A Quick Review of the 4th Down Decision

Submitted by The Mathlete on November 19th, 2013 at 5:16 PM

I’m not touching the play call itself. Most of have pretty strong feelings about it. Criticizing a failed play in hindsight is usually a pretty lazy thing to do, but Michigan has a set of plays this year that have a firm history of no success and should never be run in critical situations.

But what about the decision itself to go for the 1st down. In the situation there were two possible choices and two possible outcomes for each.

Kick the FG Success/Failure
Go for the 1st Success/Failure

Each choice has an associated odds of success and each outcome has a resulting win odds.

Kick The FG

The safe, NFL worthy decision would have been to kick the field goal (“Take the points,” because field goals are never missed). In a low scoring game this probably gets you to overtime and there are no guarantees you get another chance or that you can take advantage of it. The downside is that with about 5 minutes to go, you are opening the door to give Northwestern the ball with plenty of time to drive the field and run out the clock.

A successful field goal means kicking off in a tie game with about 5 minutes left. In this situation, the team kicking off wins about 46% of the time. A made field goal would have made Michigan a slight underdog.

In the fourth quarter of close games, college kickers make 94% of field goals from inside the 5 yard line. Those are pretty good odds, but still a 1 in 16 chance that the kick is missed or blocked. A missed kick would have given Northwestern the ball at the 20 and dropped Michigan’s odds of winning to 23%.

Go for the First Down

Picking up positive yardage has been a challenge for Michigan the last month. Had they been able to convert for a first down their win odds would jump up to 70% (74% with a touchdown). Still plenty of time for a Northwestern touchdown, but definitely putting Michigan in the driver’s seat.

The failure to secure the first down left Michigan with a 34% chance at victory. Far from over but a lot of leverage on the play.

The Break Even Point

A field goal attempt would have given Michigan a 45% chance at victory once the small chance of a miss or block is factored in. With 70% odds with a first down and 34% odds if they failed to get the first down, Michigan would need to be able to have at least a 30% chance of success to break even on going for the first down. Michigan has had its troubles on offense but a 30% break even point is a low bar. 3rd or 4th and 1’s from inside the 5 are converted at 57% historically. So even if Michigan was half as likely as an average team to convert it still would have been an even decision with kicking the field goal.

If the numbers seem too high or too low there are a couple of follow up dynamics in play. A failed fourth down would have left Northwestern with the ball and the lead late. Coaching history as taught us that this is a recipe for most coaches to curl up into a ball and try and ground out the clock and if they’re lucky get a first down or two. Because of this often failed mentality, giving the other team back the ball with a lead can be more valuable than giving them back the ball with a tie where there is some pressure to push forward.

I think this was absolutely the correct decision to go for the first down in the situation even if the “execution” was less than ideal.



November 18th, 2013 at 10:35 AM ^

Always enjoy your posts.

Interesting that the Lions had a decently similar situation that ended up not working out for them.  Of course a 9-6 game is usually a lot different than a 27-23 game, NFL vs college differences, etc.  

Would be interested in seeing the analysis for the Lions if you have an opportunity - Mike and Mike were critical of the decision this morning but of course when talking about the Michigan game only talked about the FG to end regulation and how Northwestern keeps finding ways to lose - I didn't hear mention of M's 4th down situation.


November 20th, 2013 at 1:04 PM ^

I've heard the two plays bumped against each other on local sports radio here his week and the consensus seems to be that both Hoke and Schwartz made the wrong decision, and I couldn't disagree more.

As for the Michigan game, I am firmly in The Mathlete's court on going for it on 4 down in that situation.  Hoke made the right call but Borges dialed up the wrong play.  In the Lions case, taking the points to increase your lead from 4 to 7 points puts you in an excellent position to not lose that game in regulation.  The Lions made the wrong call.


November 18th, 2013 at 10:47 AM ^

I was wondering just that when they did it. I'm glad to see that decisions analyzed coherently. Excellent execution, Mathlete. 



November 18th, 2013 at 10:55 AM ^

This makes me a feel a little bit better.  I was all for taking the points prior to the play call so won't take the hindsight angle.  The feel of the game wasn't right and I had no confidence that we would pick it up. 

Blue Mike

November 18th, 2013 at 10:58 AM ^

I'm not sure giving Michigan even a 25% chance of succeeding on that play is realistic.  Michigan hasn't been able to get a yard all season when they need it on third or fourth down.  Their OL can't get any push at all when the other team is defending short yardage.


November 20th, 2013 at 2:14 PM ^

Exactly, we were 0-10 or worse on 3rd down at that point, couldnt pick up a 3rd/4th and short to save our lives.  We had about a 1% shot of getting a first down there and anyone who watched the game knew that.  It was a delusional call and the post above is a delusional defense.  Wishful thinking and average execution of average teams does not apply to our offensive line, playcalling, and ineptitude on 3rd and short (or any other distance).


November 18th, 2013 at 11:00 AM ^

At the game I really felt like kicking was the right decision, but reading this and seeing how NW responded (conservative run clock, no passing plays) makes me think that kicking for the tie there would have likely lost us the game.  Thanks for the information.


November 19th, 2013 at 6:23 PM ^

get covered enough, the emotional impact based on the consequences of what happened. We get the first down and we score a TD, NW is going to be coming at us full bore while we might be the ones sitting back. A FG that ties it regardless of how it comes about probably relaxes both sides a tad and based on the kick may give NW the edge. Or no. The failure that occurred gave NW a relaxed - probably not the best descriptor - mind state and combined with our desperate mind state probably contributed to the outcome of their last drive.

I think taking the three was the right decision considering that despite playing a whole game they were up 3 3's to two 3's; so scoring was at a premium. Ultimately the best decision is to 'Captain Kirk' it, blast the odds and go with your gut. I guess that's what the coaching staff did?

Anyways, an interesting feature of this topic.


November 19th, 2013 at 9:43 PM ^

Any emotional impact on your chances would already be reflected in the statistics.  Maybe you could make an argument that since they didn't control for experience, we would be hit worse by it than an average team, but I really think if you start talking about some spooky momentum factor you are really overcounting effects which are already present in the data set if they have had any impact on the outcomes of games.


November 19th, 2013 at 7:35 PM ^

You can't look at the outcome with 20/20 hindsight.  You have to look it without the aftermath information. Hindsight? Probably should've kicked for a FG because they didn't convert for a 1st down.  In reality, if Gibbons makes the FG, it completely changes the playcalling of Northwestern like you said. Northwestern would be a bit more aggressive on marching down the field to get points.


This is something that people keeps forgetting is the playcall and outcome of the game will change if Michigan converts a 1st down or make a FG.


November 18th, 2013 at 11:05 AM ^

However, we're not an average team.  The odds of converting that 4th down were quite low, given the performance of this team in short yardage situations all year.  The odds of properly executing a two-minute drill to get back into range was also pretty low - again, for this particular team.  As it was we only got off the kick with milliseconds to spare, and it had far lower odds of being good than the earlier one.


While I can't argue with your averages, I don't think they apply to this team.  Had I been the coach, knowing the limitations of the team, I would have kicked it.

Ron Utah

November 19th, 2013 at 5:35 PM ^

Stats are nice, but they are only a statistical reality.  This team's inability to convert short yardage situations needs to be accounted for.

The eyeball test says it was a bad call.  While stats might say it's a good call, this Michigan team has been struggling to move the ball and score points, and our defense has been shutting opponents down.

I still think we should have kicked the FG.  I'm not furious with the decision by any means, but I would have preferred the FG try.


November 19th, 2013 at 6:19 PM ^

You say we need to take into account Michigan's ability to convert short yardarge situations. Well here you go:

"Michigan has converted 58% of 3rd/4th and 1 this season, right on the expected average." - From the mathlete later in this thread

Now taking that into account it seems like going for it was the correct call.



November 18th, 2013 at 11:06 AM ^

I really like the way you broke down the odds for all the possibilities.  I just think that our chances of making the first down were less than 30%.  After all, we hadn't converted a 3rd down all day, and we had at least 2 3rd downs of 1 or 2 yards that got stuffed on running plays, one of which was the play action bootleg that we ended up running again. We have had very little success running the ball for over a month now.  

Also, you cited 3rd or 4th and 1.  This was 4th and 2.  Small difference, but that definitely cuts down the success rate.  I think 2-pt conversions are made at a rate of a little over 40%, and that's basically 4th and 3 from the 3, so I would assume an overall success rate of 50% or so, not 57%.

Given the high number of running plays that we have done that gain a yard or less, given that we had tried this exact thing once before in the game and it didn't work, and given the fact that, with the ball at the 6, Northwestern could put basically everybody in the box, how were we going to gain 2 yards?  There is no way to quantify this, but I don't put it as high as 30%, let alone 50 or 57%.  


November 18th, 2013 at 11:20 AM ^

Given the zero percent third-down percentage Michigan had at the time, on top of an atrocious third-down percentage the prior two games, who actually thought there was a 30+ percent chance of Michigan converting that 4th-and-2?  My feeling was that if your offense is performing that poorly, you never pass up easy points that will likely get you into overtime, particularly given how well the defense was playing.  If you can somehow get to overtime, even with an offense that had done virtually nothing all game, then you've got a coin-flip chance of winning the game, which is a better chance than Michigan had in the later stages of regulation.


November 18th, 2013 at 11:22 AM ^

While I agree that running the ball on 4th and 2 might have been successfull less than 30% of the time, I believe there are less conservative playcalls that would have done better. Spreading the field and looking for a quick slant/hitch/out + have Devin scramble if nothing is open HAS to be at least 30% successful - I would suspect much more. 

Love the going for it, hate the play.


November 18th, 2013 at 11:26 AM ^

directly to the type of plays called in those situations.  Thus it was likely we were going to see another of the same type of terrible plays. 


Again, the call was not made in a vacuum for a generic team.  It was called for this team, with this set of coaches.  The odds of converting that 4th down for this team were abysmally low.


November 18th, 2013 at 12:53 PM ^

On the year, we're 38% on 3rd downs, which is OK, not particularly good or bad.  On 4th downs we're 55% (6-11).  That's from all distances, not just short-yardage.  I'm pretty sure we have in fact converted a majority of our short-yardage (2 yards or less) attempts this year.  We just remember the failures more.

The problem in recent weeks has been that a huge percentage of our 3rd down plays have come in long-yardage situations.  We haven't had many 3rd and shorts lately.



November 18th, 2013 at 12:55 PM ^

Here is a counterpoint: Up until and including that failed 4th down conversion, Michigan was a combined 0/15 on 3rd/4th down attempts, a 0% success rate. But from that point on, Michigan converted 5/6 combined 3rd and 4th down attempts, an 83% success rate. They ended the game 2/4 on 4th down, which is greater than 30%. Obviously there is a major sample size issue here. But even as bad as Michigan was, I don't think it's too much to expect a 50/50 odds of conversion there.

Here, some more stats: http://www.ncaa.com/stats/football/fbs/current/team/700/p3

That is the list of the teams in the FBS who are worst at 4th down conversion rates. Note that there are a grand total of 11 teams out of 128 in the country who have a 4th down conversion percentage this season south of 30% (even fricking Illinois is greater than 30% this year). 

Also note that Michigan is 54.5% on 4th downs this year, good for 45th on that list.

Even looking at 3rd down conversion rates, which has a ton more data, only 5 teams convert on average this year less than 30% of the time. Michigan is a middling 74th on that last, converting just 38.7% of the time.


November 18th, 2013 at 1:12 PM ^

At the time the decision had to be made, Michigan was 0/15 on third/fourth downs on the day.  Season-long conversion rates aren't really applicable because the decision is situational.  Given how that team had performed thus far that day against that particular opponent, it was foolish to expect to pick up the yards.


This is an argument of general versus specific situations.  The general analysis is a good starting point, but must be modified by the particular situation.


November 18th, 2013 at 1:32 PM ^

But how many of those attempts were from short yardage?  That we failed to convert a bunch of 3rd and longs earlier has little bearing on our abillity to convert a short-yardage situation.  I only remember a couple of failed short-yardage attempts in the NW game, and one featured a bad snap.

If you're arguing that we literally can't convert a short-yardage play three times out of ten, that's going overboard.  I think the larger point here is that kicking a FG on 4th and 2 is usually a poor decision.  Most teams can get two yards often enough to justify going for it, and the value of finishing a drive with a TD versus a FG can be big.  



November 18th, 2013 at 7:08 PM ^

using post-hoc rationalization to think that Hoke made the worst decision in the world (not accusing you, but I've read enough comments here to that effect). What if Hoke had made it?

Anyway, it wasn't meant as post-hoc rationalization. (btw I was happy with the decision before and after the play was run). I guess my point of bringing up those stats were that, how can you adequately predict when your team is going to struggle versus "flip a swicth" and start executing in those situations? The sample size was already small...as others have pointed out, there were maybe only 4 other 3rd/4th down and short situations. And you cannot expect your team to go 0% on 3rd/4th down conversions all day...even bad offenses (like Michigan) convert 30% of the time on average. You just can't expect your offense to never convert one of those plays, even if they haven't converted one up until that point. 


Blue Durham

November 18th, 2013 at 11:10 AM ^

This was a case where I understood either decision, and I was leaning going for it.

The defense was playing well and if Michigan did not get the first down, Northwestern, deep in their own territory, would probably have to give the ball back relatively quickly. Didn't really work out that way, though.


November 18th, 2013 at 11:41 AM ^

and needing two yards with over four minutes to play the decision by most good coaches is to kick the field goal tie the game and for NW to try to break the tie into a howling 20mph wind.

Now if we were not in field goal range but inside the NW 40 yard line then going for it make more sense.

I suspect Hoke made the decision because of all the heat he received about his poorly coached team. Had he made it and won the game he would look better in some peoples eyes. It was only by dumb luck he was able to tie the game and had Michigan lost by three in regulation time one can only guess to what extent he would have been criticized.


November 18th, 2013 at 12:47 PM ^

I suspect Hoke made the decision because of all the heat he received about his poorly coached team.

I highly doubt Hoke pays attention to the media after a game (win or lose).  The idea that he's going to not only read the papers after a loss but have it influence his coaching is pretty farfetched.  I don't think many coaches would do that.

Hoke has generally shown a tendency to go for it on 4th and short in our opponent's territory. This was in character for him.


November 18th, 2013 at 1:17 PM ^

I do agree that Hoke gives no fucks what the fans say, but I do think that a couple of uncharacteristically safe calls in the past that cost the team swayed his decision this time. I'm thinking of the Penn State game and the playing for a FG play-calls following the muffed punt in the Nebraska game.


November 18th, 2013 at 11:58 AM ^

I think it was a ballsy decision, supported it at the time, but really wondered why we did not do the play action pass on either 3rd or 4th down there as it seemed to me to be the perfect time to do it with NW likley to sell out against the run for sure......especially given our o-line issues for the game and over the previous two games as well.


November 18th, 2013 at 12:19 PM ^

Thanks for the great analysis as always.  Some comments and questions:

1) Caveat about NW playing with a lead vs. playing from a tie aside, in the situation M was in, they could have kicked the FG and (with the wind) almost certainly gotten a touchback.  Stopping NW 1st and 10 from deep is a *little* easier than stopping them 1st and 10 at the 25, but not much.  I'd rather have the tie and a subsequent chance to play for the win if you got the ball back.

2) As others have noted, your analysis is spot-on.  I can't disagree with any of the setup.  The only question due consideration is the likelihood of getting the 4th down play.  I think 30% is WAAAAY too generous.  Remember, we were 0 for 13 on 3rd down conversions at that point in the game.

3) To me the question is the benefit of large numbers vs. binary outcomes.  The percentages go away and you either have points or you don't; you have a tie or you don't; you have a lead or you don't.  When do you consider the 57% historically for "teams" vs. A) Michigan, B) Michigan this season, C) Michigan this season, this day, vs. this team?  Again, when you're evaluating the likelihood of making the first down vs. (C) it is different than vs. 57% success.

4) Also, consider this (again in the context of the game): Michigan had a sudden change in the form of the shanked punt which gave them 1st and goal at the 10 (just slightly worse than the outcome they were hoping for of 1st and 10 at the 4).  What did they do with that gift?  4 plays, -2 yards, FG.  sigh

I was at the game and it was wonderful to get the win and I'm very excited for the outcome.  But I still think it was absolutely the wrong call.  Your math confirms it for me.  Thanks again!


November 19th, 2013 at 6:02 PM ^

I think the only way you can confirm that it was the wrong call was by saying we had a less than 30% chance of converting the first down. I am sure we could argue all day about whether that was the case or not (jmblue and complete lunacy posted some stats about it up the thread a little.

Forget about the numbers for a second and think about this.

Say we kick a FG and make it. What about our offense had shown you that we are likely to go down and get another score to win that game? Really we are playing for OT if we do that.

Do you really want to take our chances in OT? We had struggled in the redzone all day. Like you said they gave us a gift on the 10 yard line and we couldn't do anything with it, why would we be able to do anything from the 25? I was scared shitless during OT. The longer and longer it went, the more i thought we would lose bc I didnt have any confidence in our offense.

I would much rather put all my marbles on getting 2 yards and scoring a TD, than hoping for OT.


The Mathlete

November 18th, 2013 at 12:40 PM ^

A couple points of clarification

The official PBP lists the play as 4th and 1, not 4th and 2

For those saying that the odds aren't about this team, the odds on any one single play aren't that different from the best to the worst. Do they differ, absolutely, but not that much. 

Yes Michigan hadn't converted a third down prior to the play, 7 of the 10 failures where on plays of 8+ yards, not a lot of relavance. 

Michigan has converted 58% of 3rd/4th and 1 this season, right on the expected average.

No team in the last 11 season has ever average less than 35% conversions on 1 yard to go situations. For Michigan to be at 30% expectation would mean that they were a standard deviation worse than the worst team in this situation of the last 11 years. And even then you are break even. I know if felt bad and that the play call was awful, but the numbers were firmly on Michigan's side unless you think this is actually the worst offense of all time, and then it was a break even decision.


November 18th, 2013 at 12:46 PM ^

Thanks for looking up and running the numbers.

I thought it was the wrong call at the time for this team, but that's a convincing argument.

Glad Hoke was aggressive and I hope he doens't change just because it didn't work that time.


November 18th, 2013 at 12:51 PM ^

Those are fair points.  And thanks for taking the time (that I didn't) to look up Michigan's season stats for 3rd/4th and short for this season.  Frankly, I'm surprised.

The thing is, though, I left the Nebraska game (thoroughly depressed and) thinking: "This might be the worst Michigan offensive line of all time."  That's probably not at all fair, nor is it supported by any research.  But, my GOD, has it been rough!  And I guess that's why it felt so bad at the time.  Also (as you haven't shied away from): Good HEAVENS the PLAYCALL!!!

After a day of futility, it just felt awful. 

In the end it comes down to two binary outcomes:

1) We didn't get the first down.  So that makes it feel worse.  BUT: It wasn't surprising.  Would I have taken the odds just before the play was run?  Nope.  But then again, they don't pay me to be head coach.

2) In the end, it didn't matter.  We won.  The ten of us that were at the game together were a lot happier about the outcome than we were unhappy with the go/no-go decision.

Thanks again for doing all the leg work.  


November 18th, 2013 at 12:56 PM ^

I'd be curious to see the breakdown of our short-yardage success when Gardner keeps the ball versus handoffs.  I feel like the former has worked a lot more often (and did a couple times in OT).


November 21st, 2013 at 9:13 AM ^

I'm not sure why you're attacking this point so hard, Delhi. It was just a minor observation at the end of the post where he noted a playcalling tendency that might push the numbers slightly in M's favor. It wasn't really crucial to the overall analysis.


November 18th, 2013 at 1:20 PM ^

Thanks, I was hoping you'd look into this. I didn't really like the play but I thought the numbers on average would justify it. I think the thing that might not be accurate in Michigan's case is the 34% win chance for a missed conversion. I just didn't think the chances of Michigan getting back into scoring position were that good, certainly not where the statistical average team would be. This would basically push up the "break even" percentage for a conversion much higher than 30%. As such, making or missing the conversion basically seemed like the ball game to me, fail to convert and it's all but over. That seems like a hell of a gamble when the team's just been flat out terrible in short yardage situations. Even if you convert, I still didn't like the odds of us punching it in, so risk reward seemed solidly against it for our team. On the flip side, the defense had been out playing NW the whole game so it seemed like we were taking the game out of the hands of our strength and putting it into the hands of the weakness. I'm glad it worked out, but you have to admit it was an incredibly unlikely string of events that not only kept our final drive alive but to kill NW's drive in the first place.


November 18th, 2013 at 2:11 PM ^

While, like seemingly everyone else I hated the play call. I agree with Hoke and Mathalete.

Most of the critics on this post are basing their arguments on Michigans offensive ineptitude - and I can't take exception to that. However they are not looking at the other side of the coin. Consider the following keeping in mind that if we get the touchdown we very likely win the game but if we fail:

(1) Michigan's defense was playing well and with the weather conditions NW's offense hadn't been moving the ball much better than we had.

(2) They were going into the wind and pinned deep in their own territory if we don't make it, are likely to be conservative and are unlikely to string together more than 1 or 2 first downs if that.

(3) given the above and 2 time outs we are likely to get the ball back with plenty of time.

(4) their punter was horrible especially punting into the win. So, given assumption (2) if we fail we likely get the ball back with excellent field position, and with the wind at our backs only needing  maybe 1 pass completion to get into field goal range.

(5) As a general principal I always believe that given a decent chance one should always play for the win on the road and for a tie to go to over time at home. (caveat about NW not being a real road game perhaps applies).

(6) If we tie the game NW gest the ball back on the 25 with lots of time and a great field goal kicker, even given major wind problems. I think NW's odds of moving down and getting the field goal they need are much, much better than getting a touchdown if they are down by 4.