# Good Math/Bad Math

## Wednesday, March 22, 2006

I was forwarded a link this afternoon, to some really bad political math. It seems that the great blowhard, Rush Limbaugh, had the following image on his website:

It has apparently since disappeared; but there've been a lot of similar pieces showing up in the conservative press. So let's just take a look at the numbers. They claim to be putting the number of American deaths in Iraq into perspective. So, they pick a few ways that a lot of people have died, and give the numbers:

1. Death by auto accident: 120,000
2. Death by falling: 45,000
3. Death by poisoning: 27,000
4. Death by drowning: 12,000
5. War in Iraq, all causes: 2,300

So, what's wrong with this picture?

The problem is that it's comparing apples to orchards.

The military doesn't give the exact number of soldiers in Iraq. Various reports I found on the web give the number anywhere from 120,000 to 150,000. So, let's by generous, and assume that the number of soldiers there is at the large end. That means that we're talking about 2,300 deaths out of about 150,000 people.

According to the US census bureau, the number of American citizens is 295,734,134. We'll round that down to 295,000,000. And we'll ignore the fact that there are a lot of non-citizens in America, and that the death numbers cited other than the Iraq war are for American residents, not American citizens. So we're talking about 216,000 deaths out of about 295,000,000 people.

Let's normalize those numbers, to deaths/1000 people.

1. Death by auto accident: 0.4/1000
2. Death by falling: 0.15/1000
3. Death by poisoning: 0.1/1000
4. Death by drowning: 0.04/1000
5. Death of US soldiers in Iraq: 15/1000

So, if we actually look at the numbers in a realistic context - that is, normalized to give a way to compare in a meaningful way, then the deaths of soldiers in Iraq is about 22 times larger than the sum of the most common accidental deaths in the US. Put another way, if the death rate of Americans were the same as the death rate of American soldiers in Iraq, then since the beginning of the Iraq war, we would have seen 4,425,000 accidental deaths instead of 216,300.

And as an aside, I've got to say, the image of Rush Limbaugh holding an American flag while trying to diminish the magnitude of the sacrifice made by American soldiers in this foolish war is deeply, deeply sickening. Give our soldiers the respect they deserve for the kinds of sacrifices they're making: what they're doing is a whole lot harder and more dangerous than anything any of us do in our normal lives. To pretend that the deaths of these people - not to mention the deaths of all of the innocent Iraqi's - is the equivalent of getting into a car accident is disgraceful.

• Actually, your math isn't doing all that well either. First, there's a population of between 100,000 and 150,000 soldiers at any one time --- but it isn't the same soldiers at all times. So the population against which you should be computing is considerably more, over that 3 years span.

Given that soldiers are rotating out and back, it's a good guess that the total number of soldiers who have been through Iraq is more like 300,000 --- which means your rate is an over-estimate by a factor of two. In fact, there are about 500,000 soldiers in the Army alone, and given retirements and separations, that's still a lower limit just for Army. So your estimate is probably more like a factor of four too great.

If you want to make a point about "bad math" you might weant to be a little more careful with your own.

That estimate of 300,000 is pretty rough, however; you might do better by actually referring to the Department of Defense mortality statistics. There you'll discover that there were more deaths in 2004 from accidents and illness than from hostile action.

Or, you might compare the number of deaths per year for US police officers. There are roughly 1.8 million active duty military personnel in the US, and about 1 million police employees. Compare around 800 deaths from hostile action in 2004 for the military, and 157 for a million police, and notice that the police number is probably a little high.

Or you might have compared death rates in the military against other dangerous professions.

Or you could have compared the Clinton years against the Bush_{43} years, and discovered that actually there were almost as many deaths under Clinton as under Bush, even with a war on under Bush.

• I love you

By  Anonymous, at 5:33 AM

• Seneca the younger,

This blog entry was pointing out 2 things. First, that the comparison that Rush Limbaugh was making about traffic deaths, etc. used math poorly. Second, that it is revolting to the author, and to myself, for Rush Limbaugh (or anyone else for that matter) to belittle the sacrifices of our troops in Iraq by comparing them to traffic accidents.

The fact that the analysis could have been done in other ways has no bearing on the points made about Rush's bad math.

The fact that the numbers of troops who have served in Iraq is not clear is also not germaine to his points.

Even if his estimate is a factor of four too great, it still means that American solders serving in Iraq are more than 6 times more likely to be killed than all the most common American deaths combined.

While your points are valid, they are not the point that the author of this blog was making. The Rush Limbaugh claim was bad math.

By  Flex, at 8:14 AM

• Or you could have compared the Clinton years against the Bush_{43} years, and discovered that actually there were almost as many deaths under Clinton as under Bush, even with a war on under Bush.

Or, you could do your math right, and see that those stats only go up to 2004, meaning that some of the worst years of Iraq haven't been taken into account. And then, you could normalize your numbers for the overall size of the military, which has decreased under Bush 2, to get the death rate per n soldiers. Or, if you wanted to be even more relevant in your comparison, you could only look at death due to hostile action, where there is no comparison at all; 1 under 8 years of Clinton versus 1102 under 4 years of Bush (which does not include the bloody 2005 and the not-looking-great-so-far 2006).

There you'll discover that there were more deaths in 2004 from accidents and illness than from hostile action.

Or, again, you could do the relevant thing and only look at the concerned population. If we assume that accidents and illness occur at a similar rate in Iraq and Afghanistan as elsewhere (and if they don't, then any difference should be counted as part of the war-caused casualties, so this is actually the most conservative estimate), but that all hostile deaths only occur in the war zones (which, as far as I know, was true for 2004), and we estimate that 10% of the military is in the war zones at any given time, then we see that, for 2004, 81.7 troops in war zones died of accident or illness, while 737 died of hostile action.

And the police deaths are 153, not 157. And if we look at 2004, the last year of statistics in both tables, there were about 1.4 million active duty military, not 1.8 million. So, that leads to 0.79 deaths due to hostile action/1000 military (overall, not just in the war zones) versus 0.15 deaths in the line of duty (which is not the same as hostile action; it includes things like work-related illness and non-felonious auto accidents). The police number is at a low point, but near the mean, while the military number is uncharacteristically high for the post-Vietnam era.

If you're gonna critique basic stats, please do your basic stats right.

By  Shygetz, at 8:15 AM

• seneca:

Sorry, but you're wrong about how to compute normalized casualty figures. The fact that one person rotates out and another rotates in in their place doesn't actually change the normalized numbers: the number of people in danger in Iraq remains exactly the same - the size of the pool of people out of which casualties come stays the same. When a soldier finishes their term of duty in Iraq and comes home, they're not part of the pool of people in Iraq anymore - they're now part of the pool of Americans at home.

Second, WRT the DoD mortality statistics: when an explosive overturns a vehicle, that's counted as a vehicular death, not hostile action. Hostile action deaths are deaths in combat with an enemy; passive weapons where you aren't shooting at and being shot at by an enemy don't count as "hostile action" deaths.

And third, WRT the casualty figures under other presidents: you're playing exactly the same game as Rush: you're not normalizing. The size of the military has been dramatically reduced. Redo those figures in terms of deaths per thousand active duty troops, and you'll see a rather different picture.

By  MarkCC, at 8:19 AM

• markcc already made my point: that the relevant number for soldiers in Iraq is the 'permamnent' population, not the number that have flowed through. If we needed to take the number that have flowed through, we would have to consider tourists and anyone else that had ever set foot in the US when calculating the accidental deaths in the US. Ridiculous.

By  gravitybear, at 9:08 AM

• The real number is 5/1000, not 15. The other mortality rates are deaths per thousand people per year, so you have to divide by three to make an apples to apples comparison.

By  OneEyedMan, at 10:04 AM

• It should not surprise anyone that draft-dodging drug addicted ex-welfare queens like Limbaugh would distort the numbers and belittle the very people he claims so often to love to score political points with his dimwitted worshippers.

As a veteran, I am disgusted that soldiers are used as political pawns by right-wing zealots like Limbaugh, and at the same time, I am embarrassed that so many in the military listen to and believe what thay lying scum says.

By  Doppelganger, at 10:14 AM

• Rush isn't even the worst of it. Look at this article in WorldNetDaily from back in December. Here's the headline: California homicides dwarf Iraq deaths
State lost 2,394 to murder in 2004 compared to 905 coalition lives
.

They sort of don't mention that California's population is over 33 million. Globalsecurity.org and Wikipedia seem pretty close on the estimate of non-US coalition forces in Iraq, about 20-25,000. Going with high-end figures for Iraq and low-end for California, that gives us death rates of 2394/33M vs 905/175000, or 0.07/1000 vs 5.17/1000.

Makes Rush seem almost moderate by comparison, doesn't it?

By  jackd, at 12:51 PM

• Falling Down, Poisioning, and Drowning are certainly not comparible to death in war or automobile accidents, in the sense that these things are not voluntary. One doesn't have to drive. One does not have to go half way around the planet and make war. It is interesting to note that there is a risk of death just driving to work. I know people who have decided not to take this risk, don't own a car and don't drive. I could take the bus.

I might be interested in risk analysis. Should I go into the army or be a traveling salesman? I might be interested in total deaths. I've got \$500,000,000 to spend on saftey, where do i put it to save the most lives? The Rush statistics don't really give the goal.

The Rush stats also don't address the people in Iraq, who, after all, are humans too. We have goals, yes. Is it worth the cost paid by those in Iraq?

By  Stephen, at 2:27 PM

• Whether to use absolute deaths or per capita deaths is not a mathematical choice but a political one. I hope this blog doesn't degenerate into a "My Lies vs. Your Lies" argument.

By  Randy MacDonald, at 3:39 PM

• OneEyedMan,

This link indicates on the order of 40,000 automotive deaths per year, so I suspect that the accidental death numbers have also been appropriately scaled for the time frame in question.

By  Anonymous, at 3:56 PM

• randy: sure it's a political choice which way to give the figures. But it's also the CORRECT choice to give them as per capita, instead of absolute figures, or we cannot make a proper comparison.
This does not relieve us of the responsibility to think critically about the figures presented and decide if they are meaningful.
This is not a case of duelling statistics, the rate of deaths is clearly the proper figure to look at in this situation.

By  gravitybear, at 4:31 PM

• This comment has been removed by a blog administrator.

By  Anonymous, at 4:54 PM

• I know that the accidental deaths were scaled to one year. I meant that you have to use the one year number for deaths of soldiers, which is 600, 900, or whatever, but not 2300. That gets you something more like 5 per thousand not 15 per thousand.

By  OneEyedMan, at 6:01 PM

• Ack! All you number crunchers, Rush Limboob and the rest of the chicken hawks (mostly Republican starting at 1600 Pennsylvania Avenue) have missed the most important statistic...

When the GI who is killed is the father/husband/son/daughter/mother of a child, the loss is 100% father/husband/son/daughter/mother.

When day is done, and it is lights out, that is the only stat that really matters.

11B

By  markprobert, at 8:31 PM

• I know that the accidental deaths were scaled to one year. I meant that you have to use the one year number for deaths of soldiers, which is 600, 900, or whatever, but not 2300. That gets you something more like 5 per thousand not 15 per thousand.

Exactly. If you're going to use the population of military in Iraq at any one time, it's a mistake --- at best --- to use the total number of hostile fatalities over three years to try to come up with a fatality rate. Or much of anything else.

You want an interesting comparison, look at the number of fatalities in the line of duty by police officers, per year, compared to the rate of fatailities from hostile fire in Iraq over the same year. Or deaths by illness vs death by hostile action.

But this was a mistake --- and trying to defend it this way is an embarrassment.

• Mark, I suspect (all things considered) that I've lost more friends in combat than you have; I absolutely agree with you that every death is a tragedy.

What it comes down to is whether freeing 25 million people from a murdering fascist dictator is a worthy thing, and the sacrifice an honorable one for the people doing it. I think so, it appears you don't.

But that's a political question, and a moral one, not a mathematical one.

• seneca:

I'm not going to get into a debate about whether or not this war was a good idea.

My point in this post - which you are trying to avoid - is that people are using really bad math to try to diminish the danger that our soldiers are facing, and to diminish the sacrifices that they're making.

The fact of the matter is, military service in Iraq is very damned dangerous. It is not comparable to the risk of falling down the stairs in your home. It is not comparable to the risk of getting into an accident with your car. It is far, far more dangerous, and the people facing that danger deserve to have their courage and sacrifice respected, not diminished for political purposes.

By  MarkCC, at 8:21 AM

• But whether or not you should scale to the size of the pool of people in Iraq depends on what you're trying to prove. If the intention is to compare the safety of being an American soldier in Iraq to being just an American at home, you're probably right (and if you're going to talk about the relative safety of being an active soldier under various presidents, you should probably scale to that, etc), but what Rush Limbaugh is doing could actually be relevant if you consider the number of deaths as a sort of "cost to America" (arguing in essence, perhaps, that a few thousand people is not very significant when you've got the whole American people to draw from, or that it's a "cost" that can easily be handled).

From that short ad alone, it's just impossible to see what the intention was.

By  Anonymous, at 9:07 AM

• Seneca the Younger said...
Mark, I suspect (all things considered) that I've lost more friends in combat than you have; I absolutely agree with you that every death is a tragedy.

Me: You can suspect all you wish, but 11B from 1968 to 1969 in SEA says otherwise. I still maintain close contact with several widows and my "extended children".

What it comes down to is whether freeing 25 million people from a murdering fascist dictator is a worthy thing, and the sacrifice an honorable one for the people doing it. I think so, it appears you don't.

Me: LEAPING LOGIC! My empathy for those individuals who are directly affected by the loss of loves ones allows you to conclude that? Whew...

But that's a political question, and a moral one, not a mathematical one.

Actually, it is a human one. Human decisions are often overlooked in both the mathematical and political decision making process.

By  The Probe, at 9:12 AM

• "What it comes down to is whether freeing 25 million people from a murdering fascist dictator is a worthy thing, and the sacrifice an honorable one for the people doing it. I think so, it appears you don't."

Since this is a math and logic blog, consider this: Pro-war folks used this same "killing them to save them" logic in Viet Nam. In the present war, however, we've been much more efficient: in a three years we've totally destroyed Iraq's infrastructure, and caused the murder of almost as many people (if you use independent figures rather than the US's non-counting method of determining Iraqi deaths) as 25 years of previous Iraqi government did.

Instead of puffing up about all the good we're doing by killing these people and destroying their country, why not ask THEM how they feel about it? I suspect they don't think you're doing them any favors.

By  Anonymous, at 9:35 AM

• Well, if Rush is going to "put the numbers into perspective", in order to make some argument that the deaths of soldiers isn't really that significant compared to total deaths, then why not add in the WTC deaths? Of course, he won't do that because if you put the WTC deaths up there (2752 dead), then you wonder whether the "war on terrorism" is really worth it. You might think "gee, we have a lot bigger problems than terrorism on our hands, maybe we should spend hundreds of billions on making cars safer instead of wars."

Mind you, I'm not actually arguing these points. I'm just pointing out how tortured the logic is here, and if the Right would use the same logic across all situations, it would come back to bite them in the ass.

By  BC, at 9:01 PM

• Identity and Attribution.

Am I the only person who is aware that the pictured man with the flag isn't Limbaugh?

Secondly, this image is an advertisement and has been spotted on other sites as well. It isn't something Rush or his handlers came up with, necessarily.

By  calocedrus.decurrens, at 4:04 PM

• I know that the accidental deaths were scaled to one year.

The ad itself says that the number of accidential deaths are summed over all three years.

Whether those numbers are correct or not is not for me to answer, but any error there is not on MarkCC's part.

By  JS, at 5:39 AM

• The problem is figuring out the the proper denominator. Getting the danger into the proper units is tricky.

Ideally you'd want to know what was the likelihood of dying in a consistant unit across all the dangers, but poisoning is tricky.. The others are less so, you just measure them per hour of putting yourself in danger. Compare an hour of patrol with and hour of walking the beat with an hour of driving. I'm not sure how we'd get that data, so maybe we need get all of these dangers into risk per person per year of normal exposure? Then we can take the average number of people to do the activity and assume that half do it more and half less, more or less symmetrically. How can we get all of these dangers into risk per person per year of normal exposure?

Cars:
Annual car deaths divided by number of people who rode in a car at least once or were substantive risk of dying in a car accident. Since many poor people take much safer public transport and live in neighborhoods with low speed traffic, 300 million seems like too large a denominator per year.

Police:
Annual police officers jobs dying in the line of duty divided by the average number police officers with non-office jobs in that year

Soldiers:
Annual soldiers in Iraq dying in the line of duty / average number of soldiers in Iraq

The problem with the multi year comparisons is the denominator moves for some of these measures and not for others. Take an extreme example. Looking backward, measure the likelihood of an American resident dying of terrorism in the last hundred years. You would not want to total the terrorism deaths and divide it by the average American population. Wouldn't you want the total number of people who died in that 100 years divided by either the total number of US residents or the number of US residents who died?

In the car accident case, the US population is very stable (sample people in the start and end of period) , but in the case soldiers dying, the number soldiers in Iraq is not stable. So either we must use one year comparisons or deal with creating an accurate measure of true populations.

By  OneEyedMan, at 10:43 AM

• Now, lets look at the real numbers. All war is hell but these numbers give our military the credit they deserve;

World War II...450,000 dead
War on Terror....2,300 dead

By  Anonymous, at 2:05 PM

• In fairness to both sides, why not agree to disagree stating that the military has its perks and its set backs just like any other thing i life!

By  inuthedemon, at 10:26 AM