Hoegher's Rankings: A TREATISE ON "LUCK"

Hey y’all! So my efforts on those Big Ten season previews may have dwindled toward the end there, so… sorry about that. In my defense, no one wants to hear my brand of "analysis" anyway, so the plots and tables should’ve been more than enough contribution. Plus, now there’s a record of my projections so everyone can point out how wrong I was come December.

HOWEVER, just because we’ve run the course on Big Ten teams and their upcoming streak of wildly successful eventful game days doesn’t mean that I have to stop prattling on about various topics. You, of course, are free to listen or ignore as you see fit. In this case, the topic is "luck."

I’ve referenced the concept of “luck” before (see more of an explanation on what it means and how I calculate it at my primer here), but in short: “luck” is the difference between actual winning percentage and “expected” winning percentage. I’ve also referenced that – claims of “clutch-iness”, “choke-ability”, “just-knows-how-to-win-ittude” aside – I believe that “luck” is essentially random.

I don’t make that claim out of the blue, by the way. Plenty of other smart people in various sports-math disciplines have done the work and drawn that same conclusion. However, given that they (probably) haven’t used my nebulous metrics, whether that holds true with regard to the Hoegher Rankings hasn’t been proven. That’s what this Fan Post is designed to address, as well as (hopefully) educate people on what exactly “luck” tells us about a team or coach.

First, let’s start simple. How did teams stack up in 2012 (with regards to their “luck”)? We know that OSU (Ohio State) was one of the most “lucky” teams, coming in at +24% (1st), and we know that OSU (Oklahoma State) was one for the most “unlucky” teams, coming in at -20% (123rd). For all the teams in between those extremes, this is what that distribution looks like:

Ah… that sweet Gaussian distribution, how lovely it is. Breathe it in, appreciate its timeless wonder. Do you have it? Good. Now toss those thoughts aside and realize this plot tells us nothing. It tells us that “luck” follows a normal distribution (more or less). It does not tell us how that distribution occurs. It could be distributed in the same way that finish times at the local 5k are distributed (that is, due to differences in speed and endurance). It could be distributed in the same way Plinko is distributed (that is, due to the cruel whims of the gods).

So how can we tell the difference? It’s pretty simple, actually. If we take a measurement that we assume is due to inherent skill, then that measurement should be repeatable. If I participated in a race against Usain Bolt, I would win. And I would expect to win any subsequent time that we held such an event, barring unforeseen blue shells (I should mention that this race occurs on a Mario Kart 64 circuit). Plinko does not offer me that same benefit.

Applying this to the concept of “luck” in college football, teams that finish with a high “luck” rating in one year should expect to finish with a high “luck” rating the next year as well (assuming “luck” is a skill). Apply the same reasoning for those poor “luck” yielding teams. Using the 2011 and 2012 seasons (and removing those teams that only joined in 2012), this is what we have:

Now, for me, this is pretty cut and dry. Not only is the R^2 (EDIT: guess what HTML tag doesn't work here? Yep, superscript) value essentially perfect for un-correlated data, but that trendline has a near-zero slope. Hell, while I wasn’t expecting anything indicating a strong correlation, that R^2 value still surprised me with how low it was. But maybe you’re stubborn (*cough* PROVELT *cough*). Maybe you want “luck” data trending over a period of more than two years. Well, lucky for you (HA!) I put in that work as well:

First thing to note is we’re dealing with a smaller sample size here, due to teams joining the FBS during this time. Not a huge difference (N = 120 for 2011-12, N = 117 for 2003-12), but just so y’all are aware.

Second: hey, we actually registered a noticeable R^2 value! I mean, that’s still so low as to be meaningless, but whatever makes you sleep at night. Also, there’s a definite positive slope in the trendline. While this gives the briefest bit of credence to those who cling to “luck” as characteristic trait, I’ve got other theories which I’ll expand on later.

MORE TIME RANGE, you say? That doesn’t quite make sense, but I’ll acquiesce your request nonetheless:

Well, now things get a bit interesting. That R^2 value isn’t negligible anymore (though I’d still argue that a R^2 value of 0.134 isn’t anything to get too excited over). More importantly, the correlation displayed here is actually significant in a statistical sense (p = 0.0002). I didn’t note this for the above two plots, but safe to say: those were not significant. Before I get to defending my “LUCK IS MEANINGLESS” theory, let’s spend some time talking about the teams I’ve highlighted above.

Auburn – there are two teams that have three undefeated seasons since 1993. One is Nebraska (duh). The other is Auburn (1993, 2004, 2010). Unlike Nebraska, which went undefeated with legitimately great teams, Auburn somehow managed to accomplish the same task with fairly underwhelming teams (by undefeated standards). 1993 Auburn ranked 23rd in Adj Def, 2004 Auburn ranked 14th in Adj Off, 2010 Auburn ranked 39th in Adj Def. Undefeated teams are always going to rate out as “lucky,” no matter how hard Nick Saban tries, but this effect is magnified when you do it with less-than-stellar teams.

Oregon – their luck is almost completely due to the period 2000-05, as well as the early-mid 1990’s when they first discovered themselves. Interestingly enough, Oregon actually had a down period from 2002-04, but their performances on the ends of that half-decade are enough to push them up towards the top. Chip Kelly’s teams actually hardly rate out as lucky at all, though it certainly helps never managing to go undefeated despite a stellar offense.

Air Force – Exhibit A why I think a good offense is worth more than a good defense: Air Force had a legitimately great defense in 2009 (11th) and just an average offense (56th). They went 8-5, which sounds decent until you realize they had a -19% “luck” rating, which is worth about two more wins. 1993 offers the other side of this, with an average defense (47th) and a bad offense (81st). They had a -21% “luck” rating that year.

Memphis – Memphis has always sucked. It does not surprise me to see them here.

Northwestern – Okay, this is pretty much the one team that I think might have something “special” with regards to “luck,” at least since football started in 1995. I don’t know if it’s because Northwestern is forced to adopt the underdog/upset role in a major conference to survive (as a counterpoint, Duke has atrocious “luck,” but since when does Duke care about football?). Since 1995, hell since 1990, Northwestern has had exactly two seasons with below average “luck.” 1998 (still getting their footing) and 2011 (that’s what happens when you lose to Army). If you want to go ahead and plug them in for a game more than whatever I project, that’s okay. I’m still not adjusting my formula, but I understand.

As to that statistically significant correlation in my twenty-year comparison...

See the thing is that “luck” isn’t completely independent of other variables. Obviously, un-defeated teams are “lucky” by definition and all-defeated teams are “unlucky” by definition. This extends beyond those boundaries, though. As you might expect, teams with winning records tend to be “luckier” than teams with losing records:

Winning percentage is a pretty poor metric to correlate from year-to-year (just based on strength of schedule), but it is something that is more-or-less repeatable. So it’s my opinion that the significance of “luck” across a twenty-year time period is more due to residual effects of winning percentage, rather than an inherent skill of “luck” for a specified team. But you are free to disagree :)

Just for fun, a comparison of luck across coaches (rather than teams) for 2011-12:

It’s been my opinion that “luck” would be a characteristic of a coach, rather than a team (if anything other than random). That R^2 value is still essentially meaningless, but it’s nice that my hypothesis seems to have support here (I also have 10 years summaries, but only a few coaches qualify, which is why I’m not posting them).

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