I am preparing a case study on the Dora Farms strike at the onset of Operation Iraqi Freedom. I came across this priceless calculation by General Tommy Franks and one of his subordinates:
“What the probabilities of mission success with a single aircraft?”
Buzz didn’t hesitate, “A single aircraft gives us a probability of .5.”
Again, I thought before speaking. Normally, I was a glass-half-full optimist, but tonight there could be no risk of failure. “What does it take to get to one hundred percent—two planes?”
“Probability of success goes to 1.0, General.”
“Buzz” is Michael Moseley, now Air Force Chief of Staff.
Really, is it this hard? .5 squared is .25 or a seventy-five percent chance of one or both aircraft getting through. A third F-117 would have brought the chance of mission success to nearly ninety percent.
I don’t even want to begin to explain the concept of independent errors—one of the many mistakes that bedeviled Desert One.
Of course, the entire strike was based on bad dope: No matter how many aircraft CENTCOM assigned, they couldn’t compensate for Saddam not being anywhere near the target.
According to Human Rights Watch, “The attack resulted in one civilian killed and fourteen wounded, including nine women and a child.” Naturally this will be the important point of your case study.
A later attempt to assassinate Saddam, the April 7 bombing at Al-Mansur in Baghdad, “killed an estimated eighteen civilians.”
http://hrw.org/reports/2003/usa1203/4.htm#_Toc57442243
I think a review of the history of attempted assassinations by US bombs, Predator drones, etc. since 2001 will show that it has rarely succeeded in killing its intended targets but often succeeded in destroying or shattering many times more innocent lives. The use of converted Trident SLBMs would almost certainly extend the same record without improvement.
Of course if other people do this, we call it terrorism; when we do it, we call it counterterrorism, so I guess that’s the same thing.
> Really, is it this hard?
Yes, it really is that hard for virtually everybody on the planet, including those with several stars on their shoulders.
I sometimes and quite quixotically muse that a several-semester series of courses on “How to think” should be taught in high school. Those would include how to use elementary arithmetic, basic probability, an introduction to basic logical techniques and basic logical fallacies.
But then I come to my senses and move on to more possible things.
“With four planes, we’ll get him twice, General.”
Reminds me of a systems reliability briefing I gave once. All subsystems were 95%-99% reliable, and a colonel in the front row accused me of low-balling the total system reliability.
“Come on! If everything works 95% of the time or better, how can the whole thing only work 80% of the time?”
Oy.
It is probably a little unfair to critique this exchange from a strictly statistical perspective.
Moseley’s initial response of “0.5” was not meant to be an accurate assessment of the risk of mission failure – rather, he likely intended to convey the message “one aircraft is not enough to be sure”.
Franks got the message, and asked him what was required in order to be sure. With two aircraft, Moseley had sufficient confidence of getting bombs on target to say “1.0”. What he probably meant here was “With two aircraft, it is highly unlikely we won’t get the job done”.
So I suppose my point is, its easy to lampoon this exchange, but its important to consider that neither party really intended the discussion to be a rigorous analysis of probabilities.
Rather, this is a senior commander asking a trusted subordinate what he needs to get the job done. Both probably would acknowledge that they were using the probability figures loosely in this context.
Bob Woodward’s 2004 narrative of the Dora Farms action can be found HERE
If numbers are being used metaphorically (0.5 really means “kinda iffy” and 1.0 means “pretty sure”), it would be comforting to have some indication that the military had a common understanding of it.
See, by the way, “What Percent Is ‘Slam Dunk’?”:
http://www.washingtonpost.com/wp-dyn/articles/A37115-2005Feb19.html
As someone who’s done some weaponeering in the past, this is an interesting discussion. Moseley almost certainly did not know the true figures since the actual people who do weaponeering and make Pk (probability of kill) judgments are junior officers and senior enlisted people. They use a computerized version of the JMEM or Joint Munitions Effectiveness Manual. The JMEM is a classified program that calculates conventional munition effectiveness against virtually any type of target.
A simple doubling of the number of aircraft does not necessary double the effectiveness, nor does it follow a predictable mathematical model – it all depends on the particular munitions, the specific target as well as other variables. I’ve seen Pk’s that went from .3 to .95 with the addition of a single weapon, but I’ve also seen it only go from .3 to .5 by tripling the number of weapons. It all depends on what weapons are available and how effective they are against the particular target employed from a particular aircraft flying a particular mission profile.
For practical purposes .95 is the upper limit to allow for variables like incorrect fusing and the geometry of the attack – there is inevitably some variability in a free-fall weapon’s velocity and angle-of-attack that does affect fusing and penetration, particularly on hardened, underground targets.
Additionally, intelligence gaps about the target can create problems, particularly underground bunkers. In the First Gulf War, for example, we didn’t know anything about Iraqi bunker construction until the French gave us the blueprints.
A Pk of 1.0 is really an impossibility, but likely represents a significant degree of saturation to reasonably account for any variables or unknowns.
It’s important to note Gen. Moseley’s experience as well which was exclusively in Fighter aircraft. His last flying assignment was ended in 1989. He was never a bomb-dropper so his personal knowledge of the weaponeering is likely limited.
Perhaps Franks here should be commended. A guy with his experience must certainly understand basic probability, which would suggest he intentionally used hazy thinking to avoid using more bombs necessary ensure a much higher probability than 75 percent, thereby minimizing casualties. Perhaps he himself doubted whether Saddam was in the farmhouse.
When you’re going to be snarky, it helps if you’re right. Unfortunately, you might not be.
Are the success probabilities of the two planes totally independent from each other? Could it be possible that two planes could watch each others’ backs, creating a dependency between their success probabilities? If so, the equation you chose for combining probabilities is wrong.
Btw, I could imagine situations where a single plane has a 0.1 probability, but two planes would have 0.9.
A Pk in this case may refer to the level of damage for military estimates as talked about above in the Pk calculations for weapons. In general, a Pk of 0.1 means minor damage, but still functional, 0.5 means extensive damage, still functional but at a loss of overall capability, 0.9 means unable to operate. This is also known as damage criteria, or levels of damage as a result of blast fragmentation warheads. In my opinion, bombs should not be used for assination, they are just too messy sometimes.
No matter how many complex, non-linear interactions one posits, there is still no way to get General Franks to a 1.0 probability of mission success — if that is indeed what he means by 1.0.
Given that the threat to the F-117s arose from the ground, I find it hard to believe that one could “watch the back” of the other.
Good thought, though. And probably applicable in other cases.