The math of Ferguson: percentages don’t show how bad it really is

14 Mar

The other day, I was talking to my colleague Dr Scott Roy. We were working on the second midterm exam for our genetics class at SF State, but got distracted. We started talking about the DOJ report on Ferguson and especially the numbers in the report about racial bias. These are some of the numbers we talked about:

  • 67% of the population in Ferguson is black.
  • Blacks account for 85% of vehicle stops.
  • Blacks account for 90% of citations.
  • Blacks account for 93% of arrests.
  • Blacks account for 95% of “Manner of Walking in Roadway” charges.
  • Blacks account for 94% of all “Failure to Comply” charges.
  • Nearly 90% of documented force used by FPD officers was used against African Americans.
  • Blacks account for 100% of dog bites.
  • Blacks account for 96% of cases where someone was arrested by FPD only because of an outstanding municipal warrant.

So, from reading these numbers, it is clear that there is a very strong racial bias. But, even though Scott and I are both used to working with numbers because we work in a very quantitative corner of the biological sciences, we realized that it was hard to wrap our heads around those percentages. We wanted to know: how much more likely is a black person to be arrested? How much more likely is a black person to encounter use of force by the police? In other words. How bad is the situation really? Just from the percentages, this is hard to know.

I asked 4 of my students today: if blacks account for 85% of the vehicle stops in Ferguson, how much more likely is a black person to be stopped compared to a non-black person? They guessed about two times as likely. I’ll show here, that it is much closer to three times as likely. It’s even worse than it sounds.

How bad is it?

To calculate how bad the situation really is, we need to do some math.

First of all, in stead of thinking of 67% of the population being black, let’s just look at the actual number of people. Ferguson has a population of around 21,000, so that means that there are 14070 black people and 6930 non-black people in the city.

Now, let’s look at the vehicle stops. The DOJ report says that 85% of the vehicle stops involved black drivers. The DOJ report actually gives the numbers (although we could calculate without those, see next paragraph).

“FPD [Ferguson Police Department] reported 11,610 vehicle stops between October 2012 and October 2014. African Americans accounted for 85%, or 9,875, of those stops, despite making up only 67% of the population.”

So, we now know that 9,875 vehicle stops involved one of the 14,070 black people in Ferguson, which means that each black person is stopped on average 0.7 times in two years (9,875 / 14,070 = 0.7, although  in reality, this number is definitely higher, because the 14,070 people include children and others who don’t drive, but that’s OK for calculating the difference between the probability of being stopped for black and non-black people). 1,735 vehicle stops involved one of the 6,930 non-black people in the city, giving an average of 0.25 stops per two years (1,735 / 6,930 = 0.25, again children and non-drivers included here).

Now that we have an average number of vehicle stops for black people and one for non-blacks, we can simply divide one by the other to see how much more likely a black person is to be stopped. We find 0.7 / 0.25 = 2.8. This means that a black person is 2.8 times more likely to be stopped.

Calculate how bad it is only using the percentages

Note that we can do this calculation even if we don’t know how many people were actually stopped.

We’ll have

  • Average stops for blacks = # black vehicle stops / # black people = (85% of 11,610) / (67% of 21,000)
  • Average stops for non-blacks = # non-black vehicle stops / # non-black people = (15% of 11,610) / (33% of 21,000)

Because we are going to divide the (Average stops for blacks) by the (Average stops for non-blacks), anything that appears in both terms can be left out. We can thus leave out the 21,000 and the 11,060, and write

  • (85% of stops / 67% of people) divided by (15% of stops / 33% of people) = 2.8

Blacks are 9 times as likely to be to be charged with “Manner of Walking”

We can now do the same calculation for each of the other numbers in the DOJ report.

  • Blacks account for 85% of vehicle stops : blacks are 2.8 times as likely to be stopped
  • Blacks account for 90% of citations : blacks are 4.4 times as likely to be cited
  • Blacks account for 93% of arrests : blacks are 6.5 times as likely to be arrested
  • Blacks account for 95% of Manner of Walking in Roadway charges : blacks are 9.3 times as likely to be charged with Manner of Walking in Roadway.
  • Blacks account for 94% of all Failure to Comply charges : blacks are 7.7 times as likely to be charged with failure to comply.
  • Nearly 90% of documented force used by FPD officers was used against African Americans : blacks are 4.4 times as likely to encounter use of force.
  • Blacks account for 100% of dog bites: : blacks infinitely more likely to be bitten.
  • Blacks account for 96% of cases where someone was arrested by FPD only because of an outstanding municipal warrant: blacks 11.8 times as likely to be arrested because of outstanding warrant.



Of course, it was already clear that the numbers in the DOJ report showed that the FDP is a racist institution. But I think that using percentages doesn’t reflect just how horrible of a situation it is in Ferguson.

If black people are more than 9 times as likely to be charged with “Manner of Walking” or almost 12 times as likely to be arrested because of an outstanding warrant, it really means that on a daily basis, black people have to fear things that white people rarely worry about (and this is not even including the fear of being killed by the police). They are threatened every day by the very people who are supposed to protect them. For those of us who have never lived in such a situation, we can not know how it is, or how we would react if this were to happen to us.

The numbers only tell a part of the story, but it’s an important part. We should make sure we understand what they mean. The percentages in the DOJ report should make clear to everyone that things are horrible in Ferguson, but if we want to appreciate exactly what these numbers mean, it may be better to calculate “relative risks” that tell us how much more or less likely something happens to a black person than to a non-black person.

Thanks to Andi Gros and Becca Meredith for reading and commenting on an earlier version of this post.

125 Responses to “The math of Ferguson: percentages don’t show how bad it really is”

  1. Quilt Musings March 22, 2015 at 1:00 am #

    I found this post to be a really interesting look into the reality of life in Ferguson, but one question I wondered about while reading is, what would happen if you did the same calculations based on income/economic class? That is, to what extent is this also a question of class and poverty? I know nothing about income distribution in Ferguson, but it would not surprise me if the percent of whites is higher among the upper middle and middle classes. If (just pulling a random number from my head) 75% of arrests are in low income areas, but 90% of residents of low income areas are black, how does that affect the interpretation? Not to say there is not an issue of racism, but it may well be compounded by a structure of poverty that will not be solved by changing attitudes alone.

  2. rachelakai March 22, 2015 at 1:14 pm #

    Reblogged this on Rachel's Thinking and commented:
    This is such insightful post. I read have nothing else to add. I just want everyone to read it have an understanding about how bad the situation really is.

  3. appleworth March 22, 2015 at 1:20 pm #

    Reblogged this on ONiL.

  4. theramblinggaraidh March 22, 2015 at 6:38 pm #

    Thank you for posting this.

  5. kabezya March 22, 2015 at 9:54 pm #

    Reblogged this on Behind The Glass Wall.

  6. Ideology. Vision. Discussion. March 23, 2015 at 1:36 am #

    From what I’ve seen on the news and hear stories about, black people do have a biased against them from many groups – especially the police and potential employers.

    Very brief and well put together bunch of statistics.

    I’m new to wordpress – check out my site. I recently wrote an article about UK migration. Check out my blog, which is on the topic of immigration, why people should stop scapegoating immigrants, and how immigrants are being blamed for the country’s shortcomings-

  7. kevinoflargs March 23, 2015 at 3:50 am #

    Reblogged this on Dailyfromlargs.

  8. kevinoflargs March 23, 2015 at 3:51 am #

    Great use of your skills to quantify the situation.

  9. thur6413 March 23, 2015 at 8:37 am #

    Reblogged this on Unsolved Mysteries of the World and commented:
    Although this is unrelated to the topic I generally write about, I still find this issue important and feel that it would be in my best interest for others to read.

  10. kevingharris March 23, 2015 at 9:36 am #

    Reblogged this on ideasspace.

  11. nsmgo March 23, 2015 at 9:46 am #

    Reblogged this on neosimago.

  12. The Billionist Group March 23, 2015 at 9:47 am #

    Reblogged this on theprestiged and commented:
    “Ferguson” The Numbers Are In….

  13. The Billionist Group March 23, 2015 at 9:47 am #

    Reblogged this on theprestiged and commented:
    “Ferguson” The Numbers Are In….

  14. camstlaurent March 23, 2015 at 11:57 am #

    Reblogged this on cameronstlaurent.

  15. wmmgpromotions March 23, 2015 at 7:44 pm #

    You have my attention

  16. wmmgpromotions March 23, 2015 at 7:45 pm #

    Reblogged this on Watchingmymoneygrow and commented:
    Any thoughts?

  17. Old Soul Wise Mind March 24, 2015 at 10:50 am #

    Reblogged this on growupkneego and commented:

  18. randomransoms March 24, 2015 at 7:28 pm #

    Reblogged this on randomransoms's Blog and commented:
    Great article with some insight not often recognized by the masses…

  19. politicalsociologytoday March 24, 2015 at 8:11 pm #

    Reblogged this on Political Sociology Today.

  20. jfabrycki March 25, 2015 at 2:50 am #

    This is so important

  21. madidos March 25, 2015 at 11:39 am #

    Reblogged this on Diary of an ADHD fellow and commented:
    We know there’s preferential treatment, but we don’t know to what degree.

    Interesting take on the stastics, who point out census data misleads us in children & too old to drive or disabled.

    One poster comments of course the stats will not line up – as they are being targeted in areas where the people don’t have the lawyers.

    Another person aptly points out, look at the crime stats for murder by the same Dept. of Justice for the US. Those are more carefully reported and not likely to be shake downs.

    I believe though, that the conviction rate on murder is still flawed though, as the same case of not having the cash to fund a good defense. I do believe though, those stats might provide a better look at racial biased – not a perfect one though!

    • lwk2431 March 27, 2015 at 5:02 am #

      I wonder, what if we do everything possible to prevent racial bias in law enforcement and find that blacks _still_ outrank everyone else statistically in violence and crime? Is it possible then that someone might actually give some thought to real causes and effects as opposed to the mentally lazy method of assuming that racism motivates every bad outcome for a black?

      I actually do believe that racism is a very large and real problem in America, but that racism today is not the animus of whites to blacks, but just the opposite. Modern racism in America is a carefully groomed artifact of the grievances of the Left that can never be satisfied.

      • madidos March 30, 2015 at 6:11 am #

        Bringing left versus right into this doesn’t help situations. We’re all humans. I do think that just statistics are not helpful by themselves. Also, if it really was just a statistics problem, then latino’s would actually hold the crime records, as they are the new largest minority now-a-days? Obviously not a perfect idea, but from the stand point of stats, we can see there is something else going on here that is wrong.

  22. bilalsh00 March 25, 2015 at 1:07 pm #

    Reblogged this on billsh00.

  23. erinekeeney March 25, 2015 at 5:02 pm #

    How can we know that the officers know the driver is black before pulling them over? When I’m in traffic, all I see is idiots in front me.

  24. Jason March 25, 2015 at 5:21 pm #

    Interesting. I wonder what makes them stay? And what the hell is wrong with people that they can’t use the friggin crosswalk? Don’t they realize how dangerous it is? Someone dies in the US every couple of hours because of Jawalking. I wonder what how rate of deaths from blacks jaywalking in Fervuson compare to the rest of the country?

  25. Moriah March 26, 2015 at 8:25 am #

    Reblogged this on Redeemed and commented:
    Interesting read this morning.

  26. lewisjohn132 March 26, 2015 at 9:53 am #

    MU is very good , and Ferguson is happy man

  27. Shareen HD March 26, 2015 at 10:54 am #

    Reblogged this on and commented:
    A very clear way to understand the problem in Ferguson using facts!

  28. mcdyess18 March 27, 2015 at 5:03 am #

    This is should not to focus with who commit more homicide from black and white people. A solution is citizens of united stated must obey laws like constitution says. Period.

  29. mcdyess18 March 27, 2015 at 5:08 am #

    Reblogged this on HOME JOBS OPPORTUNITY and commented:
    This should not talk about who commit more crime that black and white people. Citizens of united stated must obey the laws like constitution say. Period.

  30. therealblogger March 27, 2015 at 6:57 am #

    Even though I am against racism and even though i believe Racism unfortunately still exists, I don’t think this article truly depicts the actual situation. There have been many assumptions and situations left out. For example, this calculation ignores the possibility of the same person being charged with multiple violations. This will affect the results. I believe there are other factors too. Anyhow, the main point is that Racism unfortunately is still a huge thing in the world and we must do something!

  31. aliveatfifty March 28, 2015 at 8:58 am #

    Reblogged this on aliveatfifty's Blog.

  32. JRoycroft March 29, 2015 at 1:27 pm #

    Whether or not those numbers are accurate, one fact remains. The great majority of people tossing around the word racist have no clue what it’s true definition is, or the difference between bigot and racist. That in itself is a problem. Words have meaning.

  33. svenlovesflo March 30, 2015 at 3:40 am #

    you all know the quote and it hold true here….there are 3 kinds of lies…lies , damned lies and statistics

  34. stevebriscoe March 30, 2015 at 7:10 am #

    If ten people are pulled over by the Police Department, 6 Black, 4 White (of course your numbers dismiss Asian, Hispanic, Native American, etc., but we’ll set that aside for now) for the same offense, and if they gave a ticket to 6 Blacks, and gave no tickets to the whites, then I would agree with the racist charge. The data you use lacks other required variables that might be used to prove racisit tendancies. Many of those varaibles have been identified in previous comments, so I will not repeat them.

  35. gracefuleagle March 30, 2015 at 5:12 pm #

    Great article, really interesting statistics. I don’t think poverty and our unconscious attitudes towards race (black bad, white good) play a part in it.
    It brought to mind Bryan Stevenson’s insightful TED talk

  36. Anarchy Ron March 31, 2015 at 3:26 pm #

    Reblogged this on Leftist Views and News.

  37. filemissile March 31, 2015 at 7:57 pm #

    Thank you
    Fantastic Blog
    Good luck

  38. harrisonblakeharry April 2, 2015 at 4:57 am #

    Racism sucks!!!!!

  39. mandijohnsonp2q April 2, 2015 at 8:36 pm #

    Reblogged this on mandijohnsonp2q.

  40. guyaneseonline April 6, 2015 at 10:50 pm #

    Reblogged this on Guyanese Online.

  41. njgatiup April 7, 2015 at 10:30 am #

    Reblogged this on njgatiup.

  42. demooz April 8, 2015 at 1:36 pm #

    Reblogged this on demooz's Blog.

  43. n0nexistant April 11, 2015 at 9:27 am #

    If you look at the numbers taking a holistic look at the big picture, it actually makes sense. If more than 50% of the population is African American than the probability of an African American getting arrested/stopped at a traffic stop etc. is already higher just because of the number of people. When you think about it like that, you account for most of why African Americans are more likely to be arrested, cited etc.

  44. corley598 April 17, 2015 at 9:36 am #

    Regarding the “Manner of Walking”, it is interesting that since Missouri State Law reads, regarding pedestrians using the roadways:
    “300.405. 1. Where sidewalks are provided it shall be unlawful for any pedestrian to walk along and upon an adjacent roadway.

    2. Where sidewalks are not provided any pedestrian walking along and upon a highway shall when practicable walk only on the left side of the roadway or its shoulder facing traffic which may approach from the opposite direction.”
    that there should be such a hue and cry about ticketing individuals for walking in the roadway. Just think, if Michael Brown and his cohort had exited the roadway when asked to do so by the officer instead of refusing and telling the officer they were only going a little ways further and continuing to violate the law, where would things be now? I guess most law violations should be overlooked once the perpetrator gives his reason for ignoring the law.

  45. pausitivemind April 20, 2015 at 2:46 pm #

    Reblogged this on feministruthurts.

  46. creative1llusion April 27, 2015 at 11:59 am #

    What saddens me the most is that people try to disprove/discredit the harsh reality of these numbers. Regardless of if blacks commit more crimes or if there is a discrepancy in the numbers; that doesn’t mean there isn’t a problem.
    WHY do blacks commit more crimes? Our nation has a community is despair for some “unknown” reason. I’d like to read an article as such and see a plethora heartfelt comments. We must come together and uplift one another. Then our nation will be truly great and we will be stronger for it.

  47. andreabella518 May 24, 2015 at 9:57 pm #

    Reblogged this on submurge into oblivion and commented:
    The numbers don’t lie

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