In a recent Usenet exchange, a poster informed me that "The studies show that if you hit a pedestrian at 20mph there is a 95% survival rate, at 30mph it is 80%, at 40mph it is 10% (or 20% for a small child)." I found the size of the effect implausibly large, asked for a source, and was told that it was "A paper by Ashton and Mackay."

Curious, I turned to Google. The facts, so far as I can determine them:

The paper is cited as Aston and Mackay (1979). Many references give what appear to be the same figures, cited to a U.K. dept of Transport publication from 1992; my guess is that it's citing the paper. One webbed source gives the figures as:

"A pedestrian has a 95 per cent survival rate when hit by a car driving at less than 20mph. At less than 30mph their survival rate is 55 per cent. At 40mph, survival rates are only 5 per cent. (Ashton and Mackay 1979)"

In this version the figure is not for 20 mph but for "less than 20 mph," averaging in the collisions at five or ten miles an hour, and similarly for "less than 30 mph." Comparing "less than 30 mph" to "At 40 mph" makes the difference between 30 and 40 look a lot larger than it actually is. On the other hand, some other pages citing the figures give them as "20 mph," "30 mph," "40 mph"—with the same survival rates. The poster also strikingly exaggerated the survival rate associated with 30 mph, but that's not terribly surprising since he, like the earlier poster whose information he was attempting to clarify, was presumably working from memory. I gather the figures have been extensively used in the U.K. in attempts to persuade drivers to drive more slowly.

Which gets me to the real point of this post. Googling around, it seemed clear that the figures are routinely used by people who want to persuade other people to drive more slowly, hence people with an obvious interest in claiming that mortality rates increase rapidly with speed. I conclude that the "under 30 mph" version is probably the real one, since converting that to "at 30 mph" makes the argument look stronger. I also note that the figures are from research done nearly thirty years ago, which is at least mildly suspicious; it suggests that the people quoting those figures, with no explanation of how they were calculated, may be selecting the study that best supports what they want others to believe, not the most recent or best study. I have not been able to find any webbed version of the study itself; if a reader has actually seen it, I would be interested to know just how the figures were calculated.

Finally, I did come across one interesting bit of actual data relevant to the question:

"in Zurich, the urban area speed limit was lowered from 60 to 50 km/h [37 to 31 mph] in 1980 ... . In the year after the change in the urban speed limit there was a reduction of 16 percent in pedestrian accidents and a reduction of 25 percent in pedestrian fatalities (Walz et al, 1983)."

Curious, I turned to Google. The facts, so far as I can determine them:

The paper is cited as Aston and Mackay (1979). Many references give what appear to be the same figures, cited to a U.K. dept of Transport publication from 1992; my guess is that it's citing the paper. One webbed source gives the figures as:

"A pedestrian has a 95 per cent survival rate when hit by a car driving at less than 20mph. At less than 30mph their survival rate is 55 per cent. At 40mph, survival rates are only 5 per cent. (Ashton and Mackay 1979)"

In this version the figure is not for 20 mph but for "less than 20 mph," averaging in the collisions at five or ten miles an hour, and similarly for "less than 30 mph." Comparing "less than 30 mph" to "At 40 mph" makes the difference between 30 and 40 look a lot larger than it actually is. On the other hand, some other pages citing the figures give them as "20 mph," "30 mph," "40 mph"—with the same survival rates. The poster also strikingly exaggerated the survival rate associated with 30 mph, but that's not terribly surprising since he, like the earlier poster whose information he was attempting to clarify, was presumably working from memory. I gather the figures have been extensively used in the U.K. in attempts to persuade drivers to drive more slowly.

Which gets me to the real point of this post. Googling around, it seemed clear that the figures are routinely used by people who want to persuade other people to drive more slowly, hence people with an obvious interest in claiming that mortality rates increase rapidly with speed. I conclude that the "under 30 mph" version is probably the real one, since converting that to "at 30 mph" makes the argument look stronger. I also note that the figures are from research done nearly thirty years ago, which is at least mildly suspicious; it suggests that the people quoting those figures, with no explanation of how they were calculated, may be selecting the study that best supports what they want others to believe, not the most recent or best study. I have not been able to find any webbed version of the study itself; if a reader has actually seen it, I would be interested to know just how the figures were calculated.

Finally, I did come across one interesting bit of actual data relevant to the question:

"in Zurich, the urban area speed limit was lowered from 60 to 50 km/h [37 to 31 mph] in 1980 ... . In the year after the change in the urban speed limit there was a reduction of 16 percent in pedestrian accidents and a reduction of 25 percent in pedestrian fatalities (Walz et al, 1983)."

That implies that fatalities/accident, the relevant figure for calculating the survival rate, fell by only about 9% when maximum speed went from 37 to 31 mph. It's hard to see how that can be consistent with the sort of drastic reduction of mortality that is supposed to be associated with speed reduction within the same range according the figures attributed to the Ashton and Mackay paper.

When deciding whether to believe what someone says, it is worth first asking why he is saying it and how strong his incentives are to know whether it is true. Readers who have hard data on either side of the question are invited to submit it. Why should I do all the work?

---

After writing the above, I discovered that another Usenet poster, better at using Google than I am, has tracked down what appears to be the original paper. It contains no numbers corresponding to those cited, only a couple of figures with hand drawn graphs, one showing the frequency and one the cumulative frequency of various levels of injury as a function of speed. Trying to estimate numbers from the graphs on Figure 1, the survival rate if hit at 30 mph appears to be about 75%, at 40 mph between 20% and zero—the latter figure is very uncertain since at that point the width of the line is a significant fraction of its height above the axis.

Looking at the cumulative distribution (Figure 2), it appears that it is indeed the source for the 30 mph figure, since the ratio of fatalities to all injuries is about 45%, implying a survival rate of about 55%. So it looks as though the comparison being made is between the survival rate at under 30mph and the rate at exactly 40 mph, as I conjectured.

There is, however, a small problem. The first graph shows a considerably higher survival rate at 30 than the second shows at under thirty; since survival rates are falling as speed increases, that is impossible. Either I have misread the graphs—readers are invited to explain how—or the paper all of these numbers are supposed to be based on gives results that are striking inconsistent, indeed impossibly so.

In looking at the graphs, note that speeds are given in kph not mph.

When deciding whether to believe what someone says, it is worth first asking why he is saying it and how strong his incentives are to know whether it is true. Readers who have hard data on either side of the question are invited to submit it. Why should I do all the work?

---

After writing the above, I discovered that another Usenet poster, better at using Google than I am, has tracked down what appears to be the original paper. It contains no numbers corresponding to those cited, only a couple of figures with hand drawn graphs, one showing the frequency and one the cumulative frequency of various levels of injury as a function of speed. Trying to estimate numbers from the graphs on Figure 1, the survival rate if hit at 30 mph appears to be about 75%, at 40 mph between 20% and zero—the latter figure is very uncertain since at that point the width of the line is a significant fraction of its height above the axis.

Looking at the cumulative distribution (Figure 2), it appears that it is indeed the source for the 30 mph figure, since the ratio of fatalities to all injuries is about 45%, implying a survival rate of about 55%. So it looks as though the comparison being made is between the survival rate at under 30mph and the rate at exactly 40 mph, as I conjectured.

There is, however, a small problem. The first graph shows a considerably higher survival rate at 30 than the second shows at under thirty; since survival rates are falling as speed increases, that is impossible. Either I have misread the graphs—readers are invited to explain how—or the paper all of these numbers are supposed to be based on gives results that are striking inconsistent, indeed impossibly so.

In looking at the graphs, note that speeds are given in kph not mph.