This list is completely arbitrary and not a genuine analysis of the relative merits of state fossils.
two University of Colorado political science professors say statistical analysis indicates firing a coach for poor team performance is far from a surefire way to turn things around, and, in some cases, may actually harm a team's future performance.
Looking at results for four years after a coaching replacement, the study concluded bringing in a new coach, on average, had a negligible effect on a team's win-loss record.
"I had always watched these teams fire coaches, pay for a buyout and then hire more expensive coaches and I wondered, 'Are they actually getting anything out of this?'" said Adler, a University of Michigan alumnus and college football fan. "What we find is, as you go out to the fourth year, the difference between teams that did and didn't replace their coaches were just nonexistent. They were performing just about the same."
How a Michigan alumnus and fan could write a study concluding this is beyond me.
Seriously, though, Michigan is clearly an outlier -- we are a premiere program. I think this study is relevant to teams like Minnesota, who fire good coaches (Glen Mason) thinking that they are capable of being more than they are. But the new coach can't improve the facilities, can't change the amount of local football talent, etc.
Things We Know This is obvious territory: the Spread's "Score whenever possible" mentality renders T.O.P. moot as a way to tell which team was playing better at the end of the game. Thing is, T.O.P. was never meant to be an in-game metric, or shouldn't have been. It's an IN-GAME metric. The idea isn't to show who's dominating the game, but what shape the defense is in. Its continued popularity on networks is likely due to the ease with which it's calculated. I think we can come up with a much better metric for that, and retire T.O.P. Good guesses:
- Offenses tire less quickly than defenses. Giving blocks is better than receiving them. Reacting to a play that you didn't call puts you at a disadvantage. Pushing past a lineman to the one place he doesn't want you to is more tiresome than shoving one (a lineman) back from the one direction you know he wants to go to. There's a lot of chasing involved.
- Players recover from being tired in real time (not Game Time)
- Fatigue is generated during plays, not between them
- Greater fatigue reduces the effectiveness of a defense because a) tired players can't react as well, and b) substitutions are inherently a reduction of the talent put on the field.
- While fatigue can be recovered from during the game, the more that is drained, the lower the maximum recoverable energy.
Things We'd Like to Know I want a metric that:
- Gives an approximate likelihood of the offense scoring based on defensive fatigue.
- Since the above would be very difficult, the metric should at least standardize defensive fatigue, to be used as a reference point
- Is fairly easy to calculate with widely available stats
Pure guesses (opportunities for me to look stupid):
- Energy is recovered at an exponential (logistic? Math majors help! -- i mean a curve that slows as it goes, or y=x^[fraction]) rate.
- More plays depletes a defense's performance
- More plays in progression depletes a defense's performance faster
- Available statistics allow us to create a metric for a defense's performance based off of these fatigue factors
Let's Talk Variables It's hard to count actual time during plays, at least for us laymen. However, number of plays per drive is easy to calculate. I would like to count plays that are replayed due to penalties unless it is blown dead. I'd like to count overall time elapsed since the last defensive play.
However, actual time is hard to come by. We have the time the game took to play. We have the in-game time. But short of having a DVR with a timer, I haven't been able to find any real time metric. If someone can find me a place where that is kept and freely accessible, I will use it. Otherwise, we're going to have to ignore regeneration based on real time.
The atom for all of this is going to be plays run from scrimmage.
Defensive plays from scrimmage increase defensive fatigue. Offensive plays from scrimmage decreases defensive fatigue. Since they use so many backups, special teams plays do not count.
The test for it will be yards given up, since scoring equates too much with field position. Why yards? Because we know that yards gained and winning are correlated. A defense that gives up more yards is more likely to be scored on.
Needs a name. For now: SCHWING.
Defensive SCHWING: How it Works What we will create is a basically running play counter:
- Higher number indicates higher level of defensive fatigue
- Defensive plays count for +3 for the defensive team
- Offensive plays count for -8% for the team on offense
- No team can go into negative.
- Commercial Breaks, Time Outs and Reviews count for -15% for both teams
- Half Time reduces all fatigue by 80 percent (rounded to nearest integer)
The Spreadsheet is here. Click on each image for full size
Michigan vs. Western Michigan:
Averages: Michigan 21, Notre Dame 17
Michigan vs. Eastern Michigan:
Averages: Michigan 21, EMU 14
Remember, higher is bad. It means that Eastern Michigan, over the course of the game, faced a Michigan defense operating, maybe at like 79 percent of its capacity, because of fatigue, while Michigan faced EMU's at, say, 86 percent capacity.
Keep in mind, it's impossible to be 100 percent the whole time. But notice how much better Michigan's defense was against Western, who's not much more talented than Eastern Michigan. There's a big difference in how well the Wolverines let the defense rest in Game 1, whereas they were considerably harder on the D in Games 2 and 3, whether by turnovers or quick scores.
So....Correlation?If Michigan's defense gives up more yards when its SCHWING level is high, that would indicate the metric works, right?
Notre Dame de South Bend:
The yellow lines are offensive plays. The ones sticking out below were negatives (or holding penalties).
Michigan gave up 236 yards (5.02 yards per play) to Eastern when our SCHWING level was 20 or higher. We gave up 61 yards (2.26 yards per play) when it was 19 or lower.
It was actually more drastic than that. A lot of short yardage was given up in the 2nd half against the backups in soft, clock-killing defense. The big plays in the first half were all during high-SCHWING periods. The 3-and-outs were during low ones.
Against Notre Dame, Michigan gave up 188 yards (6 yards per play) 2 with a SCHWING under 20. Not good. We gave up 294 yards (6.125 yards per play) when SCWING was over 20. Also not good. There wasn't as much SCHWING variance, however, against Notre Dame as there was against EMU. The Wolverine defense played much more of that game tired. If you take out the 27 yards on the last play, our SCHWING under 20 YPP goes down to 5.37 (161 yards). I think that just says ND's offense was pretty good (or held like bitches).
WMU was the opposite. With SCHWING under 20, the Broncos put up 81 yards (2.79 YPP). When SCHWING went over 20, they put up 222 yards (6.17 YPP). If I excise the 73-yard TD, it's still 4.26 YPP. But it shouldn't be excised -- that happened near the peak of Michigan's defensive fatigue during the game.
Here's what yardage against us looked like against WMU as SCHWING went up:
As the season progresses, I'll do more plotting to see if this sticks, but so far this seems a little bit correlative. If I had to guess, I'd say ND and their max-protect-bomb strategy caused the difference.
All told, when Michigan's SCHWING was under 20 this year, our defense gave up 330 yards (3.79 YPP). When it was over 20, we gave up 752 yards (5.74 YPP).
I'm sure we could play around with the factors, but as a very basic statistic, it seems to be fairly predictive. When the defensive fatigue rating for a given team is high, they are likely to give up more yards, in our extremely small sample of course. Feel free to plug in other games from years past.
Obviously, scores come after drives.
The thing to look at isn't the end of drives, but the start of them: what shape is the defense in as Team X gets the ball. For example, when Michigan put up three quick scores on Western, they got the ball each time with WMU's defensive deficiency rating already well over 20.
Similarly, EMU got the ball down 38-17 and had a magnificent drive (which should have been a TD), but every drive before that in the 2nd half, Michigan's D started under 10. The real backbreaker for them was when the QB buckled and fumbled -- that gave Michigan the ball back with EMU's defensive SCHWING over 20.
Couple things jumped out, though. The quick scores (Brown's long TD run, the kick return for TD against Notre Dame, Denard's existence) were answered with scores against Michigan, or long periods of scoring drought. Interceptions, too, created a fast turnaround. Look at Stonum's return: not only did it put Michigan back on the field after a tough stop (helped by Cheeseburger Charlie's inability to get a few plays called in*), but even more it helped the Domers' defense rest away the effect of that good early drive by Michigan.
Note how different this is from Time of Possession. By basically counting plays back and forth, we can see when one team or another is particularly likely to get scored on.
I think I'm gonna keep using this as the season progresses. It's pretty easy to calculate, especially if you have the spreadsheet handy. If it holds up as a decent indicator of expected defensive performance, maybe an addition to the UFR charting?
UPDATE 9/23:Bad news. I ran all of the plays from all three games (by ND, EMU, WMU and MICH) and there's such a small correlation it's almost not worth it:
Of course, it's not conclusive. Wait until we have at least 1,000 plays from scrimmage to analyze (we're at about 450 right now).
When SCHWING was 20 or over, offenses gained 1363 yards on 251 plays, and had 23 "big" plays (15 yards or more). That's 5.45 YPP, and 9.16% chance of a big play.
When SCHWING was under 20, offenses gained 984 yards on 175 plays, with 15 big plays. That's 5.67 YPP, and 8.57% chance of a big play.
Not exactly correlating.
One thing of note: Carlos Brown's 90-yard scamper came at a SCHWING level of 17. In fact, a lot of big plays took place around a SCHWING level of 17 to 25. I don't know that that means exactly, except perhaps that's early in drives but seldom right at the start of them. Or that 17 to 25 is the bell curve. This could simply be because early in drives there's more field to go, thus more space for big yardage.
Situationally, there was a small difference. With SCWHING under 20, 26.55% of plays from scrimmage resulted in a 1st down or touchdown. When SCHWING was over 20, that number rose to a 31.62% conversion rate. The touchdown ratio went way up: 7.11% over 20, and 1.69% under 20. But I can't tell you how much of that is field position -- the likelihood of scoring goes up when you get closer to the end zone, and SCHWING goes up the longer a drive lasts, meaning high SCHWING generally takes place deep in an opponent's zone. So the TD ratio means pretty much nil. Anyway, the average SCHWING level before plays that resulted in 1st downs and touchdowns was about 24; the level before plays that didn't convert was 22. Small difference.
I'm not giving up just yet, though. I'm gonna track a few more games, because I think I'm getting thrown off by big plays late in the WMU and EMU games, when backups and whatnot were in (high SCHWING is supposed to necessitate more backups, so if the backups go in when SCHWING is low, that changes things).
Here's the big plays with Low SCHWING this year:
|40||WMU||17||WMU||43||TD||(1st and 15) Robinson, D. rush for 43 yards to the WMU0, 1ST DOWN MICH, TOUCHDOWN, clock 03:57.|
|3||ND||6||MICH||24||1ST||(2nd and 9) ALLEN rush for 24 yards to the ND45, 1ST DOWN ND (Williams, Mike).|
|6||ND||15||MICH||24||1ST||(3rd and 4) CLAUSEN pass complete to RUDOLPH for 24 yards to the MICH25, 1ST DOWN ND (Williams, Mike).|
|24||ND||19||ND||40||1ST||(3rd and 12) Forcier, Tate pass complete to Mathews, Greg for 40 yards to the ND41, 1ST DOWN MICH (WALLS).|
|37||ND||19||MICH||19||1ST||(2nd and 6) CLAUSEN pass complete to ALLEN for 19 yards to the MICH22, 1ST DOWN ND.|
|86||ND||14||ND||24||1ST||(2nd and 14) Forcier, Tate pass complete to Stonum, Darryl for 24 yards to the 50 yardline, 1ST DOWN MICH (McCARTHY, K.).|
|100||ND||17||ND||16||1ST||(1st and 10) Minor, Brandon rush for 16 yards to the ND33, 1ST DOWN MICH (McCARTHY, K.).|
|129||ND||10||MICH||15||1ST||(1st and 10) PENALTY MICH pass interference (Cissoko, B.) 15 yards to the ND19, 1ST DOWN ND.|
|205||ND||11||MICH||27||1ST||(1st and 10) CLAUSEN pass complete to TATE for 27 yards to the ND47, 1ST DOWN ND (Floyd, J.T.).|
|9||EMU||3||EMU||30||1ST||(1st and 10) Brown, Carlos rush for 30 yards to the EMU21, 1ST DOWN MICH (CARDWELL, Marty).|
|51||EMU||10||EMU||26||1ST||(1st and 10) Forcier, Tate pass complete to Odoms, M. for 26 yards to the EMU43, 1ST DOWN MICH (MAY, Chris).|
|54||EMU||19||EMU||22||1ST||(3rd and 1) Shaw, Michael rush for 22 yards to the EMU12, 1ST DOWN MICH (SEARS, Johnny).|
|63||EMU||17||EMU||90||TD||(1st and 10) Brown, Carlos rush for 90 yards to the EMU0, 1ST DOWN MICH, TOUCHDOWN, clock 07:15.|
|156||EMU||18||EMU||36||TD||(1st and 10) Robinson, D. rush for 36 yards to the EMU0, 1ST DOWN MICH, TOUCHDOWN, clock 07:14.|
|175||EMU||11||EMU||24||1ST||(1st and 10) Cox, Michael rush for 24 yards to the EMU41, 1ST DOWN MICH (PALSROK, Tyler).|
Three of those plays are garbage time (205 ND, 156 and 175 EMU). One is Shoelace's incredible Yakety Sax Moon Run. Another is Carlos Brown's 90-yard run. Three more are big plays against EMU's defense. The rest are plays from the Notre Dame game, which, like, they have a great offense.
This isn't nearly enough to put SCHWING back on the map. But they're certainly opportunities for SCHWING to look stupid.
* Weis: "It's MMFFPHHHI-RIMMMFGHT MMMPHTWINS!"
Jimmah: "What coach?!?"
Weis: "I MMMFFFPHH SAID RUNMMMMPHHH ISO MMPPPHHH RIHMMMMPPHH"
Jimmah: "Coach, I can't hear you! Take the ham sandwich out!"
Weis: "I MMMPPHHFFF RIMMMPPHHHHHHFFF SPLMMMMPHHFFF DAMMIT!"
Jimmah: "Dammit, coach? What? What? Dammit -- TIME OUT"