed out quite succinctly, early season extremes never stay extreme. If you want to estimate a team's chance of making the playoffs this early in the season, you have to take its current record and regress very heavily to the mean. And, in the case of Toronto, who have outshot their opponents and have been without their presumptive #1 goaltender for much of the season, you should probably expect them to play over .500 hockey the rest of the way.

But it's nicer to think that the Leafs have just a 1-in-60 chance of making the playoffs, isn't it? Because then you "don't need to think too much" and you can just beat up on Brian Burke for being such a crappy GM.

Oh, and if anybody out there wants to give me the Leafs at 60-1 to make the playoffs, I'll take it.