Filed Under:Claims, Auto

The Monte Carlo Method for Determining Auto Liability, Part One

Determining liability in an auto collision has often been viewed as more of an art than a science. Therefore, it shouldn’t be too surprising that a record number of disputes are being sent to Arbitration Forums for resolution. If you empower the claims adjuster with the flexibility to define the standard to which they compare a driver’s performance, then it is not particularly shocking that the resulting analysis supports their initial take on liability. Because no standard is more valid than the next, you are left with a stalemate of sorts, regardless of how hard you argue.

Although there may be some doubt about an individual liability assessment, there is no doubt about its impact on the bottom line. Not only does it affect the amount an insurer pays on the claim, but it also keeps the company from properly assessing the risk and collecting the appropriate premium. Auto collisions are particularly well suited for scientific analysis. After all, the vehicles involved are governed by the laws of physics described by Newton many centuries ago. Advances in technology not only make a scientific approach feasible, but cost-effective as well.

A collision occurs because two vehicles attempt to occupy the same space at the same time. As long as both cars reach impact at the same time, we have a common point on each vehicle’s timeline. This allows us to work backwards and calculate where they were at any point prior to impact, assuming that we know what each was doing. Our objective is to evaluate what the driver either could have—or should have—done in response to a perceived hazard. This requires taking certain factors into consideration, including acceleration rates, initial speeds, distances, perception/response times, and so on. With these variables, we can calculate the total stopping distance of the approaching vehicle. If it is at least this distance from impact, then the collision is avoidable. The adjuster will be able to collect some of these items from statements and others from police reports. During the course of the accident investigation, published research will also provide a reference and assist in making the most accurate determination possible.

The Monte Carlo Analysis

One may wonder about the reliability of these values. That is where the Monte Carlo analysis comes in.

The Monte Carlo analysis is a technique by which the collision is evaluated multiple times using a mathematical model. Each input variable is replaced with a uniform probability distribution with a reasonable range of values identified by the investigator or a normal probability distribution from research with a defined mean and standard deviation.

For instance, the approaching vehicle might be operating somewhere between 35 and 45 miles per hour. A random value within this range is selected for the series of calculations that determines whether or not the collision occurs. This process is repeated, for all of the variables, 15,000 to 100,000 times until the model accounts for almost every possible combination of values. The uncertainty of these values is addressed by the fact that we use every reasonable value in our calculations. Count how many times the collision occurs out of the sample population and it provides us a percentage representing the probability of a collision.

Because the perception/response times are calculated from compiled research, you are actually comparing this driver’s performance to the remainder of the population. Not only do you know how the average driver would have responded, but you also know how any and all drivers would have responded.

Percentiles and Liability

How is this valuable? Let’s go back and look at a path intrusion. If the Monte Carlo model suggests that 95 percent of the drivers, when presented with this hazard, would have been involved in the collision, then it is very difficult to argue that the driver of the approaching vehicle should be penalized because he or she was not in the top 5 percent of all drivers. Conversely, if the model suggests that 80 percent of drivers would have successfully avoided a collision, you can effectively demonstrate that the approaching driver’s performance was well below average and a significant contributing factor, even though they were proceeding with the statutory right of way.

Now take it a step further. How many times do you have an admission that a vehicle was traveling marginally above the posted limit? Sure it is an ordinance violation but did it make a difference? The model allows you to examine the impact of individual variables. For instance, the approaching driver admits to traveling 45 mph in a 35-mph zone. Run the model at 35 miles per hour and we may find that the probability of a collision was 45 percent. Now run the model at 45 miles per hour, and it increases to 55 percent. Even though it is only a difference of 10 miles per hour, we can say that the unlawful speed increased the probability of a collision by 10 percent and made it more likely than not (> 51 percent).

Gap acceptance is defined as the percentage of drivers that would have pulled into the roadway with a vehicle approaching at that distance. Take the speed argument and apply it to the gap acceptance evaluation. By traveling faster than the flow of traffic, the intruder would have perceived that he or she had more time that was truly available, making it more likely that they would attempt to cross.

Hopefully this helps illustrate why a math-based approach can offer a competitive advantage in liability negotiations. In the remaining segment, let’s look at a hypothetical case.

Path Intrusion from a Side Street

The insured is an elderly driver with her husband in the passenger seat of their full size sedan. She is stopped on a side street at the sign and pulls westbound to cross the roadway. She is struck in the left rear half of the vehicle by a 20-year-old male driving a sports coupe northbound in the left lane. During the course of the investigation, the young driver admits to traveling 35 or 40 miles per hour in a 25-mph zone, and claims that the insured pulled out so suddenly that he didn’t have any time to hit the brakes.

The police then cite the insured for failure to yield the right of way. The claimant driver is alleging injuries that resulted not only in treatment but also in lost wages. He retained an attorney who has filed suit for policy limits of $100,000.

 

 

After an initial evaluation of the case with a right-of-way violation, the claims adjuster felt that they could accept 80 percent and try to negotiate 20 percent on the approaching driver for unlawful speed.

The Monte Carlo collision simulations for this loss showed that there was a 58-percent probability that this collision could have been avoided by a vehicle operating between 25 and 30 miles per hour. For a vehicle approaching between 35 and 40 miles per hour, as admitted by the claimant driver, the probability of avoiding this collision dropped from 58 to 45 percent, making a collision 13 percent more likely. The young driver’s decision to speed made a collision more likely than not. The driver’s lack of response resulted in an impact over twice the speed of an average driver presented with the same circumstances.

The Monte Carlo analysis provides strong evidence that the young driver’s unlawful speed was the proximate cause of this collision and its severity. The claims adjuster is now in a position to argue for more contribution on the approaching driver, despite the fact that his or her insured was cited for failure to yield.

Next time, we’ll look at a scenario involving a left turn with approaching traffic.

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