# Category Archives: Probability Analysis

## Why are the hockey playoffs so unpredictable?

The NHL playoffs have many more upsets than the NBA. Adrian the Canadian tells me that this is ruining their product, since the most exciting teams often get unlucky and bow out early. I can’t help but agree — I stopped watching this year after my favorite team (the Red Wings), my local team (the Bruins), and probably the best team (the Penguins) got bounced. The NHL wasn’t always so unpredictable — the Canadiens, Islanders, and Oilers won 13 of 15 cups between 1975-76 and 1989-90. Adrian’s theory is that the the rise of the butterfly goalie has increased save percentages, which makes outcomes more random.

It’s pretty easy to show that increased save percentages do indeed muddy up the result. I generated 1,000 simulated games for three sets of parameters. First, the 1980s (before the butterfly):

• Both teams: 89% save percentage
• Team A: 32 shots per game on average
• Team B: 28 shots per game on average

Then, for the late 90s/early 2000s (butterfly goalies, slightly fewer shots on average perhaps due to popularity of the neutral zone trap): Continue reading

## Sloan Sports research rundown

Following on my general analysis of the Sloan Sports Analytics Conference, here’s a look at the research presentations (you’ll note: nothing on the sports side of football or soccer! I submitted one of each but they were rejected . . . ):

An Expected Goals Model for Evaluating NHL Teams and Players (Brian MacDonald)

This paper tries to predict future performance better by incorporating more measurable statistics than past models (goals, shots, blocked shots, missed shots, hits, faceoff %, etc.). His prediction tests show that he makes improvements, and at the team level, I think these results have some value. However, moving to the individual level in a sport like hockey (or basketball, football, soccer, or rugby) is hard because of complementarities between players. For example, trying to measure one player’s contribution to team wins or goal differential based on the number of shots they take is hopelessly confused with the actions of other players on the ice that affect the quality and number of these shots.

Another issue in the paper is that MacDonald controls for team level statistics (such as faceoff win percentage) in the individual level regressions, when in fact much of player value may be driven by these statistics. For example, one of Red Wing Pavel Datsyuk’s strengths is faceoff win percentage, while one of his weaknesses is hitting. The value that individuals bring through these variables is caught up in MacDonald’s team level control variables. Still, the team-level analysis is a reasonable way to improve what’s out there.

This paper categorizes the top three players on each team Continue reading

“But he’s Canadian,” you say, “So what does he know about baseball?” Well, he’s from Toronto, the team most screwed by the current system, so let’s give it a shot:

A few days ago, the MLB announced that it was expanding its playoffs to include a second wild-card team. Under the new system, the two wild-cards will play a single game that determines who goes to the divisional series. Response has been, at best, mixed. The strongest criticisms, like this one from ESPN’s Joe Sheenan, have taken a traditionalist perspective. Sheenan worries about what this new system will mean for deep-seated, and still exciting, elements of baseball like the pennant race. He sees the wild-card system as debasing what has historically been one of the most exciting parts of being a baseball fan: following your team through a tense September race to win the division. By Sheenan’s estimation, the old system encouraged top teams to play their best throughout the whole season. If you happen to be one of the two best teams in the league by regular season record but can’t win your own division, tough grapes.

I sympathize with Sheenan and other traditionalists. Baseball’s regular season is long and arduous and does a pretty good job of determining the “best” team (or, at least, a better job than other pro-sports at determining the best team). Meanwhile, baseball playoffs, due to the nature of the game, are pretty close to random. As Billy Beane said, “my shit doesn’t work in the playoffs” – seven and five game series are simply too short to give us a good idea as to which team is best. In the 17 post-seasons since the advent of the wild-card, the wild card team has won five times Continue reading

## One more Lin

My buddy Tony and I have been trying to figure out how to quantify Jeremy Lin’s recent five games. He suggested I figure out the likelihood of his start, assuming that Lin is “just” an above average point guard. So, I identified all the point guards who averaged between 16 and 18 points per game in the 2009-10 or 2010-11 season. In 2009-10, that included Devin Harris, Rodney Stuckey, Russell Westbrook, Stephen Curry, Steve Nash, and Tony Parker. In 10-11, the list is Brandon Jennings, Chauncey Billups, Gilbert Arenas (before the suspension), John Wall, Raymond Felton (while with the Knicks), and Tony Parker again.

I collected the game logs for all these guys for the relevant year(s); here’s the histogram of points scored in each game (including playoffs to bump the sample up):

In a total of 832 games, these players scored 30 or more points on 38 separate occasions (this is the total of the last three bars on the right). Likewise, they scored fewer than 5 points in 32 different games. These two tails each capture about 4-5% of the total distribution.

The Thunder and Warriors played a very entertaining game last night. All the stars showed up (Monta Ellis, career high 48 points; Kevin Durant, 33 points, game winning shot, close to a triple double). The defense wasn’t terrible — the Warriors especially made a bunch of tough shots. Close games like this are generally decided by luck, but there were two interesting decision points in the endgame where each team affected the odds:

Down one, should you shoot early or late?

With about 22 seconds left, down one point, the Thunder had Durant drive right to the hoop and go for a quick shot — air ball, but the Warriors knocked it out of bounds. On the next inbounds play, Durant pulled up immediately and banked in a (relatively) open jumper to take the lead with 16 seconds remaining. This gave the Warriors plenty of time for a rebuttal, and the Warriors announcers were confused that the Thunder didn’t run down the clock to take the last shot.

The Thunder clearly wanted to shoot quickly. Did this help or hurt their chances of winning? It gives the Warriors another chance Continue reading

## Are the Patriots truly being punished for their insolence?

The last five years for the Patriots would make many people believe in karma. Since Tom Brady left his baby mama Bridget Moynahan for Gisele and Bill Belichick got caught videotaping other teams’ run throughs, here are the Patriots season results:

• 2007: Crazy late game Super Bowl loss to the underdog Giants
• 2008: Brady tore his ACL early in the season and they missed the playoffs despite going 11-5
• 2009: Brady had a stinker in a first round loss to the Ravens
• 2010: Finished 14-2, but Brady had another stinker in a second round loss to the rival Jets
• 2011: Brady nearly blew it against the Ravens again in the AFC championship game and they sneaked into the Super Bowl, only to suffer another late game loss to the underdog Giants

Gisele continued her negative influence by blaming the loss on drops by the Patriots receivers (only Aaron Hernandez had a truly bad drop, and it was probably too late to matter). The Patriots have 60 wins over the last five years (12 per year), but no rings. If the Patriots go 15-1 next year and get a rematch with a 9-7 Giants team, the Giants will probably be favored. They can’t get past those guys.

Close games are generally decided by luck — Bill Barnwell gets into this at Grantland, but finds himself backtracking almost immediately to avoid angering Giants fans (“The Giants were not lucky to win Super Bowl XLVI because they fumbled twice and fell on both of them.”). There will be no backtracking from me! The Giants were lucky to win (as the Patriots would have been if they had won). Here’s the way the ball bounced Continue reading

## The Celtics take on Howard and win

It was a renaissance in Boston last night. Garnett was draining 20 footers, Paul Pierce was driving and kicking and hitting shots, and Jermaine O’Neal was putting the clamps on Dwight Howard. Everybody hustled. The defensive intensity never lapsed all game. To steal a line from NBA TV studio man Brent Barry, the Celtics’ “Jurassic Five” went prehistoric on the Magic and held them to a franchise-low 56 points. It was their first win over a team with a winning record, by 31 points no less.

Recently, I’ve discussed the efficacy of the hack-a-Howard strategy (or as Celtics TV mainstay Tommy Heinsohn puts it, the old “hack the Shaq”). The short answer is that Howard shoots too well from the line (59% almost every year, though lower so far this year) for a pure hack-a-Howard to be effective for most teams. However, hacking Howard only when he has the ball in good position Continue reading