Football is not transitive. What do I mean? Simple. If Team A beats Team B, and then Team B beats Team C, it does not mean that Team A will beat Team C. We all know this.
Proof of non-transitivity this year comes in the Big Ten. Let's look at the Big Ten Graph. The graph is simple to understand: each team is a node (circle), and there is an line connecting each team that played another team. The line is actually an arrow, making this a directed graph, in the obvious form: if there is an arrow from Team A's node to Team B's node, it means Team A beat Team B. Here is the graph:
The Victory Graph (Click on it for full size)
There are lots of fun cycles to find in the graph. For example, Minnesota beat Iowa, who beat Michigan State, who beat Minnesota. See how many of these three-node cycles you can find (there are plenty). Or not, depends how bored you are at work. There are bigger ones too: for example, Michigan beat Indiana who beat Purdue who beat Minnesota who beat Iowa who beat Michigan State who beat Wisconsin who beat Michigan. And it goes on.
The most amazing fact from the graph, thanks to Indiana finally getting a win, is that the graph is strongly connected. In graph terminology, this means you can get from any node in the graph to any other node, simply by following arrows, for all pairs of nodes. This really shows how non-transitive football is: you can use this graph to say any team "transitively beat" any other team, at least in the Big Ten this past year. For example, Indiana beat Purdue, who beat Minnesota, who beat Iowa, who beat Michigan State, who beat Wisconsin, who beat OSU. If football were transitive, Indiana "beat" OSU! Except when they played, of course.
One interesting metric for each pair of teams (A, B) is the shortest path to victory for A over B. Some of these "shortest paths to victory" are easy to find: for example, it is unfortunately the case that there is a short and quite direct path from OSU (at the top) to Michigan. Some are harder to see: for example, see if you can find the path where Michigan "transitively" beats OSU. This "shortest path" is actually long: 6 steps (the answer is at bottom).
We can then use this graph to order the teams a different way: what is the shortest path between a team and every other team in the Big Ten? Lower is better here: a path of length 1 means Team A directly beat Team B, whereas a path of length 2 between Team A and Team B means that Team A beat Team C who in turn beat Team B. Here is the full summary of the shortest paths between all pairs of Big Ten teams:
You can then use these to create a new ranking among teams, based on their average shortest path to victory:
This ranking kind of makes sense, too. If you beat a lot of teams directly, then you will have an average near 1 (note that even undefeated teams will average higher than 1, because teams don't all play each other). If you only beat bad teams, who in turn only beat other bad teams, your average will be higher. Thus, Michigan does poorly in this comparison; Minnesota does better because they beat Iowa, who actually beat some good teams (like MSU). Only Indiana fares worse than our boys in Blue.
You can also prune the graph to arrive at some interesting findings. For example, let's say we remove all edges where one team didn't resoundingly beat the other team. I will arbitrarily deem a win as a "strong" win when one team beats the other by more than 10 points. The graph now looks like this:
The Strong Victory Graph (Click on it for full size)
Wow, that is a much different graph! The first thing that stands out: there are no cycles in this graph. That means that if Team A "strongly beat" Team B, and Team B "strongly beat" Team C, that Team C didn't "strongly beat" Team A. There are no cycles here my friends.
We can also then use the "Strong Win" Graph to compute a new ranking. For each strong win, you get a +1, and for each strong loss, you get -1. Here are the teams, ranked by this new "Strong Win" scoring system:
This is actually a pretty reasonable ranking I think. Wisconsin is on top, because they beat the tar out of everyone (almost). Michigan State doesn't fare nearly as well as Wisconsin and OSU, because they had many close wins and one game where they were trounced (Iowa). Michigan ends up behind Illinois and Penn State in this ranking, because those two teams had a number of big wins, where Michigan only had one (Purdue, and barely "strong" at that).
Anyhow, that's a short look at how graphs can help us rank teams in different ways. And if you didn't like it, well, remember that I Hate Everything too.
[EDIT: Some people asked how I generated the graphs. All automated, given an input of games and scores. Some python code to compute shortest paths between nodes (there are some fairly standard algorithms for doing this) and then Graphviz to layout the graphs automatically. It would be easy to do this for any set of games.
One other note: the real point of the "Strong Win" graph is how silly it is that score differential is ignored in current computer rankings. A big score difference is a useful metric, and one that I think is better than many other simple ways of comparing teams. One could likely come up with a slightly more nuanced "Strong Win" definition (say, win by 10 and outgain the other team by some threshold number of yards); this was just a simple and easy way to start.]
The path for "transitive victory" of Michigan over OSU: Michigan beat Illinois who beat Northwestern who beat Iowa who beat Michigan State who beat Wisconsin who beat OSU. Ugh, it is really hard for us to beat OSU, apparently.
[Ed.: as a basis for discussion. IME, the FO-based stats are the best available for reducing noise when you're evaluating how good of a team you've got.]
Hey guys, I don't know about you, but 99% of the conversations I've seen or heard about Rich Rodriguez's future at the University of Michigan hinge on how much each person thinks the team has improved. So obviously, the question is how much have we improved, exactly?
To start off, I'm going to make a few assumptions and attempt to defend them. First, very few people can simply watch the games, watch the highlights and determine if their own team has gotten better. Frankly, we don't know enough about the game on a micro level for our eyeball test to mean anything, not to mention the TV angles don't have large parts of the play, we don't know what play was called, etc.
Secondly, no mere mortal is actually capable of rating teams, especially the mediocre ones. There are around 50 games a week during the season, and while many of us wish we could be superfans, we simply are not capable of watching that many games in any meaningful sense. If you aren't watching the games, what are you basing your eyeball rankings off of?
Because of those two assumptions, the only place we can really look for improvement is found in statistics.
Statistics? @#$@, like math?
Don't they lie or something?
Well, yeah sometimes. There are many different ways to look at football statistically, and frankly, all of them have fairly severe flaws. Football simply has too many intangibles to model mathematically as well as baseball. However, that doesn't mean that all statistical analysis of football is useless, just that you have to be careful not to overstate your case and to look at the data in as many ways as possible. For this diary, we're going to look at three major ways of quantifying football games. The goal is to compare the results and see if we can get some sort of idea of what's going on.
OK so what are these different ways? Didn't Brian post about FEI or something?
The first, and most common, are methods that mostly rely on looking at who won against who and/or by how much. This is the type of method used by Sagarin, Massey and more. For the BCS formulations, Massey and Sagarin are not allowed to use margin of victory in their calculations. However, when Massey and Sagarin use margin of victory, their models are more accurate.
The second one we'll look at is basically drive analysis. This is FEI, and is best explained by Football Outsiders:
The Fremeau Efficiency Index (FEI) considers each of the nearly 20,000 possessions every season in major college football. All drives are filtered to eliminate first-half clock-kills and end-of-game garbage drives and scores. A scoring rate analysis of the remaining possessions then determines the baseline possession efficiency expectations against which each team is measured. A team is rewarded for playing well against good teams, win or lose, and is punished more severely for playing poorly against bad teams than it is rewarded for playing well against bad teams.
The last one we'll look at is an analysis that uses a play by play analysis. Again, Football Outsiders:
The S&P+ Ratings are a college football ratings system derived from the play-by-play data of all 800+ of a season's FBS college football games (and 140,000+ plays). There are three key components to the S&P+:
There has been a lot of talk surrounding the job security of Rich Rodriguez, and I have stumbled upon something that may shed some light on the outcome. This thing goes way deeper than sabotage efforts by Herbie, or Tweet wars, or anything spoken by David Brandon in the wake of our 30 point trouncing at the hands of OSU. This thing is deep, and it spreads into realms nobody here realizes. I present my case.
Domino's Pizza Commercial, circa 2009
A year after the disasterous 3-9 season that lit a fire under Rodriguez' chair, David Brandon, who at that time was CEO of Domino's Pizza, comes up with a new advertising campaign. "Giving a bailout to main street, not Wall Street," became the ode du jour. The symbolism is outwardly obvious. Brandon is fed up with the hierarchy at the Michigan Athletic Department, namely Rodriguez and his crew. Note that Brandon grabs a pizza box from the 'old' man, and places it into the hands of a younger passerby. A proverbial passing of the torch, or pepperoni, in this instance. Also note that all the cars in that commercial are Ford's, an obvious nod to a 'Michigan Man." Message sent.
Enter the Free Press. A bastion of morality in the decaying sector of popular culture know as news print. When the old guard says jump, they ask, "Onto what phallic device?" A sweeping attack on all that is Rodriguez decended upon the land. A strike that was military in its precision blindsided the administration, and left them exposed on all sides, sitting targets for the mouth breathers at ESPN to fire shots of lead towards. And fire they did, lamenting Rich to all who would listen.
Yound Man Told by Drew Sharp That Rich Hates Redheads
Coalescence of the Old Guard
Still waters run deep. So it should be of no surprise that none other than Les Miles has become the lynchpin that has held together the Old Guard. As acting Don, Miles was responsible for issuing the kiss of death, which came in a very peculiar way:
What better moment than a decisive touchdown against a former National Champion and hated Spartan in Nick Saban's Crimson Tide to derail the outsider? Rotary phones in stodgy offices all across the midwest began to ring off the hook, as members confirmed that the sign had been cast. When grass touches the tongue, the end shall begin. The transition was to commence. Columns of white smoke would not be seen rising until the Prodigal Son returned to Ann Arbor.
A house once divided was now as focused as a Michigan receiver after a trip to the optometrist.
The Mysterious Death of a Funny Man
At first glance, the passing of one Leslie Nielsen seems to be a tragic and unavoidable course of events. He was, after all, 84 years old. A closer look reveals a sordid turn of events that left this Hollywood legend dead in Florida. It also reveals the rapid escalation and the mounting tension between the two sides.
Leslie enters the scene in 2002, when he is named an honorary citizen of West Virginia, the same year Rodriguez has his big turnaround at WVU. The two become fast friends, living as kings of West Virginia. Nielsen takes the WVU divorce especially hard, as do most denizens of that fine state, and their relationship quickly soured.
Leslie spends the remainder of his life just miles away from Harbaugh and his staff. Having a penchant for college football coaches, he makes fast friends with the former Michigan QB, and becomes outwardly critical of the Rodriguez regime. When asked about the coaching tenure of Rich Rod, Nielsen responds:
I'm sorry I can't be more optimistic, Doctor, but we've got a long road ahead of us. It's like having sex. It's a painstaking and arduous task that seems to go on and on forever, and just when you think things are going your way, nothing happens.
Speculation arises that Nielsen had joined the Old Guard.
Feeling betrayed, Rodriguez becomes spiteful. The spite gives way to unbridled anger when Rich gets word that Nielsen plans to meet with Brandon to reveal undisclosed indiscretions from his past. Last week Calvin McGee, a henchman in Rodriguez' platoon, travels down to Florida. Some are convinced it's a recruiting trip, others a job interview. But the truth is much more sinister. Nielsen got on Rod's bad side.
Alarm rings out through the Old Guard, as they become fully aware of just what they have awakened.
The Culmination of Events
Michigan fans with their ears to the ground have started to stir, as they can now confirm what the seismometers have been predicting for the last few years. Something is a brewin'. In fact, many seemingly random events can be attributed to the Cold War that will soon come to fruition.
The stitches Obama received during a 'friendly' game of basketball? That was Beilein sending a message that the President needs to back his horse. A similar message was sent by the Old Guard to Rue McLanahan after she openly supported the proliferation of the spread offense in college football. Rue was an avid college football fan.
Both sides have become brazen with their displays of power and authority. There is no telling how fast, or how far, this will go. One thing is for sure, there will be no winners. Brian, as a figure head in this debate, I'd lay low for a while. Find a nice hamlet somewhere down south and let this thing play out. I just hope it's not too late.
The season is starting to wind down, so rather than trying to pick some bad games out of the dwindling pool of options, I will instead take a look at the Big East playoff picture, which is Ugly unto itself. When there is a four-way possibility that the winner will have four losses, that deserves a look. But first:
Akron wins a game! Akron wins a game! Oh my God, Akron wins a game! The Zips beat Buffalo 22-17 to get their first win for the season. Akron's QB, P. Nicely, was 13/24 for 193 and 3 TDs. I really only mention it to say that his name is P. Nicely. Buffalo was making a game of it, until a late fumble gave the ball back to Akron to run out the clock.
North Carolina almost blew a 24-10 lead to Duke in the 4th quarter, but Duke ran out of time on their last drive. Not sure why Duke threw a 6 yard pass to the 41 as the last play, but they are Duke. Laettner must not have been open at the free-throw line. They did manage to score 19 points with 275 total yards and a 0.8 YPC rushing average. I'm sure they're happy it's basketball season.
Last, Vanderbilt dutifully lost to a 3-9 Wake Forest team 34-13. Vanderbilt's AD issued a statement saying he and Caldwell reached a "mutual agreement that the university and the football program needed to go in a new direction." Well, from where they are, there's only one way to go: up. Vandy actually had more offense than Wake, but missed two field goals (I know how that feels) and turned over on down five times to give Wake short fields.
We do have the Washington/Washington State mess, but nothing holds a candle to the impending Big East Trainwreck, so without further ado I present:
aka the "Big" East preview. There is no scenario in which the Big East winner will have fewer than three losses. First off, UConn controls their own destiny. Win and they are in the BCS. At 8-4. And probably unranked. They are 4-2 in conference, with key wins over the other contenders West Virginia, Syracuse and Pitt. They play one of the other possible title contenders, South Florida this weekend. I'm assuming here that the first tie-breaker is head-to-head, then overall record, which gets them in a head of 8-3 West Virginia, because West Virginia is also 4-2 in conference.
That's the easy part: if UConn wins, they get it. But if they lose, here come the scenarios. If UConn loses, they are 4-3 in conference. West Virginia is the next most likely winner, as they are also 4-2. They play Rutgers this weekend, who is 1-5. West Virginia has beaten USF and Pitt, so that gives them the edge in the head-to-head. So if West Virginia wins and UConn loses, they're in. Notice: after this point it starts to get meteor-hitting-a-lottery-winner level of likelihood, but I'm going to do it anyway.
If WVU loses, unlikely, though it may be, next in line is Pitt. Pitt plays on the road at Cincinnati, and is coming off a stretch versus UConn (loss), USF (win), and WVU (loss). A win would put Pitt at 7-5 overall and 5-2 in conference. And in a BCS bowl. A Pitt loss really throw a wrench in the works by making 5 teams 4-3 in conference: West Virginia, UConn, Pitt, Syracuse and USF.
I think maybe Syracuse gets the title since they beat USF, who will have beaten UConn, so by transitivity they win? Does UConn win by virtue of beating WVU, Pitt and Syracuse? I hope the Big East has enough tie-breakers to handle this, and I really hope one of them involves a 100 yard dash between the mascots to decide it. I don't know what else to do in this scenario, other than declare TCU the winner a year in advance.
Though we're not one of them, being one of the few teams that had to play all three Big Ten 2010 Champions, and since we generally hate all three, I figured Michigan bloggers might be in a good position to adjudicate the mess atop our conference this year.
Base comparisons are as follows. I would appreciate any comments, and would like to change it up based on your opinions.
|Loss||6-37 @ Iowa (-2)||18-31 @ Wis.||24-34 @ MSU|
|Ohio State's loss to Wisconsin was by more, but Wisconsin won the turnover battle by 3 and still lost to Michigan State by 10. They're pretty much even. Michigan State got beat much worse (-1) by a worse team (-1)|
|BCS OOC||34-31 ND||36-24 Miami (+1)||20-19 ASU (-1)|
|Notre Dame and Miami are both erratic, 7-5 teams against tough schedules but Ohio State didn't make it close, while MSU needed a fake punt conversion (that was covered!) to beat ND. I count both of those as better than ASU, who will finish 5-7 most likely a tough (-1) to Wisconsin, though they get the benefit of the doubt next close one.|
|Big Ten 1||34-24 Wis (+1)||20-17 @ Iowa (-1)||31-18 OSU (+1)|
|The Iowa game is Ohio State's biggest win, and it wasn't that great of a win -- as close as the 3-point spread looks (-1). MSU/Wis and OSU/Wis were dominating wins over Top 10 teams. (+1)|
|MICHIGAN||34-17 @ Mich||37-7 Mich||48-28 @ Mich (+1)|
|Easiest comparison to make. Ohio State and Michigan State both dominated thanks to Michigan mistakes, while Wisconsin made its trip to Ann Arbor a bloody affair (+1) from kickoff.|
|Purdue||35-31 Purdue (-1)||49-0 Purdue (+1)||34-13 @ Purdue|
|Ohio State murdered (+1), Wisconsin held serve, Michigan State (-1) needed a 4th quarter comeback to beat a worse Purdue team than either other one played|
|PSU/Iowa||28-22 @ Penn St||38-14 Penn St||31-30 @ Iowa|
|Iowa's a better 7-5 team than Penn State, but the close road win didn't tell us much. Ohio State got the Lions at home when they were worse, but they did better. 0s all around.|
|Minn||31-8 Minn||52-10 @ Minn (+1)||41-23 Minn|
|Pasting, bigger pasting on the road (+1), pasting.|
|Illini/NW||26-6 Illini||24-13 @ Illini||70-23 NW (+1)|
|Illinois is better than Northwestern. MSU came on late but came on. Ohio State made it a lot closer. But Wisconsin's 70-point finale against a worse Northwestern team (+1) is more impressive.|
|Ind/NW||35-27 @ NW (+1)||38-10 Ind.||83-20 Ind. (+1)|
|MSU looked to lose to Northwestern right up until the end, but they're a much better team than Indiana so (+1). Ohio State did what it was supposed to, but Wisconsin put up 83 (+1)|
|OOC||38-14 WMU||45-7 Marshall||41-21 @ UNLV|
|Pasting, pasting, slightly worse pasting but on the road.|
|OOC||30-17 Fl.Atl (-1)||43-7 Ohio||27-14 SJSt. (-1)|
|FL-Int. kind of made it close (-1) and so did SJ State (-1) while OSU rolled over Ohio|
|TomatoCan||45-7 N.Colo||73-20 EMU||70-3 Austin Peay|
|Doesn't count -- any FBS team but EMU might give Ohio State a|
It's not a perfect line-up, but it gets the job done, giving us some close and semi-close apples and oranges to compare. The +'s and -'s are simply numeric comparisons for how the teams did against each other on that line, i.e. they say how much each team disguished itself from its two conference competitors in that comparable.
You can argue a lot of my conclusions.
So Michigan State's resume, lined up as best as I can, is substantially behind that of Ohio State and Wisconsin. I wouldn't feel bad about ranking them several slots behind the other two if there are some other 1-loss teams. Remember above where I said Wisconsin gets the benefit of the doubt? There you are. I'd put them slightly over Ohio State, whom they defeated. The late-season murderous rampage worked.
Okay, bloggers. Fisk away.
These next few weeks will be crucial for the finish of Michigan's recruiting class. This weekend and next weekend will see Michigan hosting lots of talent. Here's a few updates on some of those recruits, a new visitor scheduled, and a current commitment.
6'0", 190 lbs.
Fort Lauderdale, Florida
Michigan was outside of Wayne's top list for a while, and they weren't sure if they would get an official visit from him. He decided that the Wolverines would be included in his top five, which will result in the official. He'll be in Ann Arbor this weekend with his mother to take in the campus.
I'm really just looking for comfort, and I want the coaches to make it clear to me how I'm going to fit into the system. I'm hoping to see a good environment and campus, and how the coaching staff works. I'll also be looking at depth charts, and I know Michigan needs defensive backs.
An important factor in this process will be Wayne's mother, who will be accompanying him on this visit.
My mom is really looking for a lot of the same things that I am. She wants to feel comfortable with the school, and feel comfortable enough to let me go there.
His mother has been on all his trips with him so far and will also be at his final visit to Nebraska. Lyons will be making his announcement at the Army All American game, and Michigan has been making some strides with him. Also visiting this weekend are four star Maryland DB Blake Countess, who Michigan is in good shape for, and current commit DB Delonte Hollowell. I'll update as I hear any more recruits that will be in town.
6'2", 230 lbs.
Dawson had told me a few weeks back that he wasn't as interested in Michigan as some of the other schools in his top seven. He has always maintained that Michigan is in that top seven, but they needed some work to do. They will now get a chance to do that work, as he's decided to schedule a visit to Ann Arbor.
I'm coming up there on January 22nd. Michigan's in my top seven, and I didn't get to go there for a game so I thought I'd come and take a look. I don't really have any leaders right now, but I'm looking for a place that I feel comfortable. I haven't really seen as much of Michigan, so they're still a little behind some others.
As he noted Michigan is behind, but like Lyons a visit is a step in the right direction. Dawson won't be making his decision until signing day, so there's plenty of time to think about it, plenty of time for Michigan to let him know how much they want him. The other schools he lists in his top seven are Tennessee, USC, Florida, Louisville, Kentucky, and Oregon.
6'1", 210 lbs.
Kellen's family is as excited as anyone for him to join the Michigan family. His father is an MGoBlog reader, and wanted me to share a few things with his fellow fans. The pictures below are of Kellen with former Michigan linebacker Jarrett Irons at a family get together, and the second with Coach Rodriguez and former Michigan great Desmond Howard. Below that is a highlight tape from one of Kellen's games a few weeks ago against St. Thomas, where his team won 33-28 (ED: I'm having problems with uploading the video to YouTube. I'll post it when it goes up). Enjoy.
- New Jersey TE Jack Tabb is visiting North Carolina this weekend, and most likely Arkansas on the 10th. He's hoping to have his decision made by Christmas. Michigan has put themselves in good position with Tabb after his official visit.