Safeties are so cool. Nothing fires up a defense and demoralizes an offense like a safety. They also throw off the 7 and 3-point arithmetic that football scores almost always follow. I always enjoy watching the score ticker at the bottom of the TV and thinking, “PIT 7 CLE 5?...How'd they get...oh yeah.”

But safeties are rare, with only 109 of them over the past 8 years, or about 1 in every 20 games. They’re also unique because the scoring team gets the ball. A free kick from the 20 yd-line usually means pretty good field position, and this is what makes safeties worth more than you might think.

Say you won $7 in a lottery 'scratcher.' But to go claim your prize, you’d have to use about $1 of gas. You could get stuck in traffic and it could cost $2, but you might get a ride from a friend and it would be free. But on average it would cost a buck. How much is that lottery ticket worth now? Now apply the same concept to football.

After a touchdown or field goal, the scoring team has to give possession of the ball to its opponents through a kick off. The resulting average field position is the 27 yd-line. In contrast, after a safety, the scoring team gets the ball back with average field position at its own 40.

In abstract terms, a touchdown really isn’t worth 7 points. Given enough time for the opponent to score, it’s really worth 7 points minus the expected point value of having the ball at the 27. The same principle applies to field goals.

Similarly, safeties aren’t really worth 2 points. Their ultimate value is 2 points plus the expected point value of getting the ball at the 40. Teams with 1st downs at their own 40 can expect to score 1.6 points on average, (assuming there is time to mount a drive). This makes the net value of a safety 3.6 points.

The table below lists the scoreboard point value of each type of score, the associated expected value of the ensuing kick, and the resulting net value.

Score Type | Point Value | Kick Off Value | Net Value |

Touchdown | 7 | -0.7 | 6.3 |

Field Goal | 3 | -0.7 | 2.3 |

Safety | 2 | +1.6 | 3.6 |

Two-point safeties are actually (or abstractly, if you prefer) worth more than three-point field goals. And more importantly, field goals aren't almost half the value of a touchdown. They're worth closer to a third.

Don't we need to consider the initial value of having the opponents pinned at their own 1-yard line?

What JH said. More specifically, shouldn't we subtract out the expected value of the field position BEFORE the play where the TD/FG/Safety happened?

Good point. So if we think of a score that way, a TD from the 10 yd line is really just 7 points - 5 pts - 0.7 pts = 1.3 pts. You can think of the value of the scoring play alone as worth that amount.

But what I'm thinking of is the value of the score in terms of the culmination of a drive. A lot of things can happen from the 1 or 10 yd line, but there's only one thing that can happen after a score--the ensuing kick.

But there's any number of ways of looking at it, and nothing says mine is the only correct way.

Another great column. I really appreciate your insights.

My 12-year old son and I were discussing this very issue yesterday following our discussion of the PHI/PIT game (we're stationed overseas, so he didn't see it, so we played "How could this score have occurred?). He suggested that a safety should be worth more points, to which I responded, it is worth more b/c you get the ball. He'll love this article.

Keep up the good work.

Thanks. Glad you enjoy the site. I just got back from a couple weeks overseas, and was able to watch all the games online with a high-speed connection--in Pakistan no less. Check out NFL Game Pass. It's about $20/wk to see every game, or less for the full season. I even hooked up my computer to the tv in my hotel room and watched games in HD. The only problem is the time difference, but you can go back and watch any game until Wed night. Sadly, it's not available in the States.

http://www.nfl.com/gamepass

I think a prime example of how it can vary is the Broncos/Saints game from Sunday. The Broncos stopped the Saints 3 straight times inside the 3. At the time, the score of the game was 24-17 Broncos.

The Saints had 2 options on 4th and 1, kick the field goal or go for it. Kicking the field goal makes the score 24-20 heading into halftime. More on that later.

The Saints went for it and were stopped. The Broncos took over at the 1, and on the first play tried to run it out of the endzone but didn't make it - safety for the Saints. Halftime score 24-19.

Now, for the rest of the game, the Saints were chasing that point they decided against. In the 4th quarter, the Saints were trailing 34-26 when they scred a TD. They felt obligated to go for 2 in order to tie. Had they kicked the field goal earlier, the difference would have been 1, or tied with an extra point.

The two point conversion failed, and the result was a 2-point win for the Broncos 34-32. I know this is just one example, and I'm not convinced that going for the TD in the 2nd quarter wasn't the right thing to do. But when it comes to points, 3 is greater than 2....

TSG

http://www.milehighreport.com

Right. Remember my caveat. The kick-receiving team needs time to mount at least a full drive.

It'd be interesting to compare the safety

to include the expected value for the defence (which will receive the punt from the endzone) if the offence were able to avoid the safety.

i.e. is the offence better off taking the safety, to kick the ball out to the 40 yd line, or are they better off throwing the ball out of bounds (for instance) and then punting.

TSG,

Of course, hindsight is 20/20, but I think Payton absolutely made the right call in that game. Now, to be clear - it didn't work out. He gambled and guessed wrong. But IMO the odds were clearly pointing towards taking that gamble, and the fact that it didn't work out doesn't change that.

You're right that getting the ball back is irrelevant in this case (ignoring the small chance of a return TD). What's not irrelevant is the chance they had to score a touchdown on the play before the safety.

Here is basically the calculation he has to go through:

((% chance of scoring on 4th down) + (% chance of NOT scoring on 4th down)*(% chance of getting a fumble/INT TD on defense with the Broncos backed up)) *

(% improvement in NO's chances of winning with those 4 extra points relative a FG)

+

(% chance of NOT scoring on 4th down)*(% chance of getting a safety) *

(% decline in NO's chances of winning with 1 less point relative a FG)

+

(% chance of NOT scoring on 4th down)*(% chance of Broncos running out the first half) *

(% decline in NO's chances of winning with 3 less points relative a FG)

Go ahead and plug in numbers there if you want. To me, it seems pretty clear that the odds would point in favor of going for it unless you think they had no chance of scoring the TD.

Curious: I see that you've posted there have been 109 in the past eight years, but I swear there have been a noticeable amount of safeties this year (including a game that had two - for the same team). Can you do a quick search in your DB for safeties that have occurred this season and see if it's happened more often than the previous eights seasons' 1 in 20 games?

From Wikipedia: "Under NFL rules, an unsuccessful extra-point is dead if kicked, but while attempting a two-point try, it is possible for a safety to be ruled if the defensive team forces the ball back into their own end zone and they recover. One point would be awarded [to the offense], instead of the two points that are normally awarded for safeties."

There have been an unusual amount of safeties this year-I factored 15 so far. From what I've found in the archives, this would crush the previous high-8 total in 1927. Do you have any stats to substantiate this? I can't seem to find anything. Please help. Thanks

-Chris

You can reach me at: chrisp@afsi.net

Counting safeties this way highlights a problem with this type of forward-projecting event-tree analysis. This brand of thinking stems from the same sort of framework provided by the Run Expectancy matrix in baseball. That works for baseball, though, because the game states are limited - 3 out states by eight base states = 24 possible states, and the game is capped insofar as a third out terminates the process and takes RE to 0. So it makes sense to say that a 2 rbi single with runners on 2nd and 3rd and 0 outs isn't "really" worth two runs, because it's actually 2 runs scored minus the 1.967 that were already expected in the remainder of the inning plus the .853 of the new game state (for a total of .886 runs). It's nothing to sneeze at, but it's not two.

In the analysis of the safety in this article, you're leaving out the expected points of the game state that are already established. Having an opponent inside their own five already has an expected point value, precisely because of the good chances of a safety or a punt w/ good field position or a pick-six or what have you, According to an EP post on this site, a team with ball at its own endzone expects to score -2 points. The correct assessment using the logic above is that a safety is 2 points scored minus the 2 that was already expected plus the 1.6 of ensuing field position or just 1.6 points - again, not 2, but not 3.6, either. Neglecting to include that initial expectancy is the football equivalent of crediting the 2 rbi single above with 2 runs plus the new state of .853 - so a two rbi single is "really worth" 2.853 runs, which hopefully doesn't make sense - the batter capitalized on an already rich opportunity, as does the safety here, so full credit for the two points/runs is misleading.

I think you *have* to include that EP of current state for this to make any sense. As delimited above, there's too much variety of future states to account for (without embedding them in an overall EP of the current state as in baseball). E.g., if it's third down on the opponents two and the defense succeeds, it's either going to force a turnover (and score?), get a safety, or force a fourth down punt. To know what the safety in that case is "really worth," you'd need to know values for and chances of all of the alternatives. Just limiting it to punt or safety, you would need to know what EP the punt is going to yield before evaluating the value of the safety. Let's say the average starting position after the punt is your opponent's 40 - not crazy as the average net punt is 39 yards, and the whole 10 yard instead of fifteen yard snap probably harms the punter. From your graph it looks like the EP of that field position is 2.6 points or so. Which is to say that in that restricted scenario, the value of a safety is 2 plus 1.6 for field position minus the 2.6 field position you would have gotten without the safety. So the safety is worth one point of added EP, not two and not 3.6.

That's oversimplified, and it's the reason you need an EP for the general state of "opponents pinned inside five" incorporating all outcomes, values and probabilities, in order to really get at what change to the game state and EP a safety brings. I still worry that the relative unconstrained space of the football games (to baseball) means that it's fairly arbitrary to only include the field position of the ensuing kickoff. Because that field position has an average field position that it will yield on the next possession, etc. - you could chase the expected net points to the end of the half/game, which is a very loose end-rule for the game (unlike the hard and fast three outs rule in baseball). That makes it seem like you're talking more about WPA than net points anyways, because incorporating all events out to the end of the game means you would only really care how much more likely a particular team is to win at the end given a particular decision or what have you.

Good post, and good comment from Nyet.

I don't think both the original post and Nyet Jones' comment can both be considered "good." Jones' comment politely and rigorously pointed out how poorly-reasoned the original post was. He also estimated that the true value of a safety is *less* than two points, which was exactly the opposite of what Burke claimed. Yes, I read Burke's earlier comment which vaguely argued he was looking at the value of an entire drive that happened to end in a safety. Um, recall the title of the article: "What's a Safety Really Worth?" It was not: "What's a Drive That Began at a GWP-neutral Field Position and Took No Time Off The Clock and Ended in a Safety Really Worth?" Those are not similar concepts and obviously the former is much more interesting than the latter.

Even the most simple-minded analyst out there would try to estimate the *change* in game situation from having opponent pinned deep to 2 pts. plus having the ball at the 40 -- not the raw value of 2 pts. plus having the ball at the 40 -- when calculating the "value" of a safety. That's like assessing the value of a two-point conversion and ignoring the fact that 0.99 pts. would have been scored on a PAT if the conversion att. hadn't occurred. I had to re-read the original article three times to confirm Burke was in fact being that ignorant.

For those who are skimming to end of the comments, here is an all-caps summary:

A SAFETY -- AS IN, THE ACTUAL PLAY -- IS NOT WORTH ANYWHERE NEAR 3.6 POINTS

How many teams have won games in which they score a safety? I would like to see this ratio to truely value the safety.