i think the misleading thing in the EMU game is the TOP would have been higher had UM been playing someone else. the TOP against ND was higher not because of a different strategy but, instead, because the ND line and secondary stopped runs that squirted loose. when you have players thrashing 50 yd runs, the TOP plummets.
Replacing "Time of Possession" with "SCHWING"
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"
well, yeah, that's why TOP sucks.
EMU's TOP was better than Michigan's 2-to-1. But the SWING numbers for the whole game were about the same as the ND game. They were still in EMU's favor, but a major SWING against EMU early in the 2nd half was their doom.
Having just watched the Colts beat with Dolphins with 14:53 TOP, clearly you're onto something that's changing in the game. GB is exactly right-- if EMU had linebackers and DBs who could tackle, TOP would have looked much different.
My favorite stat of the game: Michigan had 8 different players who rushed at least one time against EMU. EVERY ONE of them gained at least 10 yards on at least one carry. I would venture to say that that had never happened before in Michigan football history...
Man, I hate to say this to what is such a quality article, but I pulled a tl;dr on this one. Love what bits I actually read though.
One potential problem is that this metric conflates TOP with field position. Field position is very strongly correlated with the number of consecutive plays, and scoring is very strongly correlated with field position. This metric increases for every play that the defense is on the field, which means that the field position is getting worse and worse for the defense, and thus the likelihood that the offense is going to score is significantly higher without even accounting for fatigue.
Trying to capture fatigue on a drive-by-drive basis rather than play-by-play might work a bit better. Certainly fatigue plays an element in how the defense performs, it's just hard to tease out a metric for it from the available data.
#1: If you have a really good defense, they still get out there, stop the other team after three plays or maybe two series', and then the O is back on the field. Even if the O scores quickly, one or two first downs, drives consisting of 5-6 minutes, plus the TV tiemouts during changoe of possessions amounts to some rest. With a stout defense, TOP would still balance out because you force their offense off the field quickly.
SO--the team with the better defense, and the better conditioned team, still comes out ahead.
The X factor is turnovers: Last season saw not just tons of "3 and oots"--but many more possessions for the other teams, and those are "quick" time turnovers--no chance to even take the helmet off if you fumble a punt, kickoff, or give the ball back quickly without even generating a first down or two.
#2: At what point do you go from trying to score every play (or maybe not "trying" to score, but that is the nature of this offense, especially if you are highly skilled) to just trying to run down some clock with first downs and such. AND--can you employ an offense that does both (other than telling your players to fall down after gettin a first down or something)?
#3: At SOME point, you run into defenses that can stop you, or your offense just doesn't gel. You NEEED your defense to generate more possessions, or you just need your offense to deal with it and grind out that 23-13 win and hold onto the ball.
I don't think there's anything here to tell a spread offense to do anything but SCORE SCORE SCORE DAMMIT SCORE. However, there is a downside to that.
Remember Barry Sanders -- people talked about this same effect. Either he'd be caught behind the line for a 3-and-out, or run a TD. Either way, D is right back on the field.
If anything, as you point out, it may mean a spread team is more susceptible to being scored on after a turnover.
But, like, yeah, don't turn the ball over -- we knew that.
So no lessons here. Just hopefully a better metric for how tired guys probably are.
I'll have to take more time to digest this later but a couple of thoughts come to mind real quick.
RE: Real time per play.
Watching games on DVR I've noticed that if I hit the '30 second skip' feature right after the tackle is completed, I'll end up a few seconds before the next snap. So without going into nerd mode I think a baseline of 30-35 seconds of real time between plays is pretty solid. When Michigan is up tempo, I usually have to hit the 'back-up' feature once or twice. So maybe using 25-30 seconds of real time between plays is good here. No huddle, 20-25 seconds?
Also maybe using the duration of the game (typically available in official game books), minus 60 minutes of game time, minus 20 minutes for half time, all divided by total plays would be useful for figuring out average recovery time between plays. This would be crude but reasonable.
Example: EMU v. Michigan lasted 185 minutes. Subtracting 60 minutes of game clock, and 20 minutes for half time, leave 105 minutes of total recovery time. All told there were 6 penalties, 43 passes, and 77 rushes in the game for a total of 126 plays. This mean there was an average of 50 seconds of recovery time between each play.
This is too high b/c I haven't accounted for timeouts (there were 4), TV time outs, and 'play under review' time. It shouldn't be that hard to figure out how many TV timeouts there are per game and how long they are. Also, need to figure out how long regular timeouts are. The number of replays and the amount of time spent on them requires geek-level commitment (i.e. UFR, all due respect to Brian of course).
But I did plus-bang you for the nifty graph!
We're going to have to get some manyeyes graphs in here sooner or later. I have a feeling some of the more recent additions to this site would probably spend all day playing with them as they are slightly interactive.
This seems overly complicated. I just look at the number of total offensive plays each team runs. That's a simple, useful metric. If you take that stat and compare it to a team's average, you can get a good idea about how much more or less energy the defense is expending than usual.
....to show that this metric predicts anything you'd have to put it into, say, a logistic regression with win=1/lose=0 as the dependent variable (or something along those lines), AND you'd have to throw in a field variable position to see whether there is any explanatory power for your variable beyond this.
You are right you want logistic (the effect gets smaller as the game goes on, the curve is convex) not exponential (the effect gets larger - the curve is concave).
logistic works here, but logistic implies that the curve is s-shaped. You & the OP want logarithmic functions.
Yes you're correct, I meant to say it's a logistic regression (for the 0/1 dependent variable) but the function for the independentn variable in question is logarithmic
Anyone with that many graphs can't be wrong. Well done, sir.
I have to save this one for reading at work. +1 for Misopogon for the effort!
i would have gone for this if you had called
it "SCHWING" as in:
but you didn't.
Woah, way too late for me to comprehend. I think my brain is broken.
So let's see:
-You're trying to project how well the defense will do by measuring how tired it is.
-You measure how tired the defense is by (more or less) how many plays it has been on the field recently.
-How many plays the defense has been on the field recently is partly a function of how well the defense has been getting off the field.
-The defense gets off the field primarily by stopping the other offense.
Essentially, you end up with a metric that says "the defense is likely to stop the opposing offense if they have been stopping the opposing offense." Not very useful... and that's in-game. Once the game is over, this basically says "the defense was good at stopping the opposing offense if they were good at stopping the opposing offense."
I really appreciate the effort you put into analyzing this; I just can't see any way this adds any useful information to our understanding of the game.
Super observation, although I think there is probably a way to distinguish the two if you used a system of equations (LISREL or something along those lines), and track on a minute-by-minute basis throughout the game. You could salt in some other covariates as well
tiredness = +f(# plays) plus, say, conditioning
skill of defense = -f(# plays), plus, say, # games experience, etc.
game outcome = f(tiredness, skill of defense)
I imagine that how fast a defense gets tired depends on how good they are in the first place - the best defense makes its plays with very little expense of energy(kind of like miles per gallon). Or, imagine a defense that is not highly skilled but has been well and truly Barwis'd.
Anytime we can accept the premise that one of these constructs can go up and down without the other, it's probably possible to tease them apart statistically.
Don't mean to get all lectury on you but....wait, yes I do, it's what I do for a living. Sorry, can't be helped!
Well, yes and no.
The big question isn't actually the defense, but how much the offense affects defensive play. If the Spread mentality generates quicker offensive series, does that make the defense give up more yardage?
At the end it says "the defense was X tired and gave up Y yards." If they give up 300 yards to a crummy offense, and 300 yards to a great offense, and the SCHWING was really high against the crummy offense and really low against the great offense, doesn't that say something?
The value is in framing plays, particularly big plays. I'm still running numbers, but I'm getting close to saying that high SCHWING correlates strongly with Big Plays.
For example, if you put MICH and WMU together, they gave up 3.83 YPP when SCHWING was under 20, and 5.50 YPP when SCHWING was over 20. During that game, there were 7 plays over 15 yards. Of those, 6 took place with SCHWING values over 20. When I take all of those plays out, the >20 SCHWING defenses still gave up slightly more (3.23 YPP versus 3.16 YPP for SCHWING<20).
I'm not measuring how good the defense is. I'm measuring how much performance they lose the longer they are on the field. If being on the field longer makes them less likely to get themselves off the field, that's something good to know, isn't it?
Try charting tonights MNF game between Miami and Indy. It was an epic example of how little TOP matters. Indy had the ball for maybe 15 minutes and won, 27-23.
Miami had all sorts of strength in the rushing game, thanks to Jake Long of course ;), but Peyton Manning moved his team 80 yards in :30 seconds on the game-winning drive. I kept screaming at Mike Tirico that he may want to mention "points per possession" here...
Anyway, Miami gets the ball back with 3 minutes to go, and the Colts D was visibly out of gas, but since Miami's primary downfield strike target is Ted Ginn, they had no ability to take advantage.
I'd be wary of charting an NFL game, but I welcome anyone to chart as many college games as possible. We have way too small a sample right now to make it conclusive.
It just seemed like an interesting case. Even today, media outlets like the Jim Rome show couldn't get over the fact that TOP was so lopsided and yet it didn't matter to the outcome.
... and I will be totally on board.
I'll bet that across a sample of many games, a large TOP disadvantage is highly correlated with losing. Obviously, just like any stat other than the score, it's not perfectly correlated. But in general, letting the opponent have the ball more often than YOU have the ball is not a winning formula.
The use of Schwing as the name caused me to use Garth's voice in my head every time I read it.
It was destracting, but entertaining.
Very interesting diary all around. A better metric in the area would be very helpful for analysts and coaches.
+1 to both of you
One issue that you missed on was what is rendering TOP as meaningless in college football is the onset of up-tempo teams that try to reduce the time between plays.
TOP is really just a simple proxy for plays run by each offense. TOP as a proxy was fine when teams generally ran the ball similar amounts and generally tried to maximize the duration of each possession by working the play clock down. Not a perfect fit but a viable proxy.
Teams like Michigan that line up quickly and snap the ball well before the play clock expire have caused TOP to no longer be a proxy for the number of plays run by an offense.
Your measure of fatigue (SHWING) could be not a predictor but a consequence of scoring. When teams score a lot, they have the ball more and the defense gets more tired (higher SHWING).
As suggested by notYOURmom and others here, you need to more toward a real-time analysis ie compute the SHWING at a given point in time, then see how it affects yards per carry etc on the following play (while also accounting for other factors like down, yards to go for first down, field position, that could affect YPC).
That will certainly require a lot of data, but the analysis could be useful IF your measure still is a valid predictor. For instance, a high SHWING measure could suggest to the coach when to call a strategic time-out, when to fake an injury on the defensive side OR when to use a ball possession offense.
In any case, this is an interesting first-pass analysis of correlations and you should keep up the good work.
Wow, that was quite an analysis.
But, why not use number of plays (NOP)as an indicator? It's simple and even makes sense. For the EMU game, M had 56 plays and EMU had 74. TOP was 20 for M and 40 for EMU.
Unless you think the D gets tired standing around between plays, the NOP is a pretty good indication. Much better than TOP.
Looking only at the number of plays doesn't account for the fact that a sustained drive causes more fatigue than the same number of plays broken up over time (and different possessions).
but thanks for the work; I know most of us appreciate the effort! :)