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Assessing schedule strength for national contenders

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It's a much discussed and much debated topic in college football. It can determine how far your team can go, and how easily it can get there. It can also determine who gets invited to the prestigious BCS bowls, and even which two teams get a chance to compete for the national championship.

We're talking, of course, about scheduling. It's no secret that strength of schedule can vary greatly from team to team and often conference to conference. But how should we judge a team's strength of schedule?

Some organizations, including the NCAA itself, judges strength of schedule based on the average ranking of a team's opponents. This seems fair and straightforward enough--and it is--but it's also misleading. For a very simple example, consider two teams, A and B, each playing a 2-game schedule. Team A plays the #120 team in the nation in the opener but then must face the #1 team in the nation. Team B meanwhile plays the #48 and #49 teams (for reference, Kansas State and UConn last season). Based on using average strength, Team B would be judged to have the tougher schedule, and by a significant margin at that (48.5 to 60.5).

Now, if you are small-conference school or a bottom-feeder BCS conference school primarily worried about getting to .500 to become bowl eligible, then using average strength might be somewhat telling. In that case, Team A probably truly would have the easiest schedule in terms of getting to .500. 

Most of college football, though, is more concerned with the teams at the top, the teams competing for those BCS bowls and especially the national championship game. To judge the schedule strength for those teams--the national contenders--we need a better way to judge schedule strength. In particular, we need to know how tough a team's schedule is in terms of finishing undefeated or with at most one or two losses. In other words, for a national contender, we know Team A really has a tougher schedule. Any team at that level should easily go undefeated against Team B's schedule, while Team A's schedule would present a serious challenge for even the best teams' national title hopes.

Note: for a real life illustration of why we need to look further than average opponent strength, check out this article, which cites the NCAA schedule rankings, claiming Notre Dame had the nation's toughest schedule last season, despite only playing one opponent (Stanford) that could even remotely be considered among the nation's elite.

In what follows, we'll examine exactly how tough it is for a national/BCS contender (defined as a team in the top 10% of college football's FBS) to navigate through opponents of various levels. Much, much more after the jump.

First of all, we're going to use the Fremeau Efficiency Index for this exercise. Why the FEI rankings you say? Well, first of all, they rank all FBS teams 1-120, which is necessary to evaluate a team's entire schedule. Second, and more importantly, they do a better job of evaluating a team's true strength (or weakness) relative to rankings that only consider wins and losses. 

A good example of why I prefer them when considering opponent strength is the example of last year's Michigan State team. At the end of last year's regular season, the AP poll considered MIchigan State the #7 team in the country due to their 11-1 record, while the FEI ratings said they actually were only strong enough to be in the low 30's--a huge difference to say the least. The Capital One Bowl beatdown--perhaps the most lopsided Alabama game I've ever witnessed against a major-conference team of any caliber--suggested that the FEI ratings did a much better job assessing the true strength of a Spartan team that was in no way one of the 10 or even 20 strongest teams in the country.

With that said, let's examine how teams considered among the top 10% of FBS in strength according to the FEI ratings typically fare against opponents of varying strengths. Remember, we're examining only the top teams because in terms of BCS and national title contenders, that's all we're interested in. The data comes from all games played by teams ending the season as a top-12 team the last four seasons (the only seasons with FEI data available).

Performance v. Opponents Ranked 53 - 120 (+all FCS)
Home: 173 - 1 (0.6%)
Away: 98 - 1 (1.0%)
Neutral: 2 - 0 (0.0%)
TOTAL: 274 -2 (0.7%)

The key takeaway here is simple: top teams simply don't lose to anyone in the entire bottom half of FBS or any teams from FCS. Of course there have been two exceptions in the last four seasons--Virginia Tech's shocking home upset by FCS opponent James Madison last season, and Pitt's road blunder at #64 N.C. State in 2009--but with over 99% consistency, losses just don't happen after you get past the median point of FBS. The reason this is important in evaluating the schedules of top teams is that it really doesn't matter if you play the #58 team or the #118 team--it should be a win no matter what if you are truly among the top teams in college football. This is where rankings using average opponent strength falter. They would treat this difference the same as the difference in playing the #2 team and the #62 team.

Alabama played (56) Penn State, (59) Tennessee, (63) Ole Miss, (77) Duke, (113) San Jose State and (FCS) Georgia State last season. When examining Bama's 2010 schedule in retrospect, we would expect a true national contender or BCS-type team to win all six of those games with little to no chance of losing. Obviously, Penn State was a much better team than San Jose State, and of course playing against a team like Penn State is more difficult than playing a team like San Jose State, but at the end of the day the recent historical data suggests the results of both games should be the same for a BCS/national contender: a win.


Performance v. Opponents Ranked 26 - 52
Home: 63 - 10 (13.7%)Away: 66 - 13 (16.5%)
Neutral: 13 - 1 (7.1%)
TOTAL: 142 -24 (14.5%)


Things start to get a little interesting once you move up to the group of teams that are just outside the top 25 strongest teams. At this point, a truly elite team should still be heavily favored, but the risk of taking a loss becomes real. Elite teams playing these opponents on the road lose at a slightly higher rate (16.5% rather than 13.7% at home) but home field doesn't seem to have played a major role in upsets over the last four years to teams from this group.

In evaluating schedule strength, it does matter how many of these team appear on the schedule, but it should be noted that elite teams should be expected to win these games over 85% of the time.

Alabama played (27) Mississippi State and (36) Florida from this category last season, both at home. A national contender/BCS-type team should go 2-0 against those teams 74.5% of the time given the home win % over the last four seasons against teams in this group. Such a team should have a 23.7% chance of going 1-1 against that slate, and only a 1.9% chance of going 0-2.


Performance v. Opponents Ranked 13 - 25
Home: 34 - 13 (27.7%)
Away: 21 - 15 (41.7%)
Neutral: 19 - 6 (24.0%)
TOTAL: 74 -34 (31.5%)


It should come as no surprise that teams in the bottom half of the top 25 have been very competitive against teams in the top 12, particularly when the top team goes on the road, where the underdog wins over 40% of the time.

While teams from this group might not be quite to the level of national contenders themselves, they present serious challenges to the elite teams and their presence, especially their presence in large numbers, on a top team's schedule should certainly be noted.

Alabama played only one team from this category in its 2010 schedule: (16) South Carolina, on the road. The road part is key here as the data suggests top teams lose such games at a very high 41.7% clip. The math here is pretty simple. A top team should have a 58.3% chance of going 1-0 against this group and a 41.7% chance of going 0-1.

Performance v. Opponents Ranked 1 - 12
Home: 18 - 7 (32.0%)
Away: 7 - 18 (68.0%)
Neutral: 20 - 20 (50.0%)
TOTAL: 45 - 45 (50.0%)

By definition, since we're looking at how top 12 teams fared against other top 12 teams, we're going to end with a 50% win/loss percentage. So while it's obvious to say that when two top teams collide one must win and one must lose, it also underscores an important aspect in scheduling: the real risk in top teams taking on losses comes from playing other top teams. There's also a very interesting home/away breakdown in this data, showing that top teams are more than twice as likely to lose to other top teams when playing them on the road instead of at home. However we're dealing with a relatively small sample size of only 25 games, so there's a decent chance this difference is overstated. That said, the data does suggest that home field should be taken into account when assessing the schedule strength of top teams when playing other top teams.

In examining the schedule strength of the top teams, the most important factor of all in determining strength of schedule is how many other top teams they have played. Playing one top team on the road gives a top team the same chance of losing a game as playing three teams in the 13-25 category at home.

Alabama faced three opponents from this category in 2010: (1) Auburn, at home, and (6) LSU and (7) Arkansas on the road. A national contender/BCS-type team should only go 3-0 against this group 8.8% of the time. Even going 2-1 would be a big challenge for an elite team, as the data suggests it should only happen 34.6% of the time. Going 1-2 is the most likely scenario, with a 42.0% likelihood. Meanwhile, going 0-3 against this slate is far from out of the question, even for an elite top 12 team, with a 14.7% chance of occurring. 

Using this compiled historical data from the last four seasons, we can build a simple probability distribution chart for the number of losses a typical top-12 team would be expected to take against a given schedule. Essentially each game can be given an expected win/loss percentage based which of the four above categories the respective opponent falls in based on the FEI ratings, and whether the game was played at home, on the road or at a neutral site. For example, playing a home game against a team ranked 53-120 would give a top team a 99.4% chance of winning, while playing a team ranked 1-12 at a neutral site would give a top team a 50% chance of winning.

Let's first take a look at Alabama's 2010 schedule. We've already explained where each opponent fell in each of the above categories. The chart below shows the probability of ending that 12-game slate with a given number of losses.

These do not include bowl games, because what we're interested in is where top teams stand at the time bowl selections are decided.


The chart should be fairly self-explanatory. A typical top-12 team would have only a 3.7% chance of navigating the schedule undefeated, an 18.4% chance of incurring one loss, etc. As you can see, this was an extremely difficult schedule for even a top team to manage with an undefeated or one-loss record. It should come as no surprise given the schedule that the Tide finished last season with more than one loss.

Now, imagine if Alabama had actually been competing for the national championship game, and had to compete in an extra 13th game (the SEC Championship) before the season ended. Here's what the probabilities would look like with an extra 13th game against South Carolina at a neutral site.


No surprise here. Going undefeated would have become even less likely, same with finishing with only one loss. Now let's see how Alabama's schedule matched up against a few other interesting cases.


Oregon largely got a free pass on their schedule last year simply because they play in the Pac 10, but this was an extremely soft schedule outside of playing Stanford, and even then the Ducks got the Cardinal at home, which as discussed above seems to be a major factor when two elite teams face off. The next toughest opponent the Ducks faced was USC, who didn't even finish in the top 25 of the FEI ratings last season. What this says is that a top team is more than 10 times more likely to go undefeated against this schedule compared to Alabama's just above. The data also suggests your typical top 12 team should finish with no worse than one loss more than 70% of the time against this schedule. 


Remember how certain ratings systems said Notre Dame had the #1 schedule in the country? The truth is that an average top-12 team has nearly even odds of finishing with 1 loss or fewer, and finishing with 2 losses or fewer--meaning an automatic BCS bowl in this particular school's case--should happen a whopping 77.3% of the time. 


In case you were wondering how a very mediocre Michigan State team ended the regular season as the #7 team in the polls with only one loss, here is your answer. A similar caliber Big Ten schedule is how good-but-not-great Ohio State teams got to play in the national championship game two years in a row back in 2006 and 2007. In a different season (say, one without undefeated SEC and Pac-10 teams), that Michigan State team could have been right in the thick of the national championship discussion. Let that sink in for a minute.


This one will probably surprise very few. What it's saying is that a top team would have to really drop the ball not to finish with 1 loss or less, and has slightly better than even odds of going undefeated. In fairness, TCU was still considered among the top 12 teams in the FEI ratings last year. The truth however is that with a schedule that easy, going undefeated simply isn't very impressive. Remember, the same team that has a 50.4% chance of going undefeated against this schedule has a 2.6% chance of going undefeated against Alabama's 2010 schedule.


Questions of eligibility aside, there can be no knocking what Auburn accomplished on the field last season. Their probabilities look very similar to Alabama's. Considering they finished by knocking off yet another elite team on a neutral field in the national championship game, their end-of-year probability of going undefeated would be only 1.6%. 


* * *


In the coming weeks, we'll apply the same data and process to schedules for the upcoming season, using pre-season 1-120 ratings in lieu of FEI ratings, to assess the paths that this season's expected national contenders must navigate.

UPDATE: A few major caveats to consider....

1) No 1-120 ranking system is perfect. FEI has its own flaws, but I personally consider it to be the strongest system in terms of establishing true team strength. Whatever flaws exist in the FEI ratings will obviously influence these results, but again, I consider FEI to be the superior choice among flawed options.

2) Obviously I grouped teams together into 4 categories, or statistical bins, and assigned win probabilities based on those rather than assigning a unique win probability for each of the individual rankings 1-120. I did this simply for convenience. This means that all teams 1-12 are assessed as equally difficult opponents, while we of course know that playing the #1 team is obviously more difficult than playing #12, just as playing #13 is more difficult than playing #25 and so on. This is a weakness but it still provides a decent estimation for each game.