Never Punt with Denard?: Fourth Down Strategy Revisited

Submitted by The Mathlete on September 21st, 2010 at 10:02 AM

[Ed.: Bump. This makes sense to me: Michigan should mostly dump special teams once it gets across midfield.]

As Brian highlighted in the UMass round-up, maybe forgoing the punt altogether might not be such a bad decision. He noted my earlier look at the the topic and I wanted to pull it back and revisit and refine some of the work.

I looked at the years 2004-2009 and only looked at the top 20 rated offenses for each year. This study assumes that Michigan’s offense this year will be at a top 20 caliber and provides a broad enough definition of greatness that there is a good sample size. I did not distinguish what type of offense (Texas Tech Air Raid vs Georgia Tech triple option vs spread and shred) was used to get into the top 20. I will detail more assumptions as they are applicable along the way. In place of fourth down conversion percentages I used third down conversion percentage since the data pool is much larger and covers a wider variety of opponent levels. Since the thought process on a third down and fourth downs are roughly the same in most all (for now, anyway) situations, it seems reasonable to use the third down numbers.

Time for a you know what…


Assumptions: Top 20 offense, average defense, average punt game, average field goal kicker.

Based on these assumptions, except for long yardage, the punter should grab a seat once the offense crosses midfield. On your own side of the field the decision still makes sense starting around the 30 for shorter yardage situations and becomes more viable for longer yardage as you cross further down the field. Field goals become practical with 4+ yards to gain and only from about the 5-25 yard lines.

There are two big advantages a potent offense has that make 4th down tries more logical. The first is that they have more to gain by success. With a limited number of drives in a given game, why give them away for free? The second is that they are more likely to make them. Good offenses are more likely to be in better position on fourth down and more likely to make it.  Here is a chart of great offenses fourth down conversions compared with all offenses. The right hand column was the one used for the above chart.

To Go All Teams Great Off
1 72% 74%
2 57% 60%
3 51% 54%
4 47% 50%
5 42% 45%
6 38% 41%
7 35% 37%
8 32% 34%
9 30% 32%
10 27% 30%

It’s not a huge advantage on any one given down, but Top 20 offenses convert the same opportunities about 2-3 percentage points more often than the average offense. Note: the rate of conversion for great offenses was much higher in the original analysis and is part of the reason the chart isn’t quite as go for it as the original.

But we don’t have an average <blank>

<blank> = Kicker

Let’s start with the kicking game, which is currently 5 points below average on the season and rated third worst in the country after the first three weeks.


Assumptions: Top 20 offense, average defense, average punt game, below average field goal kicker (FG make odds are reduced by 25% everywhere on the field).

The decisions near midfield obviously aren’t changed but now attempting a field goal on 4th and 5-9 from inside the 25 is no longer the most valuable option.

<blank> = Punter

I know it hasn’t been the most Zoltanic of starts for Will Hagerup, but at this point if he can hold onto the snap, there is no point in adjusting him to below average, even if he isn’t an advantage at this point.

<blank> = Defense

This is the one that seems a bit counterintuitive and Brian and I disagree on. I say that the strength or weakness of your defense is irrelevant to your offensive decision on whether or not try a fourth down conversion. My belief that it is irrelevant is based on this chart.


Great defense obviously give up fewer points than bad defenses but the key point is that the difference between a great defense and a bad defense is consistent up and down the field. Giving the opponent a first down at midfield isn’t a guarantee of a touchdown even with a bad defense and isn’t a guarantee that pinning an opponent deep against a great defense will keep the other team off the board. In fact, the gap between the two is about .25 points per first and 10 all the way from the 1 to the 90. If this is true, then the ability of the defense is irrelevant to the offense’s decision to go for it. For that to be the case, there would have to be evidence that the difference between a good defense and a bad defense changes at different points on the field.

So what does all this mean

If Michigan can maintain their feverish offensive pace this year and fail to find an adequate kicker, I think their decision set in all but late game score specific situations should look something like this:


As I noted previously, if you buy into this mentality, it opens up another opportunity, changing your early down play calling. If your four down strategy has changed, so should your down by down playcalling. It may become more viable to risk a wasted down with deep ball knowing that you have an extra, or it might just make sense to keep the ball short in the air and on the ground knowing that over four plays instead of three the likelihood of getting the yardages greatly increases so play to have the shortest possible fourth down attempt if you don’t convert before that.


The Mathlete

September 21st, 2010 at 8:42 AM ^

Even with over 7 years worth of data there are minor inconsistencies and variations in the data. The points where two colors intersect should be considered essentially equal. The lines between two decisions aren't hard and fast, but a general approximation for where the decision should begin to change.


September 20th, 2010 at 11:45 PM ^

Mathlete, really appreciate your analyses.

I've noticed that you consistently use Excel for generating your plots. This is completely unsolicited, and I don't know anything about your background, but you might look into gnuplot, matplotlib, or even R... oftentimes it's a lot easier to generate really pretty graphs with those tools. Even if you're generating your data in Excel it's a lot easier to save it in CSV/raw text and use something else to plot with.

Sorry for the OT-ness. I've converted a decent number of people and figured I'd say something.


September 21st, 2010 at 10:39 AM ^

yeah i can see now how in the world of business they got away from hand drawing graphs in mspaint and moved to more professional layouts with fonts and right angles. I can see how my format is less convincing as a result.

If i had to do it over again i'd try to hold the mouse more steady.


September 21st, 2010 at 1:05 AM ^

Denard did have a great punt earlier this season, so why not let him kick FG's too?  I mean clearly he can do it all... and that would also make for some reallly sweet Special teams plays.


September 21st, 2010 at 3:18 AM ^

I think the reason why more coaches don't go for it more often on 4th down is because kicking the punt is considered as the safe option.  I mean listen how the announcers blew up with ND went for it with 4th and 2.  It's interesting though, they sing praises for Dantonio calling for a fake field goal because it worked.  If it hadn't worked they would have said he should have went for the tie.  Personally, I'd rather see a coach go down in flames trying to win rather than one do the safe stuff trying not to lose.


September 21st, 2010 at 1:31 PM ^

I forget the game last year but Darth Hoodie went for it on 4th and 2 around the 35 yard line.  The play went down in flames and the coach normally hailed as a genius was a goat.  I believe the bobbleheads said something of the effect that he wasn't showing he trusted his defense.  Are defenses that frail emotionally that they have to be coddled?  Wouldn't going for it more often show your faith in the offense and in situations like this aren't you showing more faith in your defense because you're giving them a shorter field to work with?


September 21st, 2010 at 6:18 AM ^

I would love to see us get more aggressive play calling.

If we know that we are going to go for it on 4th down, it makes getting the 1st down much easier.  Instead of 3 plays to get 10 yards, knowing you have a fourth allllows us to better play call on 12t, 2nd, and 3rd down to pick it up.


September 21st, 2010 at 9:23 AM ^

I would be interested in seeing some error bars on the scatter plot that shows expected points vs. field position for good defenses and bad.  Are the standard deviations small or large? 

Also, I assume that you used season data to determine "good" vs. "bad" defenses and made some sensible deliniation between the two.  (Maybe you put this in your post and I missed it the first time through.)


September 21st, 2010 at 9:44 AM ^

It's easy to see that the quality of our defense would affect our 4th down decision in the extreme cases. If we had a defense that always allowed a TD, our decision on 4th down would be to always go for it, because getting more than one score down would mean a loss. Having a defense that never allows a score would make our decision always kick, becuase a FG would be as valuable as a TD.


September 21st, 2010 at 10:27 AM ^

This is a very interesting read.  Brian Kelly took a lot of crap from Todd Blackledge over his decision to go for it on 4th and short in his own territory this past weekend but the data suggests that it's probably the right call.  Even if we don't go for it as often as the chart suggests, I'd like to see us play for 4th down from now on when it's 3rd and 6.  The past couple of weeks we have seen passes thrown into the end zone on this situation right before a missed field goal.


September 21st, 2010 at 10:32 AM ^

Kelly made the right call statistically.

But you have to coach your players to be used to going for it on fourth, you have to practice it, or else they will tighten up when the time comes. It's a mental hurdle. I think a good coach would have whole practices where the offense goes for it on fourth all the time, just to help them understand the rhythm of how that feels.

I think Kelly's a great coach. Not to dwell too much on this but I think Notre Dame is going to be a monstrous football team next season. Rats.


September 21st, 2010 at 11:22 AM ^

He made the "right" call by going for it but his play call was garbage. Armando Allen was holding his jock strap on the sidelines after having skewed MSU's D to the tune of 5.5 YPC in 13 carries.

Kelly's game management in the last two games is definately questionable. Remember that in a similar situation later in the MSU game he punted...why? Then at the end of the game the play calling was completely questionable (pass, run, kneel). In the game against us he put the ball in Montana's hands instead of kicking a field goal at the end of the first half...that was dumb.

Not going to say he's not a good coach because I still think he is. But, he screwed up some controllable things. That's on him.

The Mathlete

September 21st, 2010 at 11:41 AM ^

Agree that that the MSU decision making was very odd. However, assuming that he did not know Crist was coming back in the second half, I don't think the last play was the wrong call for ND. They didn't look like they could stop Denard and the backups hadn't been able to move the ball. A field goal at that point would have been a moral victory at best, but with stops and quality drives looking scarce for ND, I think he had to take the chance. Now if he thought Crist might be coming back it's not as much of a no-brainer in my book but still a very reasonable choice.


September 21st, 2010 at 12:31 PM ^

Fair enough on the risk/reward deal, however, even letting go of the "go vs kick" decision, the play call in that situation was not sweet. Armando Allen was KILLING Michigan (5.9 ypc), yet Kelly asks Montana to make a read/throw he had no reason to believe his QB could make.

4th down decision-making is a very small portion of game management.


September 21st, 2010 at 2:36 PM ^

You're being very gracious towards Kelly. By the middle of the second quarter ND's running backs (Allen/Wood) were gashing Michigan's D. They did start off a little slow, but they were in the groove by that point. Check it out. Moreover, Montana was most definately not in the groove at that point. Hell go Wildcat there, whatevs...maybe he got the decision right but he botched the call IMO. After all that, he gives Montana what must be his O-Face like the kid's a douche. Mind you, he started the game as 3rd string QB, how many snaps do you think Montana got going into Michigan game?

In the MSU game when he went for it, there was no such plausible excuse (cold running game). Allen had been killing them and he decides to go for (3rd and 2) and (4th and 2) in an empty set (I think, not sure) both times. Later, he has the ball and doesn't even really try to drive for a game winning FG in regulation...ON THE ROAD!

Sorry, those are major gaffes in two games against two major Rivals. He must not get it. [couldn't resist]. Now comes Standford, Pitt and USC. ND-Nation is going to melt down if this keeps up...


September 21st, 2010 at 10:39 AM ^

Great analysis and makes tremendous sense.  Several credible statistical analyses have demonstrated that in the NFL teams punt too often.  It is ingrained in coaches and most just punt as a matter of course.  Ironically the fans would almost always enthusiastically support the decision to go on 4th down.

The often unappreciated benefit to planning to go on 4th down is what it does to 3rd down.  Say you have 3rd and 4.  If you going to go on 4th a running play on 3rd now makes more sense, as you have two runs to make the 4 yards.  If you believe in the run, as we do with Denard, this strategy increases the chances of continuing the drive, as we are arguably more likely to make the 4 yards in two running plays as opposed to one pass play

To summarize, an overall strategy to go on 4th down once over midfield really becomes a 3rd down decision.  Once you hit 3rd and medium-to-long it should be viewed as a two play sequence. not two separate decisions.


September 21st, 2010 at 11:08 AM ^

is the coaches' jobs are on the line and they won't get fired if they go for conservative strategy which is punting.  But they get fired if they used an aggressive strategy which is go for 4th down almost every time and fail on half of it.  UMass used this strategy in 4th quarter which is why they were able to extend drives despite Michigan defense stopping them on 3rd down.  They were calling for 4 downs instead of 3 downs which makes a huge difference in play calling and executions.


September 21st, 2010 at 11:38 AM ^

which way playcalling would shift if coaches viewed it as 4 downs to get 10 yards instead of 3. If it's, say, 3rd and 4, would we be more likely to see plays "expecting" to get 2-4 yards assuming players execute their assignments, knowing that there's a very short 4th down if you don't get 4? Or would we be more likely to see plays with lower chances of success but "expecting" to get potentially huge yardage (downfield bombs, trick plays).

Personally, I tend to agree with you that the playcalling might get more conservative in terms of expected yardage to gain, to get to a manageable 4th down (3rd and 7, run Denard on a keeper if you hope he can get 8, but "expect" he can get 5).

As Mathlete suggests, perhaps some coaches would view it as more opportunities to take bigger risk/bigger reward gambles on playcalling.

I'm sure there isn't enough data using 4th downs (as well as it not being a consistent strategy). Perhaps the Canadian game is so different that it doesn't approximate, but I'd be curious at how "expected yardage" per play differs in 3-down CFL games, if that stat is even quantifiable.


September 21st, 2010 at 1:03 PM ^

Defenses think their job is complete if they hold on 3rd down. I'd imagine the mental aspect comes into play if the defense knew they had to defend all 4 downs and it could prove to be an advantage there as well. Teams used to doing their job for 3 downs would now be extended to doing the same for 4 downs, physically and mentally.


September 21st, 2010 at 1:27 PM ^

It's ingrained into just about everyone's head.  I mean everytime the defense stops a team on 3rd down, the bobbleheads will say, "Well they are forced to punt now".  There is nothing in the rulebook that says you have to punt on 4th down.  Put me in the camp of people that would like to see more coaches going for it on 4th down.  Especially when you are within the opponents 50 and even more especially if you are down.  but I think the key is that you use surprise because if you make it predictable, teams will clamp down on 4th downs as well.

Steve Levy Sucks

September 21st, 2010 at 10:45 AM ^

to read that we assume Michigans offense will be in the top 20.  I'm sure this is a concensus, but I love watching this offense.  I've almost gotten to the point where I expect a touchdown on every drive.


September 21st, 2010 at 10:49 AM ^

As someone who thinks math and detailed analysis ought to be far more important in sports and literally explode every time a coach talks about his "gut" this chart is the best thing since Moneyball and I love every single thing that's ever been done with it.

How far into the game do we have to be before it is a "late game scoring situation" and the score starts to come into play?


September 21st, 2010 at 11:02 AM ^

The chart doesn't make common sense to me.  Let's assume  a great D gives up 15 pts or less per game and a bad D gives up 30 pts or more.  Wouldn't it make sense that at any given starting point, the great D would give up half as many points as the bad D?  Your chart appears to say that a great D will give up 80-90% of the points a bad D does regardless of starting point (the graphs are so close together all the way up the chart).

This flies in the face of logic to me.  I guess I need to know what constitutes your bad D and good D.


September 21st, 2010 at 3:54 PM ^

He is plotting Expected points on a given posession when you know the starting field position.  As I understand it he looks at all drives that are 1st and 10 on the 20 yard line (as an example).  Then he looks at the results of those drives.  (Commence the faking of data)

  1. In 50% of those drives, the team punts or has a turnover.  (0pts)
  2. In 30% of those drives, the team kicks a field goal.  (3pts.)
  3. In 20% of those drives, the team scores a TD.  (7pts.)

So the expected points is:

0*.5+3*.3+7*.2 = 2.3 points


Now more to the point about your question.  Don't great Defenses give up <20 ppg when bad defenses give up >30ppg?  Well, yes, they do.  But the chart isn't talking about total points in a game.  It is talking about expected points per drive.  Now if the difference is about 0.5 points per drive and there are an average of 10-15 drives per game, then we are talking about a difference of 5-8 points per game based on "goodness of defense".  Maybe this is too narrow of a difference, but I also know that he throws out a bunch of things from his analysis (like PR/KR TDs and INTs returned for TDs and fumbles returned for TDs iirc.)


September 21st, 2010 at 11:00 AM ^

Great article, a follow question:

If you adopt this strategy instead of a traditional, 'take the field goal' strategy, due to a poor field goal unit, what is the average impact on your scoring offense per drive?


September 21st, 2010 at 11:10 AM ^

This seems pretty optimistic to me, given the weak defenses Michigan has played so far.  Is this a critical assumption?  If its an average offense how much does this chart change?


September 21st, 2010 at 11:23 AM ^

Mathlete, you make math way cooler than I remember it being when I was in school.

This is an excellent piece.  It shows that coaches should go for it on 4th way more than they do. 

The reason that I do not see coaches changing their 4th down decision-making matrix despite this data is that when a coach goes for it on 4th and fails to get the 1st down, the coach will be villified if the decision costs the team the game.  By contrast, if a coach does the safe thing and goes for the FG, if the kicker misses, nobody is going to crucify the coach for the desision because we are all used to it. 

That said, RR has guts (combined with terrible FG kickers), so I could see him going for it more on 4th.

tee wrecks

September 21st, 2010 at 11:24 AM ^

I appreciate the thought and effort that went into this and don't mean to nitpick, but shouldn't the gray triangle in the upper left of the chart also be white, too?  I realize you can't have 4th and X if you're inside the opponent's X yardline, which explains the gray triangle on the upper right.  That's not the case on your own side of the field.  You can have 4th and 10 from your own 5, for example.


September 21st, 2010 at 12:04 PM ^

Can the database tell you about Opponent's expected points after 3 & Outs? It seems like this would be a factor from the "How Good is My Defense" POV? Could you approach this from Time of Possession, Number of Drives?


September 21st, 2010 at 12:30 PM ^

Rich Rod should go for it more. Screw the mass media.

Mass media reeks. If you do the logical thing (going for it), but it sometimes fails, the talking heads crucify you. If you do the risk averse, conventional unwisdom thing (kicking), and it consistently fails, the media care little.

But at the end of the year, fans care about total wins and losses. Going for it produces more wins. The in season controversies are largely forgotten. Hardly anyone remembers the coaching decisions made during last year's Indiana game or any other individual game. But they do remember five wins and seven losses.


September 21st, 2010 at 12:40 PM ^

is that if you have fourth-and-one just about anywhere, you need to have your kicking team go get hot dogs or something. (Of course it sucks if you go for it on your 20 and don't make it ... but in the long run, you'll make up for it by continuing drives that would otherwise have stalled at your 20.)


September 21st, 2010 at 2:15 PM ^

This is an OUTSTANDING analysis and has COMPLETELY changed the way I view 4 downs.  Like most, I was always thinking that a 4th & 2 or 3 inside your own territory was a punting situation for sure.  NOT ANYMORE!  Let's hope the coaching staff reads this and buys into it (can't think of any reason not to after the last 3 weeks)!  This is great info and thanks for posting it!


September 21st, 2010 at 2:45 PM ^

As someone who thinks math and detailed analysis ought to be far more important in sports and literally explode every time a coach talks about his "gut" this chart is the best thing since Moneyball and I love every single thing that's ever been done with it.

How far into the game do we have to be before it is a "late game scoring situation" and the score starts to come into play?

Dan TrueBlue

September 21st, 2010 at 4:06 PM ^

I love this idea.  I really think the Coach should go for it on 4th down more often, given that his offense is by leaps and bounds the best part of the team.  However, there's one thing I'm cautious about that you fail to mention:  math is terribly bad at modeling psychology.  

You can bet that when the offense is there, facing 4th down, convert-or-die, a couple of players might secretly ask themselves what happens if they fail to make it.  Doubt creeps in.  On the other side of the ball, the defense will likely be more pumped than ever to stop them, since the rewards are so high: they could instantly get the ball back.  

Of course, it's possible that for some teams, the added pressure might swing the odds the other way.  Even so, that just makes this idea even more unpredictable, I believe, than what you present here.

You say you use 3rd down conversion rates because the data on them is much more plentiful.  But I'm betting it's not as fair of a substitute as it seems.  I would guess that a 4th-and-6 gets converted a lot less often than a 3rd-and-6 does.  I could be wrong though.  I'd be curious to see the data.

Either way, I agree that Michigan should be going for it on 4th down more often than most teams... just probably not as often as you say.