While sitting around and philosophizing, as I normally do on Tuesday mornings, I began to wonder about the correlation between a previous season’s success versus the following season’s expectations. In common terms, I was wondering, “If the Cubs finished 2009 with a winning percentage of .516, what bearing does that have on 2010?”

My basic assumption was that there would be no correlation. It seems as though baseball – perhaps more than any other sport – allows teams to turnaround rapidly and, likewise, collapse instantly (see the Tampa Bay Rays, circa 2008, or the Chicago Cubs, circa 1877*); but still, I want to see if there was statistical proof of my suspicion.

So, I decided to perform a simple, linear regression on the Chicago Cubs entire history. Using the W% of each season since 1876 (oldest active team in history, b—ches!!!), I would create two buckets: Season 0 and Season +1. The first buckt (my X axis, Season 0) would be the W% of each season from 1876 to 2008. Bucket two (the Y axis, Season +1) included all of the seasons from the rough 1877 to the disappointing 2009. I deliberately paired Season +1 with its preceding season (e.g. 2008 was my X, 2009 my Y) and then placed these into an ancient Regression Device used by Celtic heathens of the Roman era (I also did this in Excel and got the same results).

The Cubs history creates this scatter plot (sorry they look cruddy; I'm not at my computer):

And this equation:

(Next Season) = 0.2172 + 0.5835 x (Last Season)

However, as I stated before, I wanted to know the strength of correlation, not the angle of it. Not-surprisingly, R-squared was 0.317 – in other words, the previous season’s success explains about 31.7%, or a third, of the next season’s potential. But, before I could whisper the incantation to silence the Runic Regression Spirits, I became fascinated with the aforementioned formula. So, I threw a few more teams (other really old teams; the Red Sox, the Braves, and Dodgers) into the Regression Device and got a similar result:

(Next Season) = 0.2010 + 0.6099 x (Last Season)

When done individually, each teams’ histories created regression lines that crossed .500 simultaneously on both the Y and X axis, indicating (as the formula above does) that there was a central tendency towards a .500.

Observe the Master Regression’s scatter plot (which actually features an exponential regression line, but bear with me):

Take note of how the line guides us back to .500! Pretend we just finished an amazing .800 season! Now draw your greasy finger along the monitor, until you’ve traced the distance from .800 on the X axis to the regression line. If you smear your way to the Y axis, we discover that expect to finish at .700 in the following year – how depressing! Likewise, a .300 season (heaven forbid!) portends a following .400 season (heaven, still forbid it!).

Conclusion
So, using an ancient Regression Device, we have established:

1) there is very little correlation in success between seasons (likely because of roster turnover),
2) there is, however, a central tendency towards a .500 record (success eventually follows failure, and vice versa),
3) and there is apparently no way to silence the Runic Regression Spirits, and I now have F-stats where my eyes once were.

Concerning point number 2, I should make it vivid that, while we expect an .800 season would be tough to follow, it is not impossible. Frankly, it’s very possible (in a statistical sense) for the Cubs to win 110 games in 2010 and then repeat in that incredible act in 2011. Of course, it would require Michael Jordan-esque magic before we could start talking about a five-peat and six-peat, polish sausage.

What should we, as fans, take away from this little exercise? Simply that we cannot assume the previous year’s shortcomings or successes signify the coming year's potential – we must remember that, as the Spring Training motto goes, “hope springs eternal.”

[*That was a rough year for me.]

-Bradley Woodrum

Brad also writes for Cubs Stats. His email address is available through his Blogger profile.