Car Seat Placement Analysis
So during some downtime during paternity leave, I decided to really research where we should put my daughter’s car seat. After two hours of research and a small Monte Carlo simulation, this post is what I have to show for myself.
The key stat I found in my research is that putting the car seat in the middle can reduce the likelihood of fatality by 43% as compared to putting the car seat on the side [1]. That’s pretty significant, but lets look at that in context.
According to the DOT there is 1.1 fatal accidents per 100M vehicle miles driven [2]. Let’s say conservatively that 50% of those are side impact collisions.
Let me put that into my life — we typically drive my daughter about 75 miles per week to and from day care plus one longer trip during the weekend. Lets say she will be in the infant car seat (which we have to physically lift an put her into) for about 2 years. We will have driven ~7,800 miles with her in the car. Assuming that each mile driven is independent, I summed the binomial distribution (N=7,800, p = .55/100M) for k>0 to find the probability of a fatal side impact collision during my daughter’s infant car seat days to be:
\[ p ~= 3.5 * 10^-5 \]
[For those who care, this is where I got lazy and just did a Monte Carlo simulation rather than evaluate the binomial CDF which uses a regularized incomplete beta function. Apparently that’s where I draw the line for nerdiness on a post.]
Anyways…putting her in the middle reduces this by 43%. Figure 1 shows these two probabilities side by side on a graph. Note the y-axis here — I’ve zoomed WAY in to show the small numbers. Figure 2 shows the same plot zoomed to the full 0 to 1 probability range. Neither probability even registers as a single pixel on this image.
All else being equal I would obviously put my daughter in the center of the back seat and get that extra 43% of protection. But the problem is that all else is NOT equal. Let me now draw your attention to Figure 3. It shows the probability of my back giving out while putting my daughter into her car seat.
For the side position, I can just kind of put her onto my quads and click her infant carrier into place. There is some back trauma but a withstand-able amount. I put the odds of throwing out my back at 25%.
For the middle position I have (a) slide her in (b) lift her while by body is twisted in a strange position and then (c) awkwardly jiggle the infant carrier around until it f**ing clicks into place. I will, with 100% certainty, throw out my back doing that everyday. And I don’t know about you, but I like to have the ability to use my back to nice things like sitting, standing, walking, driving, etc. I’m fairly certain my daughter also likes it better when I’m not an invalid laying on the floor writhing in pain.
This is the dilemma I face. The only other option is to get rid of my fuel-efficient, compact car and get a gigantic, gas-guzzling SUV that has an easily accessible middle seat. Now I get why parents drive SUVs — it’s to protect their backs. Unfortunately driving an SUV has it’s own drawbacks of:
gas guzzler —> more reliance on Middle Eastern oil —> money to shady Saudi sheiks —> ISIS
And I don’t want to support ISIS. So for now, my daughter sits on the side. She seems pretty happy about it.