49ers: Lucky or Good? Mathematician Weighs In

Categories: Science, Sports
In Dallas, they attribute this to luck. Still.
San Francisco 49ers fans still in search or a silver lining, take heed: Rather than be blinded with science, embrace it!

Matt Lane, an S.F. native and alumnus of University High, is now a doctoral student in mathematics at UCLA. On his Math Goes Pop! blog, he recently pondered whether the 49ers were lucky this season, or good.

Lane's first analysis concerned the team's luck.

He did this by juxtaposing the quality of the team's opposition in its putrid 2010 season with this year's scintillating campaign. The 49ers didn't play a monster schedule this year: The team's opposition won 115 games and lost 141, for a .449 winning percentage. Other than New Orleans, that's the worst opposing win percentage in the NFL.

In 2010, the team's opponents went 125-131 (.488) -- middle of the pack in the league. Of course, Lane notes, there is a dangling factor here: Teams in 2010 had the benefit of playing a lousy 49ers squad. Teams in 2011 did not. The record of one's opponents is not outside of a team's control; it's no coincidence the very worst teams in the league faced opponents with the collectively highest winning percentages. Teams playing the St. Louis Rams went 151-105 (.590) -- largely because they had the benefit of playing the abysmal Rams at least once this season.

Lane helpfully factors out head-to-head matchups for both the 2010 and 2011 seasons. And while the 49ers' schedule is still closer to creampuff than thistle, the differences between strength-of-schedule from season to season are arguably negligible. Since the difference between 2010 and 2011 was far from negligible for the 49ers' win sheet, Lane argues the team's progress had more to do with actual improvements than a crap schedule.

Part II of this football-related foray into mathematics analyzes the team's skill. Lane looks at how the team's performance measured up on the stat sheets by using PossessionPoints, a proprietary system that assigns values based on an offense's ability to keep the ball and score and a defense's ability to take the ball away and prevent scoring -- with more points awarded for late-game heroics.

Lane chart.png

Here's how Lane summarized the above chart:

Offensively and defensively, the 49ers were fairly unremarkable in the 2010 season.  [From 2010 to 2011,] their offensive improvement from 64.00 to 98.55, combined with their defensive improvement from 91.91 to 57.32, gave them a net effect improvement of 69.14, by far the best improvement of any NFL team between these two seasons (the runner up is Carolina, whose net effect improved by 45.23).  The offensive improvement was 4th best in the league by this measure, (behind Carolina, Green Bay, and New Orleans), while their defensive improvement was second only to Houston's.

In short, San Francisco got a lot better between '10 and '11. The fan in Lane hopes the team will be even more improved this year.

Conclusion: While it may be better to be lucky than good -- it's best to be both.


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Pretty good. But very lucky.  They had a lot of pieces come together and they had no competition in their own division. That will not be repeated. They will be an 8-8 or 7-9 team in 2012.  You can take that to the bank.  Or your bookie.

Bogy Registrar
Bogy Registrar

 what are you smokin? they have their entire starting defense returning, and on offense everyone is back again as well with just some holes semi-plugged. 8-8 or 7-9 you are trippin....

Big Mig
Big Mig

Interestingly, the NY Giants were pretty lousy in 2011.  Perhaps they peaked at just the right time, or perhaps they got lucky.  Almost surely it's some of both.


Hey Big Mig - it's probably a bit of both.  I actually comment on this at the end of my second post; the Giants surged in the 2011 post-season.  Comparing the PossessionPoints stats over their four post season games vs the regular season, it's like looking at two different teams!

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