## The lottery of drunk driving fatality

Several years ago, I read of a news account of a mother driving with her infant son in a minivan. A drunk driver was driving on the same freeway but in the wrong direction and collided with the minivan. The mother died upon impact. Amazingly the infant survived. News accounts like this one are always heart wrenching.

I always think of dying from a crash involving an alcohol-impaired driver is a lottery. It is a negative lottery for sure since no one would want to win it. Los Angeles Angels pitcher Nick Adenhart and two of his friends were the unfortunate “winners” of this negative lottery in 2009.

What are the odds of winning this negative lottery? How often is this negative lottery “won”? Let’s compare the number of drunk driving deaths with the number of winning Lotto tickets that pay out $1 million or more. The comparison is done on an annual basis and as a rate per certain number of minutes. It turns out that winning this negative lottery is far more frequent than winning the Lotto. Driving under the influence of alcohol is a serious problem. The numerical data presented here bear that out. Drivers are considered to be alcohol-impaired when their blood alcohol concentration (BAC) is 0.08 grams per deciliter (g/dL) or higher. Thus any fatality occurring in a crash involving a driver with a BAC of 0.08 or higher is considered to be an alcohol-impaired driving fatality. According to a report from the Center for Disease Control and Prevention (CDC), one alcohol-impaired driving fatality occurs every 45 minutes (see note 1 at the end of the post). This rate of occurrence is derived from the fact that in 2008, 11,773 people were killed in alcohol-impaired driving crashes. What is the total number of Lotto winners in a year? Here, we only focus on the winning prizes of$1 million or more. Would the number of Lotto winners approaches 11,773 in a year? I do not think so. I hunted for data from the website of the California Lotto, I found that as of today’s date, there are only 247 winning tickets that pay out \$1 million or more since the inception of the California state lotto in 1985. So in 25 years, there are only about 250 winners in the state of California. Thus on average there are only about 10 “million dollar plus” Lotto winners a year in California.

Multiplying across the 50 states in the United States, the total number of “million dollar plus” Lotto winners should be no more than 500 in a year. This should be a pretty conservative estimate since California is the largest state in the country (with the largest population). Not all 50 states in the country have Lotto. Some states do not have their own Lotto and are part of a multi-state Lotto. So 500 is a good upper bound on the total number of “million dollar plus” Lotto winners in a year.

With 500 winners a year, there is one “million dollar plus” Lotto winner every 1050 minutes (see note 2). Or one winner in every 17.5 hours (see note 2). Thus alcohol-impaired driving deaths occur at least 23 times more frequently (one death per 45 minutes vs. one per at least 1050 minutes).

Of the 11,773 alcohol-impaired driving deaths in 2008, how many of them were the drunk drivers? According to a report from National Highway Traffic Safety Administration (NHTSA), an agency within the Department of Transportation, we have the following breakdown of the drunk driving fatality in 2008.

$\displaystyle \begin{pmatrix} \text{Role}&\text{Number}&\text{Percent of Total} \\{\text{ }}&\text{ }&\text{ } \\\text{Driver With BAC=0.08+}&8,027&\text{68 percent} \\\text{Passenger Riding w/Driver With BAC=0.08+}&1,875&\text{16 percent} \\\text{Occupants of Other vehicles}&1,179&\text{10 percent} \\\text{Nonoccupants}&692&\text{6 percent} \\{\text{ }}&\text{ }&\text{ } \\{\text{Total Fatalities}}&11,773&\text{100 percent}\end{pmatrix}$

Most of the deaths were self-inflicted (68%). According to the same report, 216 of the 1,875 deaths in the above table were children. The group of 2,087 (=216+1,179+692) were truly victims and their deaths were senseless. Angels pictcher Nick Adenhart and the mother mentioned at the beginning belong to this group. They did not do anything wrong and were just in the wrong place at the wrong time.

If we just focus on this group of children riding with the drunk drivers and the occupants of other vehicles and nonoccupants, the rate of occurence is still pretty high (one fatality every 252 minutes; see note 3). That comes up to be about one fatality every 4.2 hours (see note 3). Focusing on this group alone, the rate of drunk driving fatalities is over 4 times higher than winning the Lotto (one death per 252 minutes vs. one winner per at least 1050 minutes).

Eliminating the category of fatality represented by these 2,087 senseless deaths would drive down the rate of fatality and would go a long way to address the problem of drunk driving. Though this would be only modest improvement, it would be a step in the right direction.

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Note 1
To derive the rate of one death per 45 minutes, we need to calculate the total number of minutes in a year. There are 365 x 24 x 60 = 525,600 minutes in a year. Then divide 525,600 by 11,773 to obtain 44.64 minutes = 45 minuties.

We can get a perspective of this calculation by looking at an example of taking an exam. For example, if you have two hours (120 minutes) to take an exam and the exam has 10 problems, then on average you have 12 minutes to work one problem. Thus if you can work one problem per 12 minutes, you can expect to finish the exam in the allotted time.

Back to the alcohol impaired driving situation, there are 525,600 minutes in a year and there are 11,773 events. Thus on average there are 45 minutes allotted for each event.

$\displaystyle \frac{365 \times 24 \times 60}{11,773}=44.64 = 45 \text{ minutes}$

Note 2

$\displaystyle \frac{365 \times 24 \times 60}{500}=1051.2 = 1050 \text{ minutes}$

$\displaystyle \frac{1050}{60}= 17.5 \text{ hours}$

Note 3

$\displaystyle \frac{365 \times 24 \times 60}{2087}= 252 \text{ minutes}$

$\displaystyle \frac{252}{60}= 4.2 \text{ hours}$