Saturday, February 12, 2011


The Cleveland Cavaliers have been having an awful rough time lately (except tonight of course). Before their overtime victory against the Clippers tonight they had lost 26 straight, and 36 of their last 37 games. 26 straight losses ties (but does not exceed) the record for consecutive defeats by a professional sports team, equalling the mid-70's Tampa Bay Buccaneers and the 1889 Washington Capitals. Yet while 26 straight losses seems amazing, I'm maybe more impressed by losing 36 of 37. This is a question that has always bothered me, comparing runs in basketball games or streaks of losses/wins. Is it more impressive to win 3 straight or 4 of 5 ? (3 straight) Or in this case, is it more devastating to lose 26 straight, or 36 of 37? To calculate this, we'll assume the Cavs are the worst team in the league (a safe assumption) and because of that lose 76% of their games.

Odds of losing 26 straight: .00080
Odds of losing 36/37: .00049
Odds of going 9-73 (worst ever): .0027

While losing 26 consecutive games is awfully impressive, it's actually 38% less likely to lose 36 of 37. More amazingly, both of these are significantly rarer that going 9-73. They are marks fitting of a Cleveland team that has the worst power ratings since the 99-00 Clippers, even though they started off 7-9. In another parallel of history it looks like the modern day Cavaliers are just as lost as the 1600s english ones after they've lost their king.

Saturday, February 5, 2011

The Suuuuuper Bowl

Tomorrow is Super Bowl Sunday, a once a year American special. The matchup between Green Bay and Pittsburgh manages to combine two of the best three teams in football (New England just didn't show up against the Jets). In fact, the Packers and the Steelers have been at the top since the very beginning of the season. After week 3 I ran the rankings for the first time. Number 1 was Pittsburgh, number 3 was Green Bay. Both teams were among the four that spent time on top throughout the season.
Weeks 3-6: Pittsburgh
Weeks 7-9: Tennessee
Weeks 10-13: Green Bay
Weeks 14-17: New England
Okay, I don't understand Tennessee either (some mid season turmoil really threw them off), but the other three numbers ones showcased the power of predictive systems.

Points line for the game gives the following prediction:
Green Bay 22 Pittsburgh 21
The expected total points is 42.76, and the expected differential is 1.43. By the rankings system the Packers have a 52.4 percent chance of winning, but with a little twist we can also calculate the chance of victory. Calculating the game score standard deviation (and adding in uncertainty on each team's value) then averaging the two we get the expected standard error for the super bowl is 11.50 points. Importantly, it's much larger than the expected differential. A z score of .124 means the Packers should win 54.9% of the time. Interestingly, with a line of 3 for the Packers, that means there's a 55.5% chance that the Steelers cover (umm, still not endorsing gambling no matter how good the Prediction Tracker thinks I'd be). Actually though, even with the 1.43 number there's a high degree of uncertainty because each team's rating has an error of about 2.5. On the whole what it all means is that we have two of the absolute best teams in football, and picking the winner might as well be a coin flip. It's gonna be a good game.

Thursday, February 3, 2011

The Greatest Regular Season

At the beginning of this year there was a lot of talk about the Heat or even the Lakers challenging the Bulls 72-10 record. Only the surprising Spurs are left to even give it a run and they look like they'll probably end up short. How special were the 1995-96 Bulls of my childhood? How do they compare to other regular season teams? Fortunately we can use some of the random chance methods to find this all out in sports specific way.
In the NFL the better team wins about 79% of the time. That chance that the best team ends up 16-0 (like the 2007 New England Patriots) is just .79^16, or 2.3% of the time.
In the MLB and NBA we resort to a binomial distribution, with the mean and standard deviation being determined again by variance analysis (MLB wins 60%, NBA wins 77%).
In the NBA the best team then averages 63.1 wins, with a standard deviation of 3.8. In the MLB the average is 97.2, with a standard deviation of 6.2. That gives us the following probabilities for some all time great teams.

1906 Chicago Cubs (116-32): <.0001
2001 Seattle Mariners (116-42): .0014
1995-96 Chicago Bulls (72-10): .0102
2007 New England Patriots (16-0): .0230
1985 Chicago Bears (15-1): .1147
(Remember, this is the probability the best team in a season achieves this record)

A couple things clearly stand out here. First, Chicago teams are the best, but we knew that already. Second, baseball records clearly stand out more. There may be an increased variance in baseball, but it also might have to do with having effectively two leagues and over 100 seasons already. Finally, some records that appeared very impressive turn out not to be so. We should expect 16-0 teams every 40 years or so. Heck, even 72-10 is definitely repeatable. As Cubs fans all over would tell despairing teams (correctly in 1906) just wait 'til next year.

Wednesday, February 2, 2011

Challenging A Comfortable Margin

A little while back I wrote about A Comfortable Margin, what score differential is safe in basketball. It turns out it's not a point per minute as I thought when I was young, but actually 6*n^.5 where n is the number of minutes left. My dad and I met a challenge though last Friday at the Warriors-Bobcats game (on a side note, this game proved that all NBA games are exciting. Two bad teams and we had a great time cheering for Stephen Curry and laughing at Kwame Brown's free throws). With 1:46 left in the game Curry hit a 3 to put the Warriors up 8. I called it the game winner. (106/60)^.5*6 is 7.97, and 8 is barely bigger than that so I was right with my call. Nonetheless, Stephen Jackson mounted a furious comeback, sinking 3 free throws with .6 seconds left to send the game to over time where the Bobcats won. The lesson here is not that the margin isn't comfortable, it's that somebody needs to tell Monta Ellis that being comfortable doesn't mean he can miss his free throws and commit terrible fouls.