terrible metaphors

[Ed-M: Bumped because this totally punctuated my equilibrium. The best indicator yet of year-to-year defensive evolution. And great news: the mean has magnetism!]

Richard Goldschmidt hypothesized that the incremental changes to organismal phenotypes over the course of even thousands of generations was insufficient to explain the change from one species to another. He posited that evolutionary change is powered by great leaps forward, instances of saltatory mutation that generate a new species from the old. Goldschmidt’s ideas were ridiculed, mostly, and with good reason. The overwhelming evidence of population genetics and the theoretical triumph of the Neo-Darwinian synthesis seem to indicate that evolutionary change is effected gradually over time by the additive effects of allele substitutions in the genetic makeup of a given population; population change happens slowly, if at all.

But there are situations in which sudden changes to an organism’s ecological niche—a new predator or prey introduced, migration or population bottlenecks, climate change, a massive meteor falling from the sky and killing all the dinosaurs—opens up the opportunity for rapid (on the geological time scale) evolutionary change.

The defense was bad last year. And bad the year before. And the year before that. A number of reasons have been put forward for the awfulness. The defense was decimated. Really decimated. Seriously, it was decimated. GERG is a force of nature complete with his own effect. The coaches thought making in-game adjustments was tantamount to cheating. And so on. At the risk of overstraining the metaphor, it certainly felt as if we were watching the extinction of that species of animal previously known as the Wolverine defense. It’s at the very least an endangered species. But if the combination of the addition of Hoke and Mattison, Nebraska joining the BIG, and the tattoo-laden implosion of the 614 area code don’t count as a change in the environment that opens the possibility of rapid change, then my metaphor has no validity at all.*

Folks have tried to take a stab at what might happen this year, based on small sample sized studies of returning starters, even smaller sample sized bits of anecdotal evidence, and a healthy dose of Hoke-A-Mania! I collected data from http://www.cfbstats.com/ on total defense numbers from 2006 through 2010 and analyzed year to year changes for every team, based on total defense rankings. Even though I’ve got five years of data, I’m going to talk in terms of “Base year” and “Year 2;” since I wasn’t looking to find multi-year trends in defensive performance all I care about is the movement from one year to the next. So with five years of data I have four years (2006-2009) worth of data in my “Base year” set and four years (2007-2010) in my “Year 2” set

This diary doesn’t propose to do anything other than aggregate a little bit of data about what we can expect based on very recent history and to show how many teams over the last few years have been outliers. From there we can start to see what Michigan’s chances are of bucking the odds of Darwinian uniformitarianism.

Natura non facit saltum: The Case For Phyletic Gradualism

My first task was to look at the aggregated data on a very coarse grain. I wondered how much movement there was in rank from year to year, so I grouped teams into sets of ten based on their base year finish (top ten teams, teams 11-20, etc.) and then tracked where those clusters of teams finished on average in year 2.

The result:

So the 40 teams in the data set that finished in the top ten in the base year averaged a finish at around 20 year 2. If a team finished in the 111-120 rank range, they could expect to be at around 95 in year 2. The obvious thing that jumps out is regression at the two ends of the line. This suggests what should be obvious: it is difficult to sustain excellence or ineptitude. So, by staying terrible last year, Michigan is already an outlier. Yay? But as you move away from the ends of the line, the movement away from the base year gets less and less, so that teams that are average appear to stay average.

Then, since I care mostly about one of the teams at the gruesome end of the line, I looked more closely at teams that finished the base year in the 90-120 range, and got this for my troubles:

This looks at every spot in the ranking from 90 to 120 and plots the year 2 average for the teams that finished at each of those spots. There is a lot of noise here, because for each ranking spot there are only four data points, but the trend line is pretty much what we’d expect. The worse you are in the base year, the worse you can expect to be in year 2.

So the numbers look gloomy, suggesting that expecting much movement in one year is a recipe for disappointment. These numbers provide the baseline for the geological timescale. The pace of change appears to be slow.

Hopeful Monsters: The Case for Saltationism

Despite this evidence of evolutionary stasis there have been a number of teams who’ve managed macromutation from one year to the next, both up and down. Since 2006, 37 teams out of a possible 278 (obviously only teams ranked 51 or worse could possibly make a 50 spot leap) have managed a leap of 50 or more spots in the ranking from one year to the next, and 107 out of 378 possible have made jumps of 25 or more spots.

	Macromutation	Micromutation	Population size	Percentage
50 spot leap	37	243	278	13.3%
25 spot leap	107	273	378	28.3%

For what it's worth, these percentages are higher than I expected prior to compiling the numbers. It's not worth anything, by the way.

My original goal was to analyze the factors that these saltatory leaps might have in common, but finding reliable data on returning starters, experience, changes to coaches or defensive co-ordinators, etc. has proven difficult. I might try to look in detail at a few case studies to see if there are any similarities between Michigan 2011 and the hopeful monsters who point to the possibility of rapid change, but provide a link to my table so that anyone else who may want to can do the same.

Viva la evolucion.

*Yes, I’m aware my metaphor already has no validity at all.

Edit: I think this is what the first commenter is asking for.