The University of California has published a study of pedestrian crashes in Oakland, California,
The Continuing Debate about Safety in Numbers—Data from Oakland, CA
Judy Geyer, Noah Raford and David Ragland, Traffic Safety Center;
Trinh Pham, Department of Statistics, UC Berkeley
UCBITSTSC20063
The full report is available online:
http://www.escholarship.org/uc/item/5498×882
John Forester, founder of the Effective Cycling program of cyclist education, and statistician, has demonstrated that the Safety in Numbers claim of Jacobsen (also cited in the Oakland paper) is faulty. Due to faulty math, a random set of numbers will generate the curve that apparently shows a decreasing crash rate with increasing numbers of users. This is not to say that the safetyinnumbers claim is false, but rather that Jacobsen has provided no evidence to support it. (Forester also questions Jacobsen’s explanation for safety in numbers as applied to bicyclists, but that’s a different issue.)
The Oakland report expresses the same complaint about Jacobsen’s math, and goes on to use better math to look for answers. Here’s a quote from page 5 (PDF numbering) of the Oakland report:
However, others are concerned that correlating collision rate (C/P) with pedestrian volume (P), (where C equals collisions and P equals pedestrian volume) will almost always yield a decreasing relationship due to the intrinsic relationship of the variable P and the fraction 1/P.
Tom Revay has generated a Microsoft Excel Workbook demonstrating how Jacobsen’s curve may be generated with random data. Press the F9 key on a PC to refresh the random data. (Press Command [Apple] and = at the same time on a Mac. I thank Dan Carrigan for this information)
The Oakland study came up with some interesting and intriguing results. Here are a few; please correct me if I am wrong:
 The graph on p. 17, PDF numbering (click to see a larger version) shows the characteristic downward curve due to faulty math. However, the curve slopes back upwards for the intersections with the very highest numbers of pedestrians.
A better graph (graph on p. 16, PDF numbering, click to see a larger version) shows crashes increasing with a steeper slope for the highervolume intersections, worst at the intersections with the highest volume. Crash numbers are low enough, though, that the results for individual intersections are not statistically significant.
 The Oakland study examines different intersections in the same community over the same time period rather than the same intersections at different times, or different communities with different volumes of pedestrian and vehicular traffic. The study can establish whether the safety in numbers effect applies only under the conditions it examined. Data from different times of day might possibly be checked against traffic volumes, though the results would be less robust and effects of lighting, alcohol use etc. would make them harder to interpret.
 It is clear that a few intersections are outliers, with many more crashes than others. These intersections would be high on a priority list for improvements — though the actual numbers for individual intersections, again, are too low to be statistically significant. The problem with lack of statistical significance highlights the importance of applying research data and operational analysis in determining where to make infrastructure improvements — crash data for an individual intersection are not statistically robust unless the intersection has an extremely bad problem. You apply research results and operational analysis so you can avoid collecting data on each intersection by killing and injuring people.
 (See Results, p. 9, PDF numbering) Number of lanes on the primary and secondary streets, and number of marked and unmarked crosswalks, did not correlate with crash rates! (But note that this result is consistent with data on bicycling showing that riding on arterials is safer than on residential streets).
 Despite the safetyinnumbers finding, the intersections with the largest numbers of crashes are still those with high pedestrian volumes. Increasing numbers decrease the rate of crashes, but not the number of crashes.

The crash rate increases for pedestrians as the number of vehicles increases (page 18, PDF numbering), though less rapidly than the number of vehicles. Is there a safety in numbers effect for vehicle operators as the number of vehicles increases? Yes, the likelihood that any particular driver will collide with a pedestrian decreases with the amount of vehicular traffic passing through an intersection — though the study doesn’t report this. The study doesn’t answer whether the result is achieved by improved signalization at highvolume intersections, or by depressing pedestrian volume (risk homeostasis), or by what other effect. The study also doesn’t say anything about crashes overall, as it doesn’t report on crashes not involving pedestrians.
All in all — interesting, intriguing, and careful research — but more research is needed!