4th Down and 5 on the 40

I'm watching the Jaguars-Packers preseason game. In the 1st quarter with the score 0-0, the Packers decided to go for it on 4th down. They had a 4th and 5 on the Jags' 40 yd line. Putting aside this is just the preseason, is this a good idea?

After reading this study, I'd be inclined to say yes. Coaches tend to make decisions not to maximize points, but to minimize Monday morning criticism. Here is how I see a coach's decision matrix:

Make the safe but bad call = keep your job
Make a bold but correct call and suceed = keep your job
Make a bold but correct call and fail = lose your job

It's a no-brainer for most head coaches--punt. But what's safe for the coach's job may not be what's good for his teams chances to win.

[Have you ever noticed that when you are playing Madden or other football video games, yourself and others tend to go for it on 4th down far more often than in the real NFL? You'd probably think twice if it meant the unemployment line by January.]

Back to the Packers. This is a back-of-the-envelope analysis, so I will simplify the situation somewhat. Let's spell out the data we have and make some educated assumptions about the data we don't:

--I'll assume the average punt from the 40 ends up at about the 15 yd line. Sometimes it would end up a touchback, and other times it would be fair-caught or downed around the 10.
--The average play in the NFL is 5.0 yds. So the Packers have about a 50/50 shot at getting 5 yds and a 1st down. They'd end up at the 35.
--The average series success rate for the NFL in 2006 was 65%. NFL teams average a first down 65% of the time starting from a 1st and 10.
--Since the average play is 5 yds, the average successful series yields 15 yds.
--I am assuming no 'freak' plays (penalties, interceptions, fumbles).

Let's consider the punting option first. By punting from the 40 to the 15, the net difference is 25 yds. It takes 1.67 successful series on average to move 25 yards downfield (25/15 = 1.67). Since the series success rate is 65%, the probability of "1.67 successful series" is:

0.65 ^ 1.67 = 0.49

The number of successful series required to go 85 yds from a team's own 15 to the end zone is 85/15 = 5.67. The probability of 5.67 consecutive successful series is:

0.65 ^ 5.67 = 0.09

So by punting, the Packers would have effectively cut the Jags' ability to score in half. And if they go for it and fail, they've doubled the probability the Jags would score, a 0.18 probability.

But if the Packers get the 1st down, they're now at the 35 with a 1st and 10. They would need 2.33 more successful series to score a TD (35/15 = 2.33). The resulting probability is:

0.65 ^ 2.33 = 0.37

But remember, they need to get that 1st down first, which they have a 0.50 probability of obtaining. The resulting probability of a TD is:

0.50 * 0.28 = 0.18

The crucial probabilities the Packers should consider are:

Packers score a TD: 0.37 if GB makes the 1st down, 0.00 if they don't
Jaguars score a TD: 0.09 if GB punts, 0.18 if GB fails to get the 1st down

Ultimately, the Packers have a 50/50 shot at a 0.37 chance to score a TD, but only risk a net forfeit of a 0.09 chance to their opponent. It's a good call, considering only TDs.

The field goal equation also favors the Packers. If they get to the 35 with a 1st down, they only need 3 plays to get 5 yds to the 30, a range well within Longwell's ability. This is a likely close to a 50/50 proposition.

From their own 40, the Jaguars would need about 2 1st downs to get to the Packers' 30 and into field goal range. The chances of this are:

0.65 ^ 2 = 0.42

I realize this is a simplified analysis. I haven't considered the full effect of fumbles, interceptions, big pass interference calls, etc. But those considerations would have to be extremely strong, and unequal with respect to which team they favor, to overcome the balance of probabilities on the Packers' go for it side. I'd love to see more teams go for it on 4th down in the regular season.

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3 Responses to “4th Down and 5 on the 40”

  1. slash says:

    Just a few questions here. First 3rd and 5 is not normally a running situation. Lets say it is a 90% passing situation. How will that change the average yards.

    Secondly while 5 yards may be the mean is that also the median (maybe not the right term, been a while since I took stats)? If a team has 10 plays and 9 get 1 yard (skewing these from reality just to show the point better) but the last goes for 41 yards, the mean is 5 yards, but the chance to convert get a 5 yard+ gain is only 10%. Thus making this a pretty bad idea to go for it I think.

  2. slash says:

    back, was driving home from work and thought about this on the way. Feel free to bash away, ex-squid here too.

    The way I would think of this is (don't have the stats just looking at the logic):

    First percentage of passes in these situations vs. Runs. Should be pretty skewed to the pass as teams would only run taking the big chance that the D is not expecting it at all 98:2 ratio wouldn't surprise me in this situation.

    how often do you get more than 5 yards. IE in 20 pass completions 14 go for 5+ yards, thus a 70% success here so far (once again you would figure pretty high being 4th down, I don't think many would trust Yac to get them the 1st, dumping off is less of an option here)

    Finally completion percentage in these situations. Just looked at a few QB's careers and only had 4th and 3-7 yards, but McNair nor Bledsoe had over 50% here for their careers, but it really varies, Manning is 80%. Not sure on the sample size of attempts so it might not be that major of a difference though.

    then do the same with the run, how many get 5+ and grab a percentage of success

    Then you would have something like

    {run% (.02 in my example) * % of runs that are 5+ yards} + {pass% or .98 in my example * (comp% in this situation * % of completed passes that are 5+ yards)}

    Add in percentages for int/fumble/sack/loss of down penalties as necessary. Would think they would be higher taking more chances here.

    So is anything right at all in there? Didn't get to plug in fake numbers to see if my little equation was done correctly.

    But in the end (not going to count the run here) if you have a really high INT/sack/Fumble/LOD penalty % say 10%, a 45% completion percentage, and 80% of your completions go for 5+ yards in these situatiions you would be looking at success rate in the low 30's rather than 50/50.

  3. Brian Burke says:

    Slash-was going back through some older comments. All good points. Most QBs complete at least 50% of their passes, and the average pass is over 6 yds. That is skewed by some very long passes. But then again, nothing would be stopping the offense from throwing a deep pass on 4th down.

    One thing to point out is the "Passing Premium" study that showed that passes in "passing situations" are no less successful than when they occur on running downs.

    50/50 might be a little optimistic, but probably not by much. We could look at 3rd and 5 situations. The strategy would essentially be the same.

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