Tuesday, January 09, 2007

Today is the 35th anniversary of the ending of the Los Angeles Lakers' 33-game winning streak, the longest winning streak in major American professional team sports. A game-by-game log of that season, from Basketball Reference, is available here, whereas a narrative of the games during the streak, from Sports Illustrated, is available here. To mark the occasion, let's look back at that Laker team, both historically and statistically. First, here's a commemorative team picture that I recently found in my room at my parents' home in Los Angeles:

In retrospect, it's hard to imagine that the 1971-72 Lakers would dominate the NBA the way they did, with their 33-game winning streak, 69-13 regular-season ledger (an NBA record at the time), and relatively easy march through the play-offs (with no series closer than 4-2).

The Lakers had lost the NBA finals in 1968, '69, and '70, and then were eliminated in the next year's Western Conference finals as the Milwaukee Bucks -- a relatively new franchise, now featuring young star center Lew Alcindor (later Kareem Abdul-Jabbar) -- romped to the '71 NBA title.

By the start of the 1971-72 season, then, the Lakers probably would have struck most observers as an over-the-hill team (I'm inferring this after the fact, as I was only 9 years old at the time of the streak and not very sophisticated regarding players' peak performance years). Although center Wilt Chamberlain and guard Jerry West were still productive, years of knee injuries appeared to be catching up with veteran forward Elgin Baylor. The Lakers did have one newcomer who had the potential to breathe new life into the team, Coach Bill Sharman.

According to Charley Rosen's (2005) book about the 1971-72 Lakers, entitled The Pivotal Season, the Lakers started out pretty well, but there was a feeling that Baylor was holding them back. Writes Rosen, "Baylor was selfish and defenseless... There was only one thing for Sharman to do -- arrange a retirement party for Baylor" (p. 97).

(I personally found the book useful for reminding me of key points in the streak, but according to a review at Amazon.com, the book appears to have quite a few factual errors in its details.)

In fact, it was immediately after Baylor's departure that the Lakers began their streak, beating Baltimore 110-106. Along the way, the Lakers surpassed the previous NBA record winning streak -- 20 games, set the year before by none other than Milwaukee -- and the previous pro sport record of 26 straight wins by the 1916 New York (Baseball) Giants.

In addition to being the previous year's NBA champion and holding the previous NBA record winning streak, the ubiquitous Milwaukee Bucks had another place in the story, spanking the visiting Lakers 120-104 on January 9, 1972 to end L.A.'s victory streak at 33 games.

As those of you who are longtime readers of the Hot Hand page know, to estimate the probability of a perfect sequential run, we multiply the probabilities of the individual components (wins). If there were a uniform probability of the Lakers' winning each game (the way a coin always has a .50 probability of being a head), we would raise that probability to the 33rd power.

However, the 33 games in the streak would obviously have varied in their degree of difficulty. To account for this, I adopted a very simple model that pegged the difficulty of each game on whether the Lakers were at home or away and on the opponent's winning percentage from the previous season (the streak occurred early in the 1971-72 season, so same-season record probably wouldn't have added much).

Based on opposing teams' 1970-71 winning percentages, I created four classes of difficulty. The Bucks' .805 percentage put them in a class by themselves, which I called Group A. Six teams' percentages clustered within .537-.634, so I called this Group B. Another five teams' percentages ranged from .439-.512, so they were Group C. Finally, three teams that were first-year expansion franchises in 1970-71 -- Buffalo (later the Clippers), Cleveland, and Portland -- had winning percentages from .183-.354, thus constituting Group D. The Lakers did not play the remaining team, Cincinnati (later Sacramento), during the streak.

Then what I did was assign (assumed) Laker win probabilities to the 33 games based on the following rules:

D opponent at home for Lakers ---> .90
D opponent on the road ---> .85
C opponent at home ---> .80
C on road or B at home ---> .75
B opponent on road ---> .70
A opponent at home ---> .65
A opponent on road ---> .60

I purposely tried to err in the direction of making these probabilities too high, so that the product of the 33 probabilities would not be overly small. For what it's worth, my estimate of the overall probability of the Lakers winning all 33 of the games they did during the streak is...

.0002, or 1 in 5,000.

Consider the following:

*The NBA has been around for about 60 years.

*There are currently 30 NBA teams, and there have been at least 22 teams during the past 30 years.

*For as long as I can remember, each team has played 82 games per season, which creates a lot of theoretical opportunities for a team to start a 33-game winning streak (such a streak could be started after each loss).

Without doing any more math, it looks to me that over the entire history of the NBA, there would probably be several thousand opportunities for such a streak. Thus, the Lakers' streak might not be that far out of line.

Contemporary observers would probably cite travel as a factor for why a team would be unlikely to win 33 straight games today. However, if you look at the '71-'72 Lakers' game-by-game log at one of the above links, you'll see that from December 17-22, they played five games in six nights (including three straight nights), which is not done anymore. In fact, I don't believe the current NBA schedule allows a team to play any more than two nights in a row. And remember the Lakers' aging roster!

Another aspect to look at is the Lakers' margins of victory during the streak. They had one overtime game, December 10 against Phoenix. Other than that, the point differentials were distributed as follows:

*9 games won by 4-9 points
*15 games won by 10-19 points
*5 games won by 20-29 points
*3 games won by 30 or more

[A slight error in these margin-of-victory frequencies was corrected on 1/16/11.]

On the whole, the Lakers' victory margins were pretty healthy, so they may have been able to conserve some energy by blowing away some teams early.

Finally, if you want to see another perspective, I would recommend this piece by Gabe Farkas at Courtside Times. Although Farkas starts out discussing the super-streaky Laker squad, he ultimately uses the 1995-96 season, in which the Chicago Bulls surpassed the '71-'72 Lakers' 69-13 record by going 72-10, for his major analyses.


Gabe Farkas said...

Hi there Dr. Reifman!
Very interesting article about the Lakers' streak. I'm actually considering doing an analysis of the 71-72 season along the same lines of the one I did for the 95-96 season in my article you mention.

It seems to me that a 33-game win streak could theoretically begin after any loss that took place ≤ 49 games into the season (meaning there are ≥ 33 games left). That's roughly 60% of the way into a season. Since, on average, there are 41 losses per-team-per-season, it seems to me that there would be 24.5 opportunities per-team-per-season.

For a league with 22 teams, that's 539 opportunities in a given season. With 30 teams, it goes up to 735 opportunities. Thus, your 1-in-5,000 stat means it could happen about once every 9 seasons or so.

Anyway, it's great to see others doing the same kind of work.

Respectfully yours,
Gabe Farkas

Dan L. said...

I was at one of those games at the Forum.

--Dan L.