here's one vote for "John Beilein's head in a Futurama jar"
Reader will brought up an interesting question in a board posting recently: should Michigan have fouled Kentucky with about 20 seconds left, putting them at the line, but (critically) giving Michigan the ball back with a chance to tie or win?
To my surprise (especially given this crowd), there were a lot of "gut" responses based on feelings, emotions, and in some cases, how such options would be hard to explain in the media.
So I did a few small calculations. The simplifying assumptions were these:
- Kentucky has some chance of making each free throw (call this Kft)
- Kentucky has some chance of scoring when we don't foul them (Ks)
- Michigan has some chance of scoring if they have the ball back (Ms)
- There are only two-point baskets (no threes for simplicity)
- If the game went to overtime, odds are 50/50
On a missed free throw by Kentucky, Michigan gets the ball 100% of the time
(clearly a stretch in this game)
- If we let Kentucky play it out, they will get one chance to score and the game will end either with them winning or go to overtime.
- If Michigan gets the ball back with plenty of time, assume they either score (as dictacted by Ms above) or miss; no free throws, etc.
With these assumptions in place, we can start to calculate: what should Michigan have done to improve their chances of winning the game?
There are two options we will compare:
- Traditional (T): This is what we did. Play defense, and hope Kentucky misses.
- Non-traditional (NT): Foul Kentucky (hopefully a bad free-throw shooter) and get the ball back with a chance to tie (if down two), or win (if down one or still tied).
Consider the traditional approach first. Let's assume that Kentucky has a 40% of scoring to win the game in the fashion they did. Thus, 40% of the time, Michigan loses in regulation, and 60% of the time, it goes to overtime. By assumptions above, Michigan's win probability in this case is 30% (half of the overtime outcomes).
Consider the non-traditional approach, which is trickier. Assume here a low rate for Kentucky free throws: 50%. Thus, 50% of the time, Kentucky will miss the first free throw, and Michigan gets the ball back with a chance to score and win; assume again a similar 40% chance Michigan scores when they have the ball. Correspondingly, 60% of the time, the game goes to overtime with 50/50 odds. Thus, on the first miss, Michigan has a 70% win chance.
Unfortunately, 50% of the time, the Kentucky player makes the first free throw. There are two further cases to consider then. If they miss the second (which happens 50% of the time), Michigan has a 40% chance of winning in regulation, but 60% losing. If they make the second, Michigan just has a 40% chance of sending it to OT, where they have a 50/50 shot.
If you add all of those win probabiities up, the Non-Traditional (NT) approach, assuming the numbers above, has a win probability of 50%, which is 20% higher than the traditional approach (T). Thus, assuming the numbers and other things above, fouling was the better option.
However, that is a pretty low free throw percentage, and the chances I gave of Kentucky or Michigan scoring a basket (40%) were chosen arbitrarily. Thus, I varied each of these and produced the following graphs.
This first graph assumes the 50% (Kfs) as above but varies the Michigan scoring chance along the x-axis and the Kentucky scoring chance along the y-axis. Results in BLUE mean that Michigan would have increased its chances of winning with the NT approach; RED means a decrease by fouling early. The value shown is the difference in win probability between the two approaches.
As you can see, the (x=40,y=40) point shows the 20% increase calculated above.
I also made a graph assuming that Kentucky shoots free throws at a 75% rate, not 50%. It looks like this:
As you can see, it looks a bit different, with the non-traditional approach (foul early and get the ball back) not doing as well.
More broadly, what you can see from the graphs are this: if free throw shooting is bad, fouling early makes sense, especially if you have a good offense with a good chance of scoring. Fouling early also makes increasing sense if the other team is likely to make their last-second shot (no surprise).
Given the efficiency of our offense, and the relative non-goodness of Kentucky free throw shooting, I think we did the wrong thing.
Of course, I reserve the right to be wrong in the analysis (it was a little hastily thrown together); critque away, as you always do. :)
Given the weekly "Guess the score, win a T-shirt" contest, I found myself wondering what kinds of guesses people make. Unfortunately, it is pretty challenging to just scan through the posted guesses and get a real sense (other than most people pick UM, duh). Thus, I decided to collect the scores and make a graph. The result:
Predictions: Points UM will score (x-axis) vs. Points PSU will score (y-axis)
Click here for a larger version, if you'd like.
Users fill in a score prediction: the points Michigan will score and the points PSU will score. The x-axis of the graph shows the former (Michigan's point total) and the y-axis the latter. The line (y=x) divides the guesses into two groups; those below and to the right picking Michigan to win (and colored "maize") and those above and to the left picking PSU to win (colored "Nittany blue"). Some squares have a number in them: this shows how many people picked that particular score (oops to those who picked it second or later). I also colored my own guess in, in red, and I dropped one score where the guess was something like 127-3 (it would make the graph look bad). The last bits of data were collected around 10:30am this morning; later guesses are thus not included.
The main reason I did this was to be able to field a guess that had some "space" around it; closest to the right score wins, correct? If so, you not only want to guess something realistic but also something where not every spot around you in the graph is taken. Unfortunately, this week I guessed a bit early (before the full sample of data was taken). Had I waited until now, I might rather have guessed something like 50-15, which has a lot of room around it, or perhaps something in the 25-3 range.
Some other stats: Overall, 206 people picked UM; 13 picked PSU. For those that picked UM, the average score was 32.6 to 17.8. Does this collective wisdom serve as a good prediction? We will see. For those that picked PSU, the average score was much closer: 26.5 to 21.7. Three score predictions were most popular: 38-17, 31-20, and 31-16, each picked four times.
[UPDATE: Added "AFS" - actual fucking score - above]
Some time back, I created a small diary (click here to see it) which broke down the wins and losses of UM coaches in the modern era. The gist of it was simple: group wins and losses based on the size of the margin of victory or loss, and see what happens.
A few things stood out from that earlier post:
- Bo's first six years were ridiculous. His teams almost never lost! We'll likely never see a run like that again.
- Carr and Mo were quite comparable to the rest of Bo's career (excluding those six magical seasons).
- Carr's (very) slight atrophying was showing up in a few more close wins than what had been the norm.
Although I wanted to wait a few more years to do this, well, boredom set in, and thus again you get the Graph(TM), with Hoke's first two years included:
The graph breaks down each year into seven different groups: big wins (by 15 or more), medium wins (by 8-14), close wins (by 7 or less), ties (from when these used to occur), and close, medium, and big losses (the same margins apply).
There is also a summary graph for each coach (again breaking Bo into two groups, the first six years and the rest):
Cutting to the chase, we can observe the following:
- Hoke has restored one big part of the Michigan Expectation: a large number of relatively easy wins (dark blue part of the bar). Indeed, he already has 13 of these comfortable victories in just two years; RichRod had only 6 in three years.
- Hoke's current win percentage is in the expected ballpark (around .730, just short of the .750 we saw for Bo after '74, Mo, and Carr).
- Hoke isn't getting blown out a lot (also unlike the RichRod era, alas); an actual defense helps with this.
- Hoke's "close win" percentage is more like Carr's; a sign of the times, or a hint at future troubles?
Of course, all of this is quite premature, and the next few years will help us better understand how the Hoke era will likely proceed. And while 8-5 is OK in a given year, it is clearly not OK in the long run (at least, given the expectations we all have from decades of winning). Thus, as Hoke builds the team into his vision of Michigan Football, will he achieve at the level of Coach Carr (five seasons with at least ten wins, including one Mythic National Championship)? Will he continue to win the games we "should" win by large amounts? Will he secure his fair share of Big Ten Championships? Or (dare I hope) will he put together a run unseen since the legendary early days of Bo? Only time will tell.
My own feelings: having a real defense makes it all possible; stout defense makes most tough games close, and easier games into blowouts. If the offense starts to click, and "Good Borges" becomes the only Borges we see (particularly as the "right" parts are brought in via recruiting), it seems like Hoke is on his way to a successful career at UM.
What are your thoughts?
I was there.
The almost-perfect long weekend in the middle of the last semester of our senior year. Yeah, it was a little too expensive (even though we drove). Yeah, it made finishing our classes a little tougher (but who works much in their last semester of undergrad anyhow?). And it was a chance to see something special, a potential national championship. I had watched the last one on TV (and will never forget how clutch Rumeal was, hitting those two free throws). I had celebrated on South U. (as a high schooler) with the masses, but desperately wanted to see this one in person.
They held a lottery to see who got tickets. Can you imagine, not enough tickets to go see the the Final Four down in Louisiana? We won. I don't remember how many people applied, and I sure was hoping that senior status counted for something extra. But we won. And so, we went.
Welcome to New Orleans!
I was only worried about one game: Kentucky. Everybody thought they were the team to beat. And they were. A beast of a team. Led by Jamal Mashburn, they finished the season ranked #2 in the country (behind #1 Indiana, whom #9 Kansas later bounced to sneak into the Final Four); Michigan was #3, North Carolina #4. The closest (at the time) to all four #1 teams making it. How I still wonder about what would have happened had Indiana beaten Kansas...
Bobby K: Too Angry To Win
But I was there.
The Kentucky game went to overtime, Webber was a monster throughout. Look at his stat sheet: 27 points, 13 rebounds, 39 minutes of playing time. Yes, others had great games too (Howard, Jackson, Rose), but without Webber, the run would have ended. I saw a lot of Kentucky fans crying after the game. One shook my hand and offered up a weak but heartfelt "good luck"; I'll always think fondly of that small, silly moment. What luck did I need? I was just watching. Kentucky fans, man, kentucky fans.
One Kentucky Fan We Can All Get Behind
So we celebrated. A great night out on the town, as only the town that hosts Mardi Gras can deliver. And the knowledge that we had one more game, a winnable game against a good (but not great) team.
Mardi Gras Girls: No, We Didn't Meet Them
And I was there.
The team didn't seem to have their legs that infamous Monday night against UNC. I think Kentucky took a lot out of them. Watching UNC breeze by a lousy Kansas team on Saturday, I was convinced we had the tougher road, and during the last game it showed.
Don't Worry Sir, We'll Lose Easily
But those five guys (and yes, the others, too) had something, a toughness, a resilience. We managed to pull ahead with five minutes left. Someone told me one of those stupid stats which make you feel good but only in a false-bravado kind of way: Michigan hadn't lost a game that year when they were up with five minutes left. My friends and I exchanged high fives. We're going to win!
We Exchanged High Fives
But somehow they couldn't keep a guy in Donald Williams' face, and he kept making shots. Why was Jalen on him? I thought King would have been a better choice, more athletic, if shorter. But there was Williams again, making twos, making threes, and suddenly we were down.
F---ing Donald Williams (Looking Old Now)
I was there, and I remember when Webber traveled.
The whole place screamed "walk!" but somehow they didn't call it. Later, I felt thankful for the refs: they didn't want to decide the game on a stupid play like that. They just wanted to see it play out. But Webber walked, and then started dribbling like crazy up the court.
Fisher: What I Would Have Looked Like, Had We Had One More TO
Most of us were screaming "Time out!" How many goddamned basketball games have you watched where there are about 100 timeouts at the end, play moving glacially forward, the last 30 seconds taking 20 minutes? How can a team actually run out of time outs? I bet you Fisher thought about that for a long time after. If they'd just had one more timeout ...
Pelinka: Open For A Three?
Pelinka was open. The UNC guys were running around, crazy, double-teaming (turned out to be a good decision, huh?), and if Webber had just swung the ball to someone, anyone, I bet it would have made its way to Pelinka in the corner. You know, the guy who makes threes. For years, I would wake up in the night, and think about "what if Pelinka had gotten it in the corner?" Thankfully, that went away. Sport fans, we're nuts.
I was there, when all the fans looked at one another, confused.
What happened? Then some guy two rows in front of me, in that f---ing monster of a building where there wasn't much of a scoreboard anywhere near the court for players to see, said simply: "They don't have any more timeouts. That's a technical foul. We're going to lose." Our section, crazy with noise moments ago, jumping with the certainty that our guys were going to pull it out, fell slowly quiet. The UNC fans started to figure it out too; they all started to go nuts, as did their players on the bench. I still can't figure out the Dean Smith voodoo, his two championships not remembered for his team's greatness, but for the other team's failure in the clutch. For this reason, I still harbor an irrational hatred of Dean Smith.
The Dean's Voo-doo Victim #1: Fred Brown
Watching the brilliant documentary on the Fab Five the other day brought this flood of memories back. And what memories they were, and are. I've enjoyed the current season immensely, as Beilein and Co. have built up a team that is easy and fun to root for. But for two seasons in what seems like another lifetime, we had something more than that, something so rare and special that it is hard to believe it was Michigan basketball. We had rock stars for a basketball team. We cheered them on when they won, and we wept with them when they lost. We loved them, and so we wept.
It was a long drive home.
A Long Drive Home
As for the memories I have, well, scandals, banner-removals, or any other "official" process can't touch them. A memory of my own youth, a memory of a time where five kids made national headlines simply by being who they were, a memory filled with many joyous headlines, and finished with an unforgettable exclamation point, perhaps an appropriately tragic ending.
I graduated, I moved out of the state, but I will always have those memories.
You see, I was there.
[Ed-M: Bumped for excellence]
OK, this is not actually a work of staggering genius. You should definitely read the Dave Eggers book it refers to, though - good stuff.
Rather, it is a brief and simple explanation of everything that has happened or will happen in Michigan football. It is based on one simple idea: if you win a lot, you are a genius. If you win most of the time, the fans will grumble but tolerate you. If you lose a lot, you will get fired. I think we all know this.
To make this case, I have simply plotted the wins and losses over the years on the following bar chart, broken down by margin of victory. Here is the graph:
As you can see, the years increase over the x-axis (horizontal direction), and the number of wins and losses are plotted on the y-axis (wins go up from 0, losses go down; ties, when they still happened, are split as half for a win and half for a loss). Wins are broken down into three categories: wins by 15 or more (navy blue), wins by 8-14 (blue), and narrow wins by 7 or less (light blue); losses are similarly split apart, and ties are left white.
I think the graph shows a few important things. First, what an amazing run we had as fans. For almost 40 years, watching Michigan football meant losing a couple or three (close) games, and winning the rest; I wonder if there is any stretch like that in modern football history.
Second, and perhaps most key, is the era that spoiled us: Bo's first five years. What a f***ing first impression that man made! After a "pedestrian" 9-3 season in which he upset the best OSU of all time, Bo's next four years featured: a 1970 loss (by 11 to OSU), a 1971 loss to Stanford (by 1 in the Rose Bowl), a 1972 loss to OSU (by 3), 1973 tie (with OSU, and you know how that story ends), and a 1974 loss to OSU (by 2). Wow!
For those of you not old enough to remember (and this includes me, barely), can you imagine such an era? With a little more luck, Bo could have won three or four national championships. Simply stunning, and what a great way to turn yourself into a legend.
Third, the graph shows I think that in the following years, Bo settled into the pattern we are more used to, with a few losses here and there, and one Year of Infinite Pain before such years were named and blogged about. That year of course was 1984, a year in which Bo went 6-6, almost beat "national champion" BYU in a bowl game, and caused Bo to rededicate himself for his final stretch run.
Fourth, I think the graph shows why some people were unhappy with the Lloyd Carr era - though the general year-to-year record remained very similar to Bo's steady state (which I will demonstrate further below), there are a lot more close wins; in other words, the team continued to win at about the same pace, but more of those wins were in games that could have gone either way. And this makes sense: think back to all those last-second wins against Penn State, Michigan State, and others - we were continuing to win, but not in as dominant a fashion as we were used to.
Finally, I think the graph shows why RichRod was in no way going to get a chance to continue: too many losses, and too many of those in non-competitive games. It was just too much.
Anyhow, to sum up each coach, I also made a plot of their overall win/loss percentage. It is available here:
Instead of just showing Bo's entire history smashed into one bar, though, I separated it into the first 5 years and the rest. The first conclusion from this graph: how similar Bo, Mo, and Carr were, once you take away Bo's first five years! Almost identical, except for that one small difference: that Carr had a noticeable number more of close wins, and both Mo and Carr had a few more not-so-close losses.
And though it's unfair to take Bo's first five years out, those five years were so crazy and unusual, they should be separated and celebrated for what they were: one of the best five-year runs in modern football history. It is those years, I think, where we derive our modern expectations. We think we should always be like that, when in reality it's quite difficult to expect such near-perfection year to year. I think that expectation is what drove all the Carr grumbling, and perhaps caused us all to look to "reboot" the program instead of just "maintain" it.
Imagine a different universe where Bill Martin, instead of looking for the best national coach, was looking for someone steeped in the Michigan way, to maintain its current glory? Who would he have hired? Would one young coach at Stanford, full of Michigan spirit and not yet too full of himself, be considered for the opening? One can only wonder at what might have been, had we been happier with what we had.
[Edit: when I talk about Bo's first "five" years, I mean 1969 through 1974, which as you might have noticed, is six years.]
[Edit (2): Replaced stupid imageshack links with links to Picasa. Imageshack banned the photos; apparently too much traffic!]
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.