
Drinking vs. Nondrinking Drivers
Americans' annual consumption of pure alcohol is 2.1 gallons or 277 ounces per capita. The Gallup Poll notes that a third of the population abstains from drinking completely, and that 60% has had a drink within the last week, 35% of whom had a drink within the last 24 hours. 65 million men and 53.7 million women over age 14 consumed 76 billion ounces of alcohol, which is an average of 1.75 ounces each per day. Men consume an average of 2.3 ounces each per day and women consume an average of one ounce each per day. This is enough to keep the blood alcohol content (BAC) of each of these 65 million men above 0.17 and each of these 53.7 million women above 0.09 each and every day of the year. The Montana Highway Traffic Safety Division notes that "An average person's body will eliminate alcohol at the rate of .015 BAC per hour." This means that it takes 11 hours for the average man who drank 2.3 ounces of alcohol and 6 hours for the average woman who drank one ounce of alcohol to reduce their BAC to 0.015. The higher probability that nondrinking drivers will have an accident contributes to an increase in the accident rate for drinking drivers. To determine exactly how much higher the accident rate for drinking drivers is because of nondrinking drivers it is necessary to calculate the rate at which both drinkers and nondrinkers are expected to have an accident. The total number of accidents that a drinking driver is expected to have per million miles is the sum of his probability of having a single driver accident, plus the square of this number to represent a two driver accident involving another drinking driver, plus his expected number times the number of accidents per million miles which a nondrinking driver is expected to have, or N_{n}. If we let N_{d} = The number of single driver accidents that drinking drivers is expected to have per million miles. N_{d}^{2} = The number of accidents per million miles that a drinking driver is expected to have with another drinking driver. N_{d} x N_{n} = The number of accidents per million miles that a drinking driver is expected to have with a nondrinking driver. then we have two equations and two variables. Number of accidents per year by drinking drivers = 1,400,000 accidents Number of miles driven per year by drinking drivers = 1 trillion miles N_{d}^{ + }N_{d}^{2} + N_{d} x N_{n }= 1.4 accidents per million miles The equation for nondrinking drivers is similar: N_{n} = The number of single driver accidents that nondrinking drivers would be expected to have per million miles. N_{n}^{2} = The number of accidents per million miles that a nondrinking driver would be expected to have with another nondrinking driver. N_{d} x N_{n} = The number of accidents per million miles that a drinking driver would be expected to have with a nondrinking driver. Number of accidents per year by nondrinking drivers = 2,800,000 accidents Number of miles driven per year by nondrinking drivers = 1,000,000 million miles Accident rate per million miles = 5.6 accidents per one million miles = 1 accident per 178,571 miles N_{n}^{ + }N_{n}^{2} + N_{d} x N_{n }= 5.6 accidents per million miles N_{d} = (5.6  N_{n}  N_{n}^{2})/N_{n} (5.6  N_{n } N_{n}^{2})/N_{n} + (31.36 11.2N_{n}  10.2N_{n}^{2} + 2N_{n}^{3} + N_{n}^{4} )/N_{n}^{2} + 5.6 N_{n}^{ }N_{n}^{2} = 1.4 5.6N_{n } N_{n}^{2}  N_{n}^{3} + 31.36 11.2N_{n}  10.2N_{n}^{2} + 2N_{n}^{3} + N_{n}^{4} + 5.6N_{n}^{2 } N_{n}^{3  }N_{n}^{4 = }1.4N_{n}^{2} 31.36 5.6N_{n}  7N_{n}^{2} = 0 7N_{n}^{2} +5.6N_{n} = 31.36 N_{n} = 1.755 = Number of accidents per million miles that a nondrinking driver is expected to have. N_{d} = 0.436 = Number of accidents per million miles that a drinking driver is expected to have. If nondrinking drivers were not colliding with drinking drivers, and if drinking drivers drove all 1,500 billion of the miles currently driven by both nondrinking and drinking drivers, there would be (N_{d} + N_{d}^{2}) x 1,500,000 million miles = 939,144 drivers in accidents per year, which is only 22.4% as many are there currently are. If only nondrinking drivers drove all 1,500 billion of the miles currently driven by both nondrinking and drinking drivers, there would be (N_{n} + N_{n}^{2}) x 1,500,000 million miles = 7,252,538 drivers in accidents per year, which is 73% more than there currently are. If only nondrinking drivers drove there would be 7.7 times as many accidents than if only drinking drivers drove. But there is a serious problem with MADD's statistics, because where MADD claims that one third [and where some headlines proclaim that one half] of all serious or fatal accidents are alcoholinvolved, reports from police departments across the nation show that only 4% are. This means that 96% and not 66% of accidents involve only nondrinking drivers, which changes the accident probabilities significantly.
(N_{d} + N_{d}^{2} + N_{d}N_{n}) x 1,000,000 million miles driven = 170,000 accidents N_{d} + N_{d}^{2} + N_{d}N_{n }= 0.17 The equation for nondrinking drivers is similar: (N_{n} + N_{n}^{2} + N_{n}N_{d}) x 500,000 million miles driven = 4,030,000 accidents N_{n} + N_{n}^{2} + N_{n}N_{d} = 8.06 N_{d} = (8.06  N_{n}  N_{n}^{2})/N_{n} (8.06  N_{n } N_{n}^{2})/N_{n} + (64.96 16.12N_{n}  15.12N_{n}^{2} + 2N_{n}^{3} + N_{n}^{4} )/N_{n}^{2} + 8.06 N_{n}^{ }N_{n}^{2} = 0.17 8.06N_{n } N_{n}^{2}  N_{n}^{3} + 64.96 16.12N_{n}  15.12N_{n}^{2} + 2N_{n}^{3} + N_{n}^{4} + 8.06N_{n}^{2 } N_{n}^{3  }N_{n}^{4 = }0.17N_{n}^{2} 64.96  8.06N_{n}  8.23N_{n}^{2} = 0 8.23N_{n}^{2} +8.06N_{n} = 64.96 N_{n} = 2.6321 = Number of accidents per million miles that a nondrinking driver is expected to have. N_{d} = 0.05 = Number of accidents per million miles that a drinking driver is expected to have. If nondrinking drivers were not colliding with drinking drivers, and if drinking drivers drove all 1,500 billion of the miles currently driven by both nondrinking and drinking drivers, there would be (N_{d} + N_{d}^{2}) x 1,500,000 million miles = 78,750 drivers in accidents per year, which is only 1.9% as many are there currently are. If only nondrinking drivers drove all 1,500 billion of the miles currently driven by both nondrinking and drinking drivers, there would be (N_{n} + N_{n}^{2}) x 1,500,000 million miles = 14,340,076 drivers in accidents per year, which is 3.4 times more than there currently are. According to police reports only, if only nondrinking drivers drove there would be 182 times as many accidents than if only drinking drivers drove.


