Over the past few weeks, other SB Nation blogs have featured excellent articles about Northwestern football. First, Bill Connelly of Football Study Hall wrote a statistically oriented preview of the 2011 Wildcats, and he was quite enamored with Pat Fitzgerald:

[Northwestern] finished 6-6 despite getting outscored in 2007, they finished 7-6 despite being outscored in 2010, and they finished 17-9 in 2008-09 despite a scoring margin that would suggest something much closer to a .500 record.

Quite simply, Northwestern just keeps figuring out how to win close games. And it's driving the stats crazy. Under Fitzgerald, Northwestern has gone 21-9 in games decided by eight points or less. Take bowl games -- which Northwestern is obviously never, ever, ever going to win again (last bowl win: January 1, 1949) -- out of the equation, and they're 21-6. 21-6! That's like a hitter posting a .425 batting average on balls in play (BABIP) one year, then hitting

.450the next.

YearW-LWin%Close

W-L% Of

Pts2006 4-8 .333 1-1 .387 2007 6-6 .500 4-1 .455 2008 9-4 .692 5-2 .547 2009 8-5 .615 6-2 .515 2010 7-6 .538 5-3 .476 TOTAL34-29.54021-9.476

It's not supposed to happen that way. One of the mores in most sports is that things like close games and turnovers balance out after a while. But this isn't the case with a Northwestern team whose record under Fitzgerald would be something around 28-35 if they were to win close games at a normal, closer-to-50% rate.So how good a coach

isPat Fitzgerald? Northwestern's on-field performance and recruiting levels aren't really any better now than they were in his first couple of years on the job, and that is certainly on him (though it is obviously a more difficult part of the job at a school like Northwestern) ... but as a puregamecoach, there might not be a better one in the country

High praise. Then earlier this week, Patrick Vint from Black Heart Gold Pants wrote a terrific article breaking down the pythagorean expectation (if you don't know what that means, he explains it) for every Big Ten team over the past decade. Like Connelly, Vint's calculations left him quite impressed with Fitzgerald:

It's also a credit to Pat Fitzgerald and the late Randy Walker at Northwestern. Even in its worst years, jNWU has outperformed its pythagorean expectations. In every year included in this study, Northwestern had a positive overall pythagorean margin, and in all but one the LOLcats had a positive margin in conference play. Their gigantic lead in the chart above isn't due to one season; it's consistently winning a game to a game and a half more than expected. Northwestern's nine seasons are all within the top 30 overall (eight are within the top 20), and all but 2002's 1-7 Big Ten mark are within the top 22 in conference play. Once may be a random occurrence, and twice a coincidence, but if three is a trend, nine is gospel. Northwestern wins close games.

I must say that as a Northwestern fan who's watched just about every game of the Pat Fitzgerald era, these results surprised me. I've never thought of Fitz as a great in-game coach; in fact after his first team blew a 5 touchdown lead to Michigan State, and his second team lost at home to putrid Duke (during which Fitz made several colossal tactical blunders, specifically taking a made field goal off the board so he could go for it on 4th and 3 in the 2nd quarter), many Northwestern fans considered him an incompetent game manager and wondered if he was in over his head. Since then, Fitz's teams have improved and the fan base almost unanimously applauded his recent contract extension, but I don't think most fans view him as a tactical genius (although I could be wrong, I won't presume to speak for the fan base).

Still, the numbers above don't lie: Northwestern has had tremendous success in close games, and I'm really curious as to why. Is Fitzgerald truly a brilliant in-game coach? Is Northwestern's system responsible, or is it some other factor? Or is Fitz simply getting lucky? Let's take a closer look.

To start, let's look at just how much of a role luck could be playing. Both of the linked articles above briefly consider this issue but dismiss it, arguing that the sample size in question is large enough that luck can't possibly be the only explanation.

Time for some math to see if the sample size is indeed large enough (some relatively advanced math is upcoming, if you're not a mathematician just skip ahead to where I've bolded conclusion). Northwestern is 21-9 in close games (games decided by 8 points or less) under Fitzgerald, quite a bit above expectation. We're going to assume for now that Northwestern was 50% to win each close game, which may not be exactly right in NU's case (more on that later), but is obviously right for an average college football team since the NCAA as a whole has a .500 record in close games.

So using our 50% win percentage assumption, we'll use a binomial distribution with p= 0.5 and n=30 to calculate the chances of NU winning 21 or more of their 30 close games under Fitz (you can think of this as follows: if you flip a coin 30 times, how often will it land heads 21 or more times?). This calculation leads to a result of 2.138%, which makes it seem unlikely that Fitz's success is merely a result of luck. We're not talking about the odds of winning the lottery here, but two percent is still quite a long shot.

However, this analysis isn't quite enough, because it fails to consider the size of the population (i.e. the number of teams in college football). With so many schools in FBS (120 to be exact), it may be possible, even likely, for one of those schools to go on a lengthy hot streak in close games even if the results were entirely random. Consider flipping a fair coin 3600 times in a row; eventually you're probably going to get a run of heads or a run of tails.

In fact, it would be quite surprising to find that at least one of the 120 FBS teams hadn't won at least 21 of their past 30 close games. A quick probability calculation shows the odds no one in FBS has won at least 21 of their last 30 close games to be (1-0.02138)^120= 7.47%, meaning there's a 92.53% chance that someone has managed to win 21 of 30. So it's entirely within the realm of possibility that Fitzgerald's success in close games is completely luck.

As the sample size gets larger, it becomes much less likely that luck is the only factor involved. For example, over a 100 game sample size, the odds of him maintaining at least a 70% win percentage all on luck would be 0.003925%, and the odds of anyone in FBS doing it would be 0.5%. In that case, we could easily conclude that it's much more than luck, but we can't here.

**Conclusion**: While Fitzgerald has unquestionably won a lot more close games than mathematics would expect, it's still been just 30 games, which isn't enough of a sample to confidently conclude that his success has been due to more than just luck. Further study is required.

Sticking with math, let's take a closer look at the assumption used above, where we assumed that Northwestern had a 50% chance to win each close game. As already mentioned, that assumption holds for the average NCAA team, but not for every individual team. The reason is in any individual game, the team that's favored is more likely to win a close game than lose a close game.

Here's why: if Northwestern is favored over Central Michigan by 10 points, then NU winning by 10 is both the mean and the most likely outcome (the margin of victory is going to be normally distributed* with mean 10. The normal distribution is best known to laymen as the bell curve used to score the SATs, if that helps you visualize.)

** The normal distribution doesn't work perfectly for football margins of victory because points are scored 3 or 7 at a time. That said, the normal is still a close enough approximation for our purposes here.*

In this hypothetical, Northwestern winning by 10 points is the most likely outcome. As the margin of victory deviates farther and farther from the mean, that margin becomes increasingly unlikely. So NU winning by 7 is slightly more likely than NU winning by 3, which is slightly more likely than NU losing by 3, which is slightly more likely than NU losing by 7, etc.

All this is only relevant if Northwestern was usually a favorite or an underdog in their close games. If they were usually a favorite, then we'd expect them to be a bit over .500, and if they were an underdog, we'd expect them to be a bit under .500. So I looked at the point spreads for all 30 of the close games over the past 5 years (source: covers.com), and found that the average point spread was NU -0.5. Since you can't tie in a college football game, this means that NU was evenly matched on average with their close game opponents, so the 50% assumption used above was accurate.

Ok, that was quite a bit of math and probably not all that interesting, but all that math is necessary to fully cover the whole issue and address the luck factor. It would have been nice to conclude that his success had to be more than just luck, but unfortunately the data, at this point, is inconclusive. Part 2, which appears next week, will feature more direct analysis of the close games and shed a lot more light on Pat Fitzgerald's in-game coaching skills.