Aaron Rodgers is the best quarterback in the NFL, and should be the highest-paid. We can all agree on that. But this guest column by Kevin Kolbe explains why salaries for other quarterbacks are all out of whack.

*Guest column by Conor McGovern*

You hear it all the time from commentators on TV: the closer you get to an opponent’s goal line, the easier it is to tighten up and make a stop. Of course, the caveat here is that it seems to become much easier to punch the ball in when you have a first down inside the opponent’s 5-yard line. But what about scoring touchdowns from farther out, say six to 15 yards from the goal?

On most of the football field, gaining more yardage on a given play is always desirable. For example, a play that goes for a first down on your own 45 is better than a play that goes for a first down on your own 43. But inside the opponent’s red zone, things start to get hazy. For one, according to the wisdom of the commentators, the closer the offense gets to the goal line, the less territory the defense has to cover. This is often summed up in the "bend but don’t break" mentality that some teams like to exhibit. (Patriots, I’m looking at you.)

A second potential wrench in the idea that being closer to the end zone is always better is that a first down from 11-to-15 yards out offers the opportunity for a team to get a first down inside the opponent’s 5-yard line, where the probability of scoring a touchdown is very high. What football fan hasn’t cringed as a running back bulls just inside the 10 rather than falling down at the 12, where the former results in first-and-goal and the latter would offer the opportunity for another first down inside the 2?

I decided to investigate whether there was anything to the idea that closer may not always be better. Using complete play-by-play from the 2000 through 2011 regular seasons and playoffs, I tested if a team with a first down 15 to 11 yards from their opponent’s goal is, on average, more likely to score a touchdown than a team with a first down 10 to 6 yards from the goal line (first-and-[long]-goal) because of more open field and the opportunity to get another first down inside the 5.

For the most part, closer is better. As shown in the bar chart, an offense with a first-and-goal between the opponent’s 6-to-9 yard line can expect to score touchdowns at a higher clip than those offenses outside the 10 who can still get a first down inside the 5. While the probability decreases at a gradual pace over that interval, it remains higher at the 9-yard line than at any subsequent yardage marker. Typically, teams with a first-and-goal from inside the 10 score a touchdown 64 percent of the time. On average, those with a first-and-goal right at the 10 reach the end zone on about 53 percent of drives, while offenses with a first-and-10 between the 11 and 15 will go on to score a touchdown 57 percent of the time.

That said, there is something to that cringing feeling that we get from the running back described above. An offense facing first-and-goal with 10 yards to the opponent’s end zone typically has the lowest probability of scoring a touchdown. Had he fallen down at the 12 instead of diving forward, his team could expect to score a touchdown about 9.1 percent more often on average –- a difference that is highly statistically and substantively significant.

Additionally, having a first-and-10 from the opponent’s 11 is only marginally better (3.8 percent higher probability of scoring a touchdown) than a first-and-goal from the 10. While some of this is probably statistical noise, we can be 95 percent certain that there is a systematic difference. One possible explanation for this odd finding is that this difference is a result of the unlikelihood of getting a first down at or inside the 1-yard line. Instead, offenses generally either score or get stopped. A drive with first-and-10 at the 11 is about 10 percent less likely than one with first-and-10 at the 12 to get a new set of downs by gaining ten yards, and the odds of getting a new set of downs increases from there.

While it appears that the probability of a drive ending in a touchdown for an offense with first-and-10 from the opponent’s 12 is only 1.35 percent lower than that for an offense with first-and-goal from the opponent’s 9-yard line, and the probability of scoring with a first down from the 15 is actually two percent higher than from the 14, we cannot be confident that these small differences are not just noise resulting from the selection of the sample.

Once an offense has a first down inside the 5-yard line, the end zone has to be the goal of every play. The chart shows the probability of scoring a touchdown based on down, yard line, and play choice.

At first glance, this hardly tells us anything we don’t know about today’s NFL. Except at the opponent’s 1-yard line, a passing play is typically preferable to running on any given play, and the probability of scoring a touchdown on any given play is lower the farther a team gets from the opponent’s end zone.

However, because running plays are more likely to result in a positive gain that does not score, probability may dictate that certain combinations of play choices are preferable to passing. For example, electing to pass on all three downs from the 5-yard line results in a 66.4 percent chance of scoring a touchdown on average, assuming that no play ends in a sack and field position does not change due to penalty. On the other hand, running three times from the 5 seems like it would be a worse choice. However, if the play can be assumed to achieve a positive result -– either gain two yards or score –- on each of first and second down, the probability of scoring a touchdown increases to 74.6 percent if a running play is called on third down, or 70.7 percent if a passing play is called.

Of course, this all rests on the competence of the rushing player and his offensive line. If you expect that a running play will gain one yard or score from the 5 and then pass on third down from the 3-yard line, the probability of scoring a touchdown is only 58.9 percent -- in other words, the offense with a below-average running game would be significantly better off passing three times from the 5.

While many teams choose to pass the ball on third-and-goal from the 1-yard line, the chance of scoring a touchdown is actually 12 percent lower when passing on third down as opposed to running. The standard selection of plays on first through third down from the 1 results in a touchdown 88.9 percent of the time, but running on all three downs increases this to 90.4 percent -- a small but not insignificant difference.

Therefore, inside the opponent’s 5-yard line, running is generally preferable to passing assuming a coach has some confidence in the ability of his running back and offensive line to gain positive yardage on a given play. Moreover, the chance of a catastrophic loss of yardage that would make scoring a touchdown on subsequent plays very unlikely is much lower for rushing plays than for passing plays, not only because of sacks, but because of the possibility of offensive holding penalties.

*Conor McGovern is a lifelong Patriots fan who remembers days when trips to the red zone were rare enough that any bit of help for Tommy Hodson or Hugh Millen was a godsend. He works in DC as a policy wonk on social and economic justice issues. If you are interested in writing a guest column, something that takes a new angle on the NFL, please email us your idea at info-at-footballoutsiders.com*

## Comments

## Re: A Closer Look at Touchdowns in the Red Zone

Karl Cuba:: Fri, 04/19/2013 - 12:50pmIn the second diagram is running blue and passing red?

Other than that, good stuff. The 'ten yard ditch' is interesting.

## Re: A Closer Look at Touchdowns in the Red Zone

Dean:: Fri, 04/19/2013 - 1:01pmIf the probability from the 10 is .531 and the probability from the 12 is .584, how could his team expect to score a touchdown about 9.1 percent more often on average? Wouldn’t that be 5.3%?

## Re: A Closer Look at Touchdowns in the Red Zone

BaconAndWaffles:: Fri, 04/19/2013 - 1:08pm9.1% is the percent increase above 534. So 584-531=53, and 53/531=9.1.

## Re: A Closer Look at Touchdowns in the Red Zone

Dean:: Fri, 04/19/2013 - 3:47pmAnd it's incredibly disengenious. It may be factually accurate, but it's deliberately misleading in order to artifically emphasize the point. Sort of like seeign a Pringles can with an extra inch of cardboard loudly proclaiming "9.1% more - FREE!" when in truth you're getting 5 more potato crisps.

## Re: A Closer Look at Touchdowns in the Red Zone

mgoetze (not verified):: Fri, 04/19/2013 - 7:08pmI disagree. The much more common opposite practice (of saying "percent" when what is meant is "percentage points") is the one which is misleading.

## Re: A Closer Look at Touchdowns in the Red Zone

LionInAZ:: Fri, 04/19/2013 - 8:21pmPotato chips are not sold as the same basis as touchdowms. It is not possible to measure TDs in a way to make them worth less than 6 points, unlike products, which be measured in multiple ways, eg, "This product is sold by weight, not by volume."

## Re: A Closer Look at Touchdowns in the Red Zone

Perfundle:: Sat, 04/20/2013 - 6:18am"Sort of like seeing a Pringles can with an extra inch of cardboard loudly proclaiming "9.1% more - FREE!" when in truth you're getting 5 more potato crisps."

Uhh... how is that misleading in any way? You think people will think that they're getting 9.1 more potato chips or something? People will think they'll get slightly more potato chips that previous cans held.

## Re: A Closer Look at Touchdowns in the Red Zone

Anonymous_me (not verified):: Sun, 04/21/2013 - 11:52pmThis is a tough one. If someone says "A is 100% (more/greater) than B", then I would expect that A = 2B. But if someone says "A is 5% and B is 10%", then I would be comfortable saying "B is 5% greater than A" because the units are all the same (like "A is 5 Cars and B is 10 Cars, so B is 5 Cars greater than A")

It just seems weird to say 10% is 100% greater than 5%.

If the article were written with the units being expected points from a TD (or some other unit), rather than probability of scoring a TD, then I think the confusion would be much reduced. I was greatly confused reading the article then looking at the charts wondering what I was missing...

## Re: A Closer Look at Touchdowns in the Red Zone

LionInAZ:: Mon, 04/22/2013 - 5:20pmIt becomes much clearer if you remember that percentages are actually *fractions*. 5% is the same as 5/100, and 10% is the same as 10/100. Does any doubt that 0.1 is twice as big as 0.05 (that is, it's 100% greater)?

## Re: A Closer Look at Touchdowns in the Red Zone

Anonymous_me (not verified):: Mon, 04/22/2013 - 9:53pmBut 0.10 is also 0.05 greater than 0.05.

(10 parts per hundred is 5 parts per hundred greater then 5 parts per hundred)

Both statements are true (or false, perhaps), but it is also clearly confusing or no one would be commenting.

## Re: A Closer Look at Touchdowns in the Red Zone

Perfundle:: Sat, 04/20/2013 - 6:21amSo if event A happens with 25% chance and event B with 50% chance, you'd say that event B is 50-25 = 25% more likely to happen? Everyone would say that it's twice as likely, or (50-25)/25 = 100% more likely.

## Re: A Closer Look at Touchdowns in the Red Zone

Jeremy (not verified):: Sat, 04/20/2013 - 7:33amno. 53.1% is 9.1(%) less than 58.4%. Not just 5.3 percentages points less than 58.4% out of 100 percentage points. .531/.584 =.909

## Re: A Closer Look at Touchdowns in the Red Zone

Aaron Brooks Go...:: Sat, 04/20/2013 - 2:40pmI have reservations about your usage, primarily because of its ambiguity.

When you're working in ratios (which is what % is), you're dealing with unitless constructs. Because a ratio of a ratio is itself also a ratio (%/% = %), without specific clarification, a reader cannot easily discern whether the difference is additive (5.3%) or multiplicative (9.1%).

I see this abused frequently in analyses of risk functions, where going from 1% risk to 0.5% risk is referred to as a 50% decrease in risk. It is not; it's a 0.5% decrease in risk. It's a 50% decrease in relative risk.

## Re: A Closer Look at Touchdowns in the Red Zone

RickD:: Sun, 04/21/2013 - 3:27pm(putting on math hat)

using % increase to describe the increse in two percentage values, where you divide by the original percentage, is inherently misleading and is bad form.

(/math)

Not that I'm a big fan of percentages in general, but to describe the increase from 50% to 60% as a "20% increase" instead of a "10% increase" is a good way to mislead the vast majority of readers.

## Re: A Closer Look at Touchdowns in the Red Zone

Perfundle:: Mon, 04/22/2013 - 2:20pmSo using the mathematically wrong number is more preferable to you because most people are mathematically illiterate?

Personally, I would be able to understand both versions. But what's the point of saying that the mathematically accurate version is misleading? If someone said that a batter's chance of hitting a ball increased by 50% this year when it was .200 last year, would you think he's at .700 or .300?

## Re: A Closer Look at Touchdowns in the Red Zone

zenbitz:: Fri, 04/19/2013 - 3:01pmYou know, excel can calculate P-values and such for you. I would like to know if the 10-to-go result was statistically significant (it probably is, given 11 years of play-by-play). Or at least how many plays are in each bin.

Other than that nerdly nitpit, good article.

## Re: A Closer Look at Touchdowns in the Red Zone

JDW (not verified):: Fri, 04/19/2013 - 3:48pmHow do you put this info to good use? I think you could teach it to scrambling quarterbacks, for when they run out of bounds. If you've got the first down already, but you know you you're going to get hit if you go inside the 10 (and your coach doesn't like it when you get hit), it makes perfect sense to ease off and run out at the 12 instead.

For the same reasons, it might be a useful strategy for all other players during end-of-half scenarios, if they find themselves intentionally running out of bounds. Aside from that, though, I think you'd want your skill players not to overthink it. You're better off if they try to break the tackle or gain a couple yards after contact to get to the 9 or closer.

## Re: A Closer Look at Touchdowns in the Red Zone

jpg30@earthlink.net:: Fri, 04/19/2013 - 4:43pmKarl, I'm quite sure that blue is scoring a touchdown & red is not scoring, on every particular down & distance. Colin, I would like to see a breakdown of running & passing plays on a separate chart, along with success rates by particular play choice.

## Re: A Closer Look at Touchdowns in the Red Zone

bhauck:: Fri, 04/19/2013 - 4:53pmNo, that doesn't make sense. The height of the bar is the probability, and there's two bars, one for passing, one for throwing. They don't add to 100%.

## Re: A Closer Look at Touchdowns in the Red Zone

chasehas:: Fri, 04/19/2013 - 5:26pmBased on "Except at the opponent’s 1-yard line, a passing play is typically preferable to running on any given play," I'm pretty certain blue is running and red is passing. Needs a legend.

Other than that, nifty article.

## Re: A Closer Look at Touchdowns in the Red Zone

RickD:: Sun, 04/21/2013 - 3:29pmThis.

## Re: A Closer Look at Touchdowns in the Red Zone

Steve in WI:: Fri, 04/19/2013 - 5:40pmI think the Lovie Smith-era Bears screw up the statistics, because as I recall their probability of scoring a touchdown with 1st-and-goal inside the 5 was virtually zero.

## Re: A Closer Look at Touchdowns in the Red Zone

Perfundle:: Sat, 04/20/2013 - 6:54am"The standard selection of plays on first through third down from the 1 results in a touchdown 88.9 percent of the time, but running on all three downs increases this to 90.4 percent -- a small but not insignificant difference."

No, running on all three downs from the 1 doesn't result in touchdowns 90.4% of the time. The probability of the average run from the 1 succeeding on first down, plus the probability of the average run from the 1 succeeding on second down after gaining zero yards on the first run, plus the probability of the average run from the 1 succeeding on third down after gaining zero yards on the second run, is 90.4%. But failing to get a touchdown on first down in no way guarantees you a second-and-goal from the 1. You could gain half a yard, in which case QB sneaks come into play; you could lose yards if the opponent gets backfield penetration; you could even turn it over if the ball is fumbled.

Sabermetrics like this work in baseball and basketball to determine betting order and shot selection because teams have essentially perfect information; managers know the expected batting average of their players against different types of pitchers in baseball, and the expected shooting percentage at different spots on the floor of their players in basketball; in football the added element of deceit complicates matters. I would imagine that play-action and QB draws on supposed rushing and passing situations are more successful than the average pass or run, but only if they're used judiciously. It'd be interesting to see the probability of teams scoring touchdowns with three straight runs after getting a first down at the 1, compared to three straight passes.

## Re: A Closer Look at Touchdowns in the Red Zone

RickD:: Sun, 04/21/2013 - 3:41pm"No, running on all three downs from the 1 doesn't result in touchdowns 90.4% of the time. The probability of the average run from the 1 succeeding on first down, plus the probability of the average run from the 1 succeeding on second down after gaining zero yards on the first run, plus the probability of the average run from the 1 succeeding on third down after gaining zero yards on the second run, is 90.4%. But failing to get a touchdown on first down in no way guarantees you a second-and-goal from the 1. "

This is a bit pedantic.

But, what the heck, I'll go one further. I'd wager that the conditional probability of scoring a TD on third down by a running play from the 1 yard line,

conditioned on having tried two prior running plays from exactly that spot, and failed both times, is considerably lower than the general conditional probability of scoring a TD on third down by a running play from the 1 yard line.The probability of 90.4% is probably* a good approximation. But to know what the exact probability is, you really have to look at situations where three running plays were called in a row.

From my non-scientific observations of this question, the more consecutive short-yardage runs a team tries, the less successful it becomes. Of course, that's a side-effect of selection: the best running attacks don't need three tries to score. So the running attacks that have not scored on their first two attempts are more likely to be weaker attacks. Whereas the general "3rd and 1 from the 1" statistic also includes the team that got 8 yards of rushing from 1st and 9 and 2nd and 5.

*for some unspecified value of "probably"

## Re: A Closer Look at Touchdowns in the Red Zone

Perfundle:: Mon, 04/22/2013 - 2:26pm"This is a bit pedantic."

Well, yes. This entire article is quite pedantic, wouldn't you say? When the author is writing "The standard selection of plays on first through third down from the 1 results in a touchdown 88.9 percent of the time, but running on all three downs increases this to 90.4 percent -- a small but not insignificant difference," only pedantry can show that he's wrong.

"The probability of 90.4% is probably* a good approximation."

It might be a good approximation, yes. That the number was used to show that running three straight times is more likely to get a touchdown than passing three straight times was what my issue was.

## Re: A Closer Look at Touchdowns in the Red Zone

stevent (not verified):: Sun, 04/21/2013 - 3:18pmI think it would definitely be a mistake to coach ball carriers to do anything other than try for as many yards as possible. I would never confuse the issue by telling them sometimes to pull up deliberately short (i.e. just before the ten).

first of all, it gives them too much to think about and would lead to the occasional total bonehead move through confusion in an intense situation.

second, I think you would take away the chance of breaking a tackle and scoring. Let's say you are carrying the ball and approaching the ten with a tackler in front of you and in good position to stop you. Presumably, this is the situation where you might deliberately choose to fall or run out of bounds or otherwise give yourself up just short of the ten. But how can you KNOW that tackler would stop you? If you give yourself up, you will never know...you might have beat him and scored (or taken it to the three or whatever).

In summary, ball-carriers should have the simple, aggressive thought of fighting for every possible yard. That way you avoid confusing the issue, possibly making a blunder, and occasionally score the improbable TD.

## Re: A Closer Look at Touchdowns in the Red Zone

JDW (not verified):: Sun, 04/21/2013 - 6:14pmIf you're at the 25, couldn't you mention to rodgers, (or RGIII, or any other smart quarterback that scrambles a lot) "If you scramble, don't run out of bounds right at the 10?" Players are often better than we expect at estimating their field position on the fly, and quarterbacks are already playing it safe because they're trying not to get hit.

## Re: A Closer Look at Touchdowns in the Red Zone

andrewm (not verified):: Sun, 04/21/2013 - 4:04pmHey, this is a point that does not undercut the overall point of the article, but... isn't there a selection bias in the data in the first chart? Aren't teams with better offenses more likely to get first downs closer to the end zone? And aren't teams with better offenses more likely to then score, because they are better? I am sure the effect is small (we are only talking about a yard or two here) but all the effects here are small and the sample size is large.

That wouldn't affect the significance of the dip at ten, but might flatten the curve 0-10.

## Re: A Closer Look at Touchdowns in the Red Zone

Kevin Skogg (not verified):: Sun, 12/22/2013 - 5:37pmWhat is the percentage of TDs scored in the NFL from outside the Red Zone?