What's a Safety Really Worth?
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.
Posts
12 comments:
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
Post a Comment