mesmerism! presidential assassinations! circuses on fire!
As you most likely know, the National Association of College Directors of Athletics (NACDA) awards an annual Director's Cup to the nation's top athletic program, based on a points formula that encompasses all men's and women's varsity sports (more info here). Stanford has won the award for the past 17 years in a row, but Michigan has been among the top performing schools in the annual standings, finishing in the top ten in 14 of the 18 years the rankings have been compiled.
Unfortunately, the past two seasons have been down years, with Michigan placing 25th (2009-2010) and 15th (2010-2011). With some resurgent programs this year, I have been hoping that our maize and blue heroes could return to their rightful place in the top ten. I decided to take a look at MIchigan's current status and forward-looking expectations.
In the last published update (3/22/12), Michigan fell from 5th place to 12th place in the standings. This Thursday, the updated Winter standings will be released, adding results for men's and women's basketball, men's swimming, and fencing. If my figurin' is correct, the updated standings should look something like this:
Michigan should climb barely back into the top ten, while Ohio State shoots up to the number two spot, based not only on basketball success, but also on winning the recent national fencing championships held in Columbus. Unfortunately, the NACDA points accumulated by the Buckeye sabre-rattlers will exceed the total points registered by the combined efforts of Michigan's men's and women's basketball teams plus Ice Hockey team. Curses! Foiled again. Yeah, the scoring system is a little flakey.
Looking ahead to the home stretch, some schools are traditionally stronger in spring sports and are likely to make a late move. If we were to project that each school's spring teams will match their performance from last year and tally up the resulting standings (allowing points for no more than 10 sports in either men's or women's categories), the projected final standings would turn out like this:
Of course, there is likely to be a great deal of variance in actual results, but this should pretty well identify who the top contenders are.
Michigan's spring prospects vary by team. Wolverine men and women gymnasts and tennis racketeers are likely to pile up some points, but it will be a challenge to just match the output of last year's successful teams. Struggling golf teams on both men's and women's side will be hard pressed to make the NCAA's this year (still, we can hope). The inaugural men's lacrosse team will not register any NACDA points this year, but it can only help to have a men's and women's varsity lacrosse program in years to come. Prospects also do not look very promising for the baseball team or either track and field team. Surprise us, please!
On the plus side, there is room for improvement over last year from the young and developing softball team, the women's rowing team, and the women's water polo team. Gals, we're counting on you!
It is all but certain that Stanford will repeat as the trophy winner for the 18th straight year. Ohio State, Florida, and California are likely to battle it out for the runner-up spot.
Michigan has a very realistic shot at returning to the top ten. We should almost certainly improve over the past two seasons. Sadly, there is very little chance of a top five finish this year or of overtaking that ohio school. Don't taze me bro', I'm just crunching numbers here. I personally have faith in Dave Brandon's determination to continue to elevate the competitive level of all of Michigan's varsity programs and I expect that we will once again become a consistent top finisher in the NACDA standings. Go Blue, one and all!
Signing day is fast approaching and anticipation is rising to fever pitch. So where will Michigan's 2012 class wind up ranked? I thought I would do a little prognosticating with a heavy dose of disclaimers. This analysis is based only on Scout, since they provide the most visibility into their ranking system. Their scoring system is somewhat arbitrary (maybe even a little silly?) and the final rankings are not profoundly meaningful, as I'm sure we all know. Still, we are just trying to have a little fun here as we bide our time ever so impatiently.
Also, I am referencing their "Commitment Tracker" which contains information some may classify as dubious. The finalist lists are somewhat suspect, and the predictions of the two analysts are arguable (some of the picks are from outside the finalist lists). So, take it all with a mountain of salt and let's have at it!
Here are the current top 10(ish):
So how might this change from now to Signing Day? Let's focus first on Michigan's prospects. Here are the most likely additions to the class and the number of points they would add to Michigan's point total:
So if Michigan were able to bring in the mother lode and sign all of these prospects, it would push their total points to 4810 (counting only top 25) and move them into the #1 slot! (if nobody else signed anyone). Of course, it is highly unlikely that Michigan will strike pure gold while everyone else strikes out, so let's look at this a bit more realistically.
It does seem likely that the Maize and Blue will add to their current commitments and a jump of 600 points or more is not out of the question. So which schools would be in a position to finish above them? This will depend on whether the other schools have roster space to add more scholarship players and how likely they are to land additional blue chips.
On the subject of how they might close, I considered how many prospects in the Scout 300 they are considered finalists for. I also make note of who at least one Scout analyst thinks they lead for. Of course, they could also sign additional players outside the top 300 and each such player would add about 75-125 points to their total. Let's look at each contender.
Alabama- With 27 commits, they can only add one more at most? (I may be mistaken, but I believe the SEC is planning to limit schools to 28 this year). They are in the running for 6 top prospects and are projected by at least one analyst to lead for two: Eddie Goldman (worth 298 points) and Dalvin Tomlinson (209). The Tide will be tough to roll.
Texas - I'm not sure how much room they have beyond their 24 commits, but they are finalists for 4 top prospects and lead for one: Dalton Santos (215). Michigan could pass them if the Longhorns come up short.
Ohio State - There is some question as to whether the Buckaroos are already over the scholarship limit. We will have to see whether or not that is an Urban myth. They are listed as a finalist for 7 top prospects and are said to lead for 2: Armani Reeves (fergodsakes no!) and Kyle Dodson (207). Assuming they stay within their limits, it would seem Michigan has a good chance to pass them up in the final rankings.
Florida - The Gators, at 20 commits, may have available space (or not; available scholarship info is hard to come by and I'm not going to turn a fun little exercise into a major research project). They are finalists for 8 top prospects and are projected to lead for two: Stefon Diggs (299) and Nelson Agholor (217). Still, Michigan should have a big enough cushion to avoid becoming gator bait.
Miami (YTM) - The Hurricanes already have 31 commits so (wait, what?!) so I really don't know what to make of that. They are listed as a finalist for 5 top prospects and projected leader for one: Tyriq McCord (208). If Miami passes Michigan in the final rankings it's time to open up yet another NCAA investigation.
LSU - Listed as a finalist for 3 top prospects and a leader for none; highly unlikely to close the gap with the good guys.
Notre Dame - Not known for oversigning, the home stretch for the Irish may be limited by available slots. They are on the finalist list of 9 top prospects but the Scout guys don't see them landing any of them. Barring unforeseen leprauchan chicanery, likely to remain behind Michigan.
South Carolina - With 24 commits in the fold, only 2 top prospects on the radar (with no projected signings) and a sizeable gap, they Gamecocks are unlikely to rise in the pecking order.
Florida State - The Seminoles are the real wild card with only 16 current commits and 9 top prospects in the wings. Four are predicted signees: Ronald Darby (300), Eddie Goldman (298), Jameis Winston (299), and Tracy Howard (298). With the ACC apparently determined to win the oversigning cup, Florida State seems to be the team most likely to close strongly. It's even possible they could jump MIchigan, but I wouldn't stick a spear in that.
UCLA - With a class of 25 already, and no projected signings among the blue chippers, the Bruins are too far back to maul Michigan in the rankings.
The Rest - Everyone else is most likely too far back, point-wise, to threaten Michigan's final class ranking. Texas A&M, Oklahoma, Georgia, Auburn and Stanford may be candidates for a strong closing stretch.
Well I hope we all had fun and are not taking this too seriously. Anyway, there is actually an outside chance that, if all the planets align properly, Michigan's recruiting class could finish with the top ranking on Scout. More likely. a third place finish seems about right. I highly doubt we could drop below the #5 spot. The one thing we can almost certainly predict is that there will be some surprises. We will all know soon enough.
Edit: - I corrected the point values associated with each recruit caused by a slight misunderstanding of Scout's formula. It was mostly just a point or two adjustment upward. More importantly, as elaydin points out, Scout only counts the top 25 recruits, so I made that adjustment as well.
“The Game” has come and gone, the good guys prevailed, and our collective mindset has mostly reoriented to the future, as visions of Sugar Bowls dance in our heads. So is there any reason to rehash the already much-debated issue of the Toussaint Touchdown Takeaway?
Of course there is, because such things live on in Michigan lore forever and sometimes, you have to beat a dead horse just for the sheer fun of it. Besides, I had an unsatisfied curiosity combined with some unaccustomed free time, so I set about to try to resolve the controversy once and for all.
This analysis may not appeal to you unless you are almost equal parts Michigan football fanatic and geometry geek, but in the end, I believe there is an important point to be made here. To discover my purpose, you will have to read on (or cheat and jump to the end).
The Evidence Speaks to Us
I start with Exhibit A below, a camera view that seems to suggest that Fitz planted his knee with the ball just short of the goal line. Almost certainly, it was this view that convinced the replay official to reverse the call on the field and overturn the touchdown. The shot appears to have been taken by a crane-mounted camera hovering about 10 feet in the air just beyond the goal line. It is not an ideal angle from which to make a definitive call. The knee may or may not be in contact with the ground and the relative position of the ball is distorted slightly by the angle. (Note: for formatting reasons, I am including scaled down versions of these screen shots; full resolution captures were used for the actual analysis. Click the photos for larger versions).
I use Exhibit A not to attempt to resolve the issue at hand, but to call attention to the item highlighted in magenta. There is a cameraman clearly visible in the shot and it is his footage that will provide the basis for further analysis. We don’t know his name (Abe Zapruder?), but we have a very good idea of the physical position of his camera. The dashed boundary line he is standing very close to runs 12 feet outside the sideline. By analyzing statistical data on the average height of college cheerleaders, we can fairly accurately estimate the center of the lens to be 5’ 4” off the ground. I estimate his standing position to be 11 feet east of the side line and 2.5 feet south of the goal line. These estimates probably place the camera position reliably within an error sphere less than 1 foot in radius. This is important as we move forward with the analysis.
Let us move on to Exhibit B, which was definitively taken before Toussaint’s knee fell to earth, and Exhibit C, a shot in which he is definitely down. The time interval between these two shots is presumably 1/60th of a second, given the parameters of 720p HD video. I will focus my attention on Exhibit C.
The time has come to let mathematics work its wonderful magic. Again, the viewing angle is not perfect, but because we were able to accurately determine the viewing position of the source camera, some surprisingly precise calculations are possible.
The dimensions and positions of the gridiron lines and hash marks are well known and presumably accurate. The only thing I am not quite sure of is the crown of the playing surface, which appears to be about 6-9 inches at midfield.
This allowed me to create a three-dimensional computer model of the playing surface and made it possible to determine the orientation of the camera (azimuth, elevation, zoom, and tilt) by matching the grid lines appearing within the frame with that of the rendered computer model.
Knowing this, we can now focus on the position of the ball within the frame. A more closely-cropped view is presented in Exhibit D. The projection of the ball in the frame spans about 40 pixels. Therefore we can determine its position within the 2 dimensional space of the video frame to an accuracy of about a quarter of an inch.
The real world has the inconvenient habit of being three-dimensional, so there is one additional parameter required to ascertain the position of the ball relative to the plane of the goal line. This would be the distance from the camera to the ball, or alternatively, the perpendicular distance from the near (Zapruder) sideline to the ball. By examining other angles from the game video and observing grid lines, hash marks, and end zone lettering, this can be determined to be about 90 feet, plus or minus 2 feet.
The final calculation will be slightly sensitive to this distance, so I went ahead and determined the corresponding position of the ball over a range of two foot intervals between 88 and 92 foot distant from the sideline. The plot below (Exhibit E) shows a top down projection of the ball’s position relative to the goal line over the range of possible values. Due to the near perpendicular viewing angle from just off the goal line, the error contribution from this uncertainty is quite small (.3 inches per foot of error) and yet this is the largest source of potential error. Any imprecision in establishing camera position is largely cancelled by adjusting angles to precisely overlay grid line positions within the frame. I won’t bury you with an avalanche of error sensitivity equations; suffice it to say that I am confident that the final estimate of ball position relative to the goal line is accurate to within half an inch.
Based on the best estimate of distance from the sideline (center ball), the results sadly report that Toussaint is holding the ball 2.5 inches short of the goal line with his knee clearly down. So, technically, the officials got the call right. Did the replay official have irrefutable evidence to overturn the call? Of course not! The ball was just inches from the goal line and he did not have the resources to make a definitive determination.
The play was so close that it was not humanly possible for an official on the field to make the call with complete certainty. The difference between touchdown and being down short of the goal line was a matter of inches and hundredths of a second. While the determination was ultimately correct, I think we can also safely claim that the replay official overstepped his authority by reversing the call on the field, based on the “irrefutable evidence” criterion and the limited technology available to him.
But my real point in all of this is to call attention to the fact that making an accurate determination is possible and current technology could accomplish this in real time, using techniques very similar to those employed to superimpose the first down line over the playing field, or track pitch trajectories in a baseball game. There is no need to put sensors in the ball or anything like that and accuracy within a fraction of an inch can be achieved. Higher frame rates and faster shutter speeds (super slow motion) improve the accuracy further.Multiple camera angles help as well. Cameras already have sensors to report their positions and orientations. I am calling on companies like SportVision that do enhanced sports graphics to develop the software to provide accurate ball positioning information to the fans and, dare I say, to the replay officials so that in the future, key plays like this can be accurately adjudicated.
We all love the in-depth analysis provided by Brian's UFR posts on MGoBlog. But sometimes the voluminous stream of information can be daunting.
I have created a web application to make viewing of UFR data easier and more powerful. You can step through the game analysis play by play or search and filter using a wide range of criteria. For any play, you are just one click away from viewing the corresponding video clip. I am now happy to make this app available to the MGoBlog community.
Disclaimer: This is a user-generated project and not an official feature of MGoBlog. I am offering this on a trial basis. While I intend to continue to support and update the program throughout the season, I can offer no firm promises or guarantees.
I have created a simple web site from which you can launch the viewer for your game of choice. There is more information at the web site. It can be found here:
In the future, UFR data should be viewable in the utility within 15 minutes of the UFR being posted on the main page of MGoBlog.