Index Home About Blog
From: gmk@falstaff.MAE.CWRU.EDU (Geoff Kotzar)
Subject: Handgun Stopping Power (Review-Part 1 LONG)
Organization: Case Western Reserve University

Handgun Stopping Power: The Definitive Study
by  Evan P. Marshall & Edwin J. Sanow

224 pp.      Hardbound
Paladin Press, Boulder CO      ISBN 0-87364-653-3
$39.95 plus $4.00 shipping.

Table of Contents:


Chapter 1   Mechanisms of Collapse
Chapter 2   A Neurologist's View of Stopping Power
Chapter 3   Hatcher's Theory of Relative Stopping Power
Chapter 4   Relative Incapacitation Index
Chapter 5   Southwestern Institute of Forensic Sciences Methodology
Chapter 6   Federal Bureau of Investigation Methodology
Chapter 7   Introduction to Results from the Street (criteria)
Chapter 8   Actual Street Results for All Calibers (90 case reports & tables)
Chapter 9   Short Barrel Ballistics
Chapter 10  Non-Hollowpoint Options for Police
Chapter 11  Specialty Ammunition
Chapter 12  Tactical Penetration
Chapter 13  Point of Aim
Chapter 14  Tissue Simulants
Chapter 15  Ordnance Gelatin
Chapter 16  Ideal Bullet Performance
Chapter 17  Predicting Stopping Power from Street Results
Chapter 18  New Ammo Developments   (9mm +P+, .40 S&W, 10mm, .41 AE, .45 +P)
Appendix A  Terms
Appendix B  Test Weapons for Velocity
Appendix C  Actual Bullet Effectiveness (compilation of tables in Chap.8)
Appendix D  Validity of Various Theories of Handgun Stopping Power
Appendix E  Shot Placement, Body Size, Clothing
Appendix F  Select Muzzle Velocities from Specialty Ammo
Appendix G  Addresses of Ammunition Manufacturers, Importers, and Distributors

I started out to give a summary of the major flaws that I found and was going
to skip all of the minor ones. Even at that the length was excessive so I am
going to split my criticisms into three postings. The first, this one, will
list only the claimed contents and the central failings, the second will list
additional major flaws, and the third will list some analyses I made of what
little raw data was presented.

The subject matter of this book can be broken down into four basic areas:
street results, predicting stopping power for new or under used loads, back-
ground info, and padding. There is quite a bit of this last.

There are two distinct writing styles: the first is sincere and rather polished
which would be Marshall, the second is arrogant and crude and that would be
Sanow. Sanow's writing style is very offensive for a work that purports to be
scholarly and definitive. The "jello junky" barbs are completely out of place.
You can almost hear him snear as he writes. If his work had been rigorous it
would be one thing, but there are so many serious flaws his style becomes
inexcusable. I guess if you like his style in his magazine articles you will
love him here. He still believes he is the bearer of the one true light. Follow
me, he says, follow me!

There have been accusations posted in this group that Marshall "cooked" his
data. After reading this I don't think that is true. There is a serious flaw,
in my opinion, in one criterion that distorts his data, but I do not think it
was intentional. There are 6 criteria listed in Chapter 7:

1) Only torso shots were used;
2) Multiple hits were also discarded. "Again, I didn't consider it a true
   indication of any round's performance to include instances where the victim
   took three hollowpoints in the chest and collapsed. ... If I included
   multiple hits this study could legitimately be attacked on the grounds that
   multiple hits are not a reliable indicator as to any round's stopping
3) A stop was defined as: "if a victim was assualting someone, he collapsed
   without being able to fire another shot or strike another blow. If he was
   fleeing, he collapsed within 10 feet.";
4) "In order to include a shooting in this study, I insisted on either having
   or being able to review some of the folowing: police reports, evidence tech-
   nician reports, statements by the victim (if he survived), homicide reports,
   autopsy results and photos. Whenever possible, I also talked to the emer-
   gency room doctors and attending physicians";
5) Recovered bullets were either personally examined or photographed by
   Marshall or photos were provided by a second party. He noted that there
   were several stops where the hollowpoints failed to expand convincing him
   that bullet placement is the real key to stopping power.
6) A minimum number of five shootings was required for the load to be included
   in the study.

The flaw stems from the multiple hit criterion, and a failing of the study as
a whole is due to Marshall's failure to analyse his data from the point of
view of his conclusion stated in criterion #5.

He does not state the following specifically, but as I understand his work, he
broke a shooting down into one of four classifications: single-hit stop,
single-hit failure to stop, multiple-hit stop, and multiple-hit failure to
stop. Criterion 2 states that all multiple hit shootings are discarded, but
in fact that appears to not be the case. The case reports list a number of
multiple-hit failures to stop. The logic probably runs that if "1+n" hits
failed to stop then clearly the first hit failed to stop. This is not a major
problem for me. The problem arises from the multiple-hit successes group. If
the first shot failed to stop then technically you have a ONE-SHOT FAILURE TO
STOP, but if additional rounds are fired and the individual finally ceases
his activity it is logged as a MULTIPLE-HIT SUCCESS and is DISCARDED from the
study. How many of these there are only Marshall knows, and he makes no mention
of even being aware of the problem. My intuition says that there should be a
sizable number. In fact Marshall pointed out in the introduction that he would
examine 50 cases and wind up with perhaps 10 shootings that could be included.
If this 5 to 1 ratio is representative then the total number of shootings that
Marshall examined could be as large as 33-35000. Your guess is as good as mine
as to how many of these were one-shot failures that were incorrectly discarded
as multiple-hit successes.

My intuition also says that many one-shot failures to stop involved poor shot
placement which bring us to another weakness of this work: the imprecise lan-
guage used to denote impact locations in the 90 case studies supplied. For
example, when Marshall states that the bullet hit the stomach does he mean
the organ as a clinician would or is he referring to the region below the
sternum and above the belt as a layman might. The same applies to the use of
the term abdomen; for the clinician this is the region below the waist and
above the hips. A layman is often less precise. I am not accusing Marshall
here just questioning what can be implied from the data in the case studies.
In Appendix-A they supply a list of terms, but they are all irrelevant at least
for this part of the study.

The next sore point for me was that while Marshall was apparently aware that
shot placement was probably a significant parameter contributing to a load's
stopping power he never examined his data to determine how the success rate
was tied to the tissues involved. He also did not present any information
relative to the distribution of shootings in his study between police and
civilians. It has been reported by Ed Sanow that civilians shoot 3 times as
many bad guys as police, Massad Ayoob reported that DOJ records indicate
civilians shoot 1.3 times as many as police. This discrepancy aside, in going
through the 90 case reports I found that the overall ratio of police to civil-
ian shootings was 62 to 28. Now whether these 90 case were representative of
the entire study we also do not know because Marshall neglected to document
this statistic. If it is representative then Marshall's data clearly deals
only with a very skewed subset of the population of shooting incidents and as
some of the people on the net have indicated this could have affected the

There were so many more points that could have been examined and that Marshall
ignored; the question that he asked appears to have been the simplest one
possible. The sad thing is that given the ready availability of powerful
personal computers and affordable powerful relational database software, most
of these questions could have been addressed easily.

In summary it is a long way from being definitive, scholarly, comprehensive,
or rigorous. Their arrogance aside, the book is in general a disappointment.
The quality of the material presented is spotty and there is simply not enough
with any real substance. They had a chance to produce a really useful text
and instead they assembled a number of magazine articles. All those articles
that have been missing from the gun rags for the last year are in here.

On the inside of the front dust jacket an advertising type claims:

"The results offer what is perhaps the most accurate prediction of the stopping
power of specific loads in calibers from .380 Auto to .45 ACP as well as such
specialty rounds as the Glaser Safety Slug, Federal Hydra-Shok, MagSafe, and

To which I say Horsefeathers. The last claim on the jacket is

"There is no more need for "expert" opinions and outdated theories. HANDGUN
STOPPING POWER is the definitive study"

WE are the EXPERTS. WE will control the horizontal, WE will control the
vertical...WE will change the focus to a soft blur or sharpen it to
crystal clarity.

geoff kotzar

From: gmk@falstaff.MAE.CWRU.EDU (Geoff Kotzar)
Subject: Handgun Stopping Power (Review-Part 2 LONG)
Organization: Case Western Reserve University

Handgun Stopping Power: The Definitive Study
by  Evan P. Marshall & Edwin J. Sanow

Chapters 1 and 2 are really just an orientation to the problem of gunshot
trauma-induced incapacitation. There is nothing profound here but it makes
for interesting reading.

Chapters 3 through 6 present background info on the previous mainstream
stopping power/wound ballistics studies. They feign being critical reviews
and that is what they should have been and easily could have been but they
fall short. The failings range from severe in the discussion of Hatcher's work
to minor in the presentation of the National Institute of Justice and Southwes-
tern Institute of Forensic Science studies. The chapter on the FBI study prom-
ised to be valuable but there was no data only a list of definitions.

Chapters 7 through 11 provide the meat of the book and the first of two
subjects that are of widespread interest.

Chapter 7 supplies the criteria that Evan Marshall applied to his data; as the
case studies are presented it appears that Marshall did not adhere strictly to
the criterion that only single hits were included. See Part-1 for a discussion.

Chapter 8 contains the tables of street results: Total Shootings, One-Shot
Stops, Percentage, and Muzzle Velocity. Also presented are a total of 90 case
reports: .32 ACP (5), .380 ACP (10), .38 Special (9), .357 Mag (9), 9mm (12),
.41 Mag (5), .44 Special (9), .44 Mag (6), .45 ACP (17) and .45 Colt (8).
There is a wealth of information contained in these reports and in fact these
are the only real source of new or useful raw information and not one word was
written about any of it by the authors. More on this later.

Chapter 9 confines its scope to the street results for short barreled guns.
Included here are the data for .380 Auto (exactly the same data presented in
Chapter 8) and .38 Special (standard and +P) from a 2" barrel. There are NO
results for .357 Mag from the snubbies. There is an additional table that
presents oddly enough the dependence of muzzle velocity on barrel length for
only four loads: .38 SPL +P 110 JHP, .38 SPL +P 158 JHP, .357 Mag 110 JHP,
and .357 Mag 158 JHP. Barrel lengths are 2/2.5, 4 and 6 inches. The accom-
panying text talks about velocities, expansion, and penetration. The signifi-
cance of this data is for the most part left to the reader to determine.

Chapter 10 data is confined to Non-Hollow Point ammunition and its street per-
formance. The cartridges/loads presented are .380 ACP, .38 SPL, 9mm, .357 Mag
and .45 ACP. The data presented is exactly the same as that in Chapter 8, it
is just a subset dealing with JSP's, SWC's, RNL or FMJ's. The discussion
centers mostly around which police agencies are carrying or did carry some
of these loads and some anecdotal information about rounds that did not meet
the minimum quantity criterion for inclusion.

Chapter 11 deals with the specialty ammunition: Glaser, Magsafe, Power Plus
Beehive, the original Hydra-Shok (as opposed to the Federal offering), the
Federal Hydra-Shok, and the brass hollowpoints (GECO Action Safety, MEN Quick
Defense, and the MPP/MMC's from Hi-Vel, Inc.), THV, Equalloy SWC, multiple
bullet loads, exploding bullets, sabot bullets, handgun shotshells, PMC Ultra-
mag, and finally the Federal NyClad. Now for the punch line: there is no
information in the street results table in this chapter on any of the more
exotic ammo listed here. All you will get here is a subset of the data pre-
sented in the Chapter 8 tables, again.

If you were waiting for the definitive results on the track record of those
Glasers you have been hoarding, you are just going to have to wait a little
longer. Not to worry, I have heard that hell is going to freeze over soon and
then they will release the results. Ironically enough, 3 or 4 weeks ago I
posted a summary of a Combat Handguns article from April 1989 by Ed Sanow
that presented the results from 14 shooting involving Glasers. Those same 14
shootings are discussed here and no others. You might think that with 2 addi-
tional years of data there would be more to report but the conclusion that we
must draw is that noone has been shot with a Glaser since early 1989. It is
also ironic that even though the 14 shootings presented anecdotaly are more
than required by the minimality criterion, these shootings are not classified
under Marshall's system. Some of these same shootings are discussed in more
than one place throughout this text, but then what the hell, the same tabular
data is presented many times throughout the text. This is what the authors
have to say about the Glasers, "This sampling of Glaser shootings adds valuable
objectivity to a reputation that has perhaps gotten out of proportion with
reality." Perhaps?

Chapters 12 and 13 deal with tactical penetration and aiming points. These are
both worth reading. Tactical pentration is of value if you have not given a
lot of thought to reaching an opponent protected by some intermediate target.
There is a table of penetration of 1/2" thick plywood planks for 47 loads
ranging from birdshot, buckshot and slug from a 12 gauge to the various hand-
gun rounds. It is a nice little summary and I would be willing to post it if
anyone was interested. There is also a very poorly presented summary of a test
that Ed Sanow's police department ran on pentration of auto bodies and windows.
I say poorly presented because the text is incomplete and it is not until you
examine the accompanying table that some of what the author is trying to say
becomes clear. Also, only two loads are compared: .357 Mag Rem 125 S-JHP and
the Win 145 STHP. I would have thought that THE DEFINITIVE STUDY would have
been a little more thorough. The discussion of aiming points is really signi-
ficant, however. A lot of it is just a rehash of the NIJ study conclusions but
there is one nugget of wisdom: "This general purpose point-of-aim recommend-
ation for police and civilian handgunners is exactly the same location taught
to military snipers. Perfect bullet placement is anywhere inside a triangle
formed by the base of the neck and the two nipples. This kind of shot place-
ment is the essence of handgun stopping power." This last statement is import-
ant for two reasons: first, it indicates that all of the silhouette targets
that we practice with have their scoring rings and, hence, their aiming points
much too low, second, it underlines a major failing of a work that purports to
be definitive. The authors had 6572 shooting records (the data is already out
of date as they are now reporting over 6800 in their data base) and could have
examined them for the relationship between point of impact and the likelihood
of a one-shot stop. They did not do it. Maybe it will show up in the sequel.

These next four chapters (14-17) are essentially the metier of Ed Sanow, or at
least he thinks so. Chap. 14 deals with tissue simulants. There is a certain
amount of arm waving that goes on here and some questionable experimental
technique but there is actually some useful information here as well. Soaking
wet newspapers and straight water are pretty good simulants. If you want to
do some informal but reliable expansion testing and even penetration testing,
waterlogged newspaper is a pretty good medium. Shades of Ross Seyfried and
Finn Aagaard. Chap. 15 discusses ordnance gelatin and presents some of Sanow's
criteria for predicting handgun stopping power. The "dominant wound predictor"
is the permanent cavity (PC) while the temporary cavity (TC) is "of profound
but secondary importance". I am getting ahead of myself but when Sanow predicts
stopping power he uses the PC to predict a value and then uses the TC to pre-
dict a second value and then simply averages them. In this case the weighting
values are both 1/2, indicating that they are really both of equal importance.
Inconsistencies like this run throughout Sanow's work here. This chapter is
where I found the first evidence of Sanow's cheating.

Sanow does not have the expensive lab equipment to record the TC dynamically
as the bullet passes through the gelatin block so instead he has to resort to
approximating it by measuring the radial cracks surrounding the PC. There are
two competing methods to estimate the TC using these cracks: the Total Crack
Length Method and the Wound Profile Method (this latter method is attributed
to M.L. Fackler). This is what Sanow says in HSP-TDS: "These two measurement
techniques can produce significantly different estimates of the temporary
cavity. An independent source, Dr. Bruce Ragsdale of..., tested [these] tech-
niques against a high-speed calibrated movie of the temporary cavity. The
results were mixed and debatable but seemed to favor the two radii method (the
WPM)." I have this paper in my files and Ragsdale came to an entirely different
conclusion. This is what Ragsdale had to say: "In 4 of 14 instances the WPM
gave predictions within 10% of the true diameters. None of the TCLM predictions
were within 10% of the true circumferences. .... Both the WPM and TCLM gener-
ally underestimated the true TC size. ... The computed "r" for the TCLM is
0.540... [which] just exceeds the threshold value of 0.5324 at the 0.05 confi-
dence level. ... For the WPM data set, r=0.047, little better than from the
laws of chance." Mixed results yes, debatable no. Now is as good a time as any
to point out another failing of this work: not a single reference is given to
allow the reader to verify that what the authors chose to present is consistent
with the literature. Sanow does point out that the Secret Service and the
German firm MEN use the TCLM. Sanow employs the WPM because it is "better",
it must be since this is The Definitive Study.

Chapter 16: Ideal bullet performance. Expansion must be to 1.67 diameters and
pentration depth to 12 inches in gelatin. Aside from a discussion about feeding
reliablity and recoil impulse there is not much here.

Chapter 17 deals with the second major aspect of this work: predicting handgun
stopping power. They selected 24 loads from their database of 91, representing
1800 shootings, and fired an unspecified number of each into gelatin. They took
3 measurements: expanded dia., penetration depth, and the length of the two
longest radial cracks. From these they calculated the PC=exp-dia x penetration
and the TC. The TC was calculated by sectioning the gelatin block in 1 inch
intervals and measuring the two largest cracks which "equal" the TC diameter
at that depth; the total temporary cavity volume was then estimated by taking
the product of the cavity area derived from the diameter times the slice thick-
ness and then summing over all of the slices. They then ran 1st-order least
square fits with one independent variable (exp. dia., pen. depth, PC, or TC)
and the street results as the dependent variable. What I found truly amazing
was that the raw data was included in a table; it is not documented anywhere
in the text but it is the only conclusion to which I can come. Another table
presents the regression equations. Oddly, for having only 4 indep. variables
they have 6 eqns. This came about because they further split their data out.
When they included the data from loads with MV's over 1300 fps the correlation
coeff's were not very good, r=.68 and r=.60 for exp. dia. and PC respectively.
When they eliminated those loads the r's increased to .82 and .87 respectively.
I typed their data into Quattro Pro and used the internal routine to perform
the various regressions and could not quite come up with their values, close
but not identical (I think they deleted not only loads with MV's>1300 fps but
also two additional loads with MV's=1299fps). Anyhow, the two extra eqn's come
from the full data set and are used to predict the stopping power for the high
velocity loads (MV>1300fps). After the various gelatin data are fed into the
regression eqn's to estimate street effectivness for these high-vel loads the
predictions are "corrected" by multiplying the predicted effectiveness by 1.15.
BTW, only 2 of the loads in the data set have MV's over 1300 fps so this fudge
factor works "fairly" well at getting the predictions to agree with this gener-
ating data set. Rigorous, no? Where in the hell this 1.15 factor came from is
anybody's guess. With the predicted performances from the PC and TC in hand
they are simply averaged. That then is the your predicted stopping power. Why
they simply did not perform a multi-variable linear regression I do not know.

To be fair there is a little more to the justification of the 1.15 fudge
factor. In other sources published more recently (magazine articles) Sanow
describes how high velocity hollow points will fragment by blowing off the
skirt of the expanded nose. This results in a recovered expanded diameter that
is smaller than the functional in-tissue diameter and as a result underesti-
mates the permanent cavity (PC) on which the predicted stopping power depends.
For that reason we are allowed to apply the ad hoc correction factor, yeh we
are! Let me take you on a little tour. The two loads in question are:

                 EXP    PEN   PC    TC    % STOPS  % STOPS % STOPS  PRED.
                 DIA   DPTH                ACTUAL   PRE-PC  PRE-TC  TOTAL

Fed 115 JHP +P+  .53   12.7   2.8   20.3     89.3   68/78     75    72/78  9mm

Fed 125 JHP      .55   13.3   3.2   44.3     96.1   70/81     97    84/89 .357

The units are English, inches and inches^3.

In the above where there are 2 numbers in a column, mm/nn, the first is the raw
prediction and the second is the corrected prediction employing the 1.15

I know, I know, you want the equations.

A) penetration distance  %-stops = -0.733*(distance) + 85             r = -.37

B) expanded diameter
           MV<1300 fps   %-stops = 62.9*(diameter) + 35.7             r = .82
           MV>=1300 fps  %-stops = [58.7*(diameter) + 40.6] * 1.15    r = .68

C) permanent cavity volume (= (distance)*(diameter))
           MV<1300 fps   %-stops = 6.3*(volume) + 45                  r = .87
           MV>=1300 fps  %-stops = [5.3*(volume) + 53] * 1.15         r = .60

D) temp. cavity volume   %-stops = .92*(volume) + .56                 r = .80

The correction factor really does not do a very good job of bringing the pre-
dictions into agreement with the raw data. Maybe someone out there can figure
out why they used 1.15 instead of some other value since it appears to be ar-
bitrarily choosen. I will include the data for the 24 loads in the next part.

Chapter 18 deals with primarily with the .40/10mm/.41AE loads along with the
+P .45 ACP and +P+ 9mm loads. A little history and some predicted performance.
If anyone out there really could take this seriously I would be willing to
summarize it.

The first 2 appendices are self-explanatory, the third lists a summary of the
actual street performance. The data in this table does not agree completely
with the data in the body of the text. There are more actual cases listed here.
Apparently, they did not update the other data tables. The rest of the appen-
dices are irrelevant with one exception: Appendix E. This one lists four loads
where the impact is specified to have been between the sternum and the shoulders
and under two different clothing conditions. They are non-winter clothing and
winter clothing. The four loads were Fed .357 125 JHP, .38 SPL 158 LHP +P, 9mm
Fed 9BP, and .45 hardball. In all cases the 1-shot stop percentages decreased
slightly for the winter clothing condition. There is no discussion what so ever
so the significance of this is not clear. It is, however, as close as they came
to looking at the question of stopping power as a function of bullet placement.

In part 3 I'll present a summary of some of the data contained in the case
reports and the data used to generate their predictive relations.

geoff kotzar   

From: gmk@falstaff.MAE.CWRU.EDU (Geoff Kotzar)
Subject: Handgun Stopping Power (Part-3 Long)
Organization: Case Western Reserve University

Handgun Stopping Power: The Definitive Study
by  Evan P. Marshall & Edwin J. Sanow

Part 3
My appologies, this thing is getting very goddamned long and I will have to
split it into four parts.

I want to get the references out of the way right now:

Ragsdale, B.D. and A. Josselson, Predicting Temporary Cavity Size From Radial
Fissure Measurements in Ordnance Gelatin, J. Trauma, Vol 28, No. 1 Supplement,
January 1988, pp. S5-S8.

Ayoob, M., Careful Statistical Study of Your Gunpoints Shows Important Trends,
American Handgunner, Sept/Oct 1988, pg 22.

Sanow, E.J., Cor-Bon Super-Performance Ammo, Handguns for Sport And Defense,
Oct 1991, pp. 54-61.

Sanow, E.J., Rounup: Latest Loads for the .40 S&W, Handguns for Sport and
Defense, Feb 1992, pp. 49-54.

Smith, V., Jacketed Bullet Performance with Cast Bullets, published by Lead
Bullets Technology, HCR 62, Box 145, Moyie Springs, Idaho, 83845

The raw data from Chapter 17 that form the basis for Ed Sanow's predictions
of handgun stopping power are presented below.

I have again included the equations that Sanow derived from these data for
convenience. There was an error in the first version of these eqn's but I
have corrected it and marked it with carats for purposes of identification.
There was a second error in the derived data for the Fed 115 JHP +P+ load:
the average of 78 and 75 is obviously not 78 as I first listed:

                 EXP    PEN   PC    TC    % STOPS  % STOPS % STOPS  PRED.
                 DIA   DPTH                ACTUAL   PRE-PC  PRE-TC  TOTAL

Fed 115 JHP +P+  .53   12.7   2.8   20.3     89.3   68/78     75    72/76  9mm.
Sanow and Marshall listed their %-successes to two decimal places in the text.
I rounded all of their data to a single decimal place and all of mine to inte-
ger values. I did not feel that for the purposes of looking for trends in
the data their precision was necessary. If anyone wants to do any additional
massaging of the data, the rest of their raw data is presented as it was in
Table 17-1.


              Handgun Gelatin Results: All 24 Data Sets

     CTG     Make & Load    Pen  Ex Dia   PC     TC   % Stops   MV
                           (in.)  (in.) (in^3) (in^3)  1-shot  (fps)

  .380 ACP   Fed 90 JHP     14.4   0.36    1.5    8.3    63.8   1003
             Rem 88 JHP     12.8   0.41    1.7   10.5    54.8   1001
             Fed 95 FMJ     17.0   0.36    1.7    6.8    51.3    929

  .38 Spl  Win 158 SWC-HP   15.2   0.60    4.3   11.9    72.8    992
            Rem 125 SJHP    11.1   0.46    3.6   13.4    65.1    929
             Fed 158 RNL    28.5   0.36    2.9    8.6    52.3    704

    9mm    Fed 115 JHP +P+  12.7   0.53    2.8   20.3    89.3   1304
           Win 115 JHP +P+   7.9   0.79    3.9   37.3    88.2   1299
             Rem 115 JHP    14.5   0.62    4.4   18.7    76.4   1163
            Fed 124 Ny-HP   12.4   0.68    4.5   18.3    82.1   1101
             Win 147 JHP    15.9   0.57    4.1   19.6    68.5    887
             Win 115 FMJ    22.1   0.36    2.2    8.8    60.8   1149

  .357 Mag   Fed 125 JHP    13.3   0.55    3.2   44.3    96.1   1453
           Rem 125 SJHP-MV  15.5   0.75    6.8   20.9    83.3   1280
             Rem 158 SWC    27.5   0.36    2.8   12.9    67.6   1149

  .41 Mag   Win 175 STHP    17.0   0.70    6.5   41.2    88.6   1299
             Rem 210 JSP    23.5   0.41    3.1   32.5    80.0   1219
             Win 210 SWC    30.0   0.41    4.0   11.3    74.4    956

  .44 Spl   Win 200 STHP    10.4   0.61    3.0   10.7    71.1    819
             Win 246 RNL    23.0   0.43    3.3    8.0    67.4    704

  .45 ACP  Fed 230 HS-JHP   13.3   0.76    6.0   17.5    88.4    819
             Fed 185 JHP    13.6   0.68    4.9   18.1    84.6   1001
             Rem 185 JHP    17.1   0.59    4.7   14.0    78.6    944
             Rem 230 FMJ    27.0   0.45    4.3    9.0    60.7    799

The regression equations that supposedly were generated from these data are
below. The reason I say suposedly is that I was unable to generate these
values from the above data. I typed the above data into Quattro Pro and using
the internal routines derived the data listed in Table-2 below.

A) penetration distance  %-stops = -0.733*(distance) + 85             r = -.37

B) expanded diameter
           MV<1300 fps   %-stops = 62.9*(diameter) + 35.7             r = .82
           MV>=1300 fps  %-stops = [58.7*(diameter) + 40.6] * 1.15    r = .68

C) permanent cavity volume (= (distance)*(diameter))
           MV<1300 fps   %-stops = 6.3*(volume) + 45                  r = .87
           MV>=1300 fps  %-stops = [5.3*(volume) + 53] * 1.15         r = .60

D) temp. cavity volume   %-stops = .92*(volume) + 56                  r = .80

The variable listed opposite the "Regression Output:" header was the indepen-
dent variable and the street results were obviously the dependent variable.

#From the complete data set:

Regression Output:    PenDpth   ExpDia   PC-Vol   TC-Vol
Constant               88.087   38.600   53.329   57.542
Std Err of Y Est       11.791    8.610   10.333    8.201
R Squared               0.169    0.557    0.362    0.598
R                      -0.411    0.746    0.602    0.773
No. of Observations        24       24       24       24
Degrees of Freedom         22       22       22       22
X Coefficient(s)       -0.837   65.609    5.391    0.911
Std Err of Coef.        0.395   12.472    1.526    0.159

Regression Output:     PC&TC          ALL
Constant              48.350        34.798
Std Err of Y Est       7.166         6.767
R Squared              0.707         0.764
R                      0.841         0.874
No. of Observations       24            24
Degrees of Freedom        21            19

                         PC     TC    Pen     Exp    PC     TC
X Coefficient(s)       3.204  0.749  0.181  47.129 -0.111  0.621
Std Err of Coef.       1.146  0.151  0.447  32.182  2.515  0.154

#From the reduced data set ( MV<1300 fps ):

Regression Output:    PenDpth   ExpDia   PC-Vol   TC-Vol
Constant               84.311   37.983   48.850   57.742
Std Err of Y Est       11.302    6.863    7.882    8.333
R Squared               0.130    0.679    0.577    0.527
R                      -0.361    0.824    0.760    0.726
No. of Observations        22       22       22       22
Degrees of Freedom         20       20       20       20
X Coefficient(s)       -0.670   64.699    6.166    0.903
Std Err of Coef.        0.388    9.945    1.181    0.191

As I said in Part-2 of this epic, the regression eqn's that I got do not agree
with their's; the same applies to the correlation coefficients. They are close
for the most part. I am troubled, however, by the discrepancy between the cor-
relation coefficient that they show for the low velocity permanent cavity data
and the one I found: .87 vs .76 respectively. I felt that there are three poss-
ble conclusions: they don't know what they are doing, I don't know what I am
doing, or I don't know what they are doing. The second is very likely I admit.
If it is the last, it is because they have again written one thing and done
another. Also, if the .87 value for R is correct it would imply either the use
of a much larger data set or one with much more tightly clustered values. The
other regression data do not seem to support this though. Any ideas?

I also ran a couple of multi-variable linear regressions while I was at it to
see how such predictions would compare with Sanow's method. In the table below
I have listed the predicted stopping percentages for the various methods along
with the actual values (column 3). This is one area where, even if the data in
Table-1 above are not the generating data for the regressions, we can get an
idea of how accurate Sanow's predictions are likely to be. As you look through
the data below be aware that the predictions from the Sanow Mthd are based on
the equations provided by Sanow and Marshall and listed above and in Part-2.
They do not equal the averages of the values from PC-Vol and TC-Vol in the
table because the base equations are very different.


                                Predicted % 1-Shot Stops

  CTG     Make & Load    % Stops Sanow MultiV MultiV  Pen   Exp   PC    TC
                          1-shot  Mthd  PC&TC 4-Indp  Dpth  Dia   Vol   Vol

  .380    Fed 90 JHP        63.8    59    59    59     76    62    61    65
          Rem 88 JHP        54.8    61    62    63     77    65    62    67
          Fed 95 FMJ        51.3    59    59    59     74    62    62    64

.38 Spl Win 158 SWC-HP      72.8    70    71    73     75    78    77    68
         Rem 125 SJHP       65.1    68    70    66     79    69    73    70
          Fed 158 RNL       52.3    64    64    62     64    62    69    65

  9mm   Fed 115 JHP +P+     89.3    76    72    74     77    73    68    76
        Win 115 JHP +P+     88.2    80    89    96     81    90    74    92
          Rem 115 JHP       76.4    73    76    78     76    79    77    75
         Fed 124 Ny-HP      82.1    73    76    80     78    83    78    74
          Win 147 JHP       68.5    72    76    76     75    76    75    75
          Win 115 FMJ       60.8    61    62    61     70    62    65    66

  .357    Fed 125 JHP       96.1    89    92    90     77    75    71    98
        Rem 125 SJHP-MV     83.3    82    86    85     75    88    90    77
          Rem 158 SWC       67.6    65    67    64     65    62    68    69

.41 Mag  Win 175 STHP       88.6    90   100    96     74    85    88    95
          Rem 210 JSP       80.0    75    83    78     68    65    70    87
          Win 210 SWC       74.4    68    70    66     63    65    75    68

.44 Spl  Win 200 STHP       71.1    65    66    72     79    79    70    67
          Win 246 RNL       67.4    65    65    64     69    67    71    65

.45 ACP Fed 230 HS-JHP      88.4    77    81    83     77    88    86    73
          Fed 185 JHP       84.6    74    78    80     77    83    80    74
          Rem 185 JHP       78.6    72    74    74     74    77    79    70
          Rem 230 FMJ       60.7    68    69    66     65    68    77    66

Now for some observations. The data are definitely correlated but the
correlation is not strong enough to allow meaningful predictions. For example,
look at the Sanow Mthd predictions for the .45. The 9% difference predicted
between the 230 FMJ and the 230 HS-JHP are mapped into a 28% difference on the
street. You might argue that as long as the predictions are always low you
would get a reliable lower bound on the street performance, but how would you
decide on a load for a new cartridge? The Hydra-Shok LOOKS like it should be
more effective than the FMJ, and LOOKS like it should be at least 20% MORE
effective, right? Now examine the .38 Spl data. A difference of 6% predicted
translates into a 20% difference on the street. The 9mm shows more of the same
thing: Win 147 JHP at 72% and the Win 115 JHP +P+ at 80% pred. are really 68%
and 88%. I deliberately ignored the data for the 9mm Fed 115 JHP +P+ because
it is so anamolous. This brings up the next flaw with this work. The authors
clearly recognised that the high velocity data (MV's > 1300 fps) needed special
attention. Why they did not cull the 15 loads from their data set with the high
MV's and run a regression for them seperately is not clear. Remember that the
reason for the poor correlation for the high MV loads according to Sanow is
that the bullets fragment as they mushroom resulting in small expanded dia-
meters. I guess it is up to the reader to decide if he or she is going to
believe the predictions for the .40/10mm loads or for the new loads like those
from the small semi-custom shops.

There is an additional error in the methodology used here, I believe. In his
book, Veral Smith described an experiment he performed to determine which
part of the bullet actually did the work in inflicting a wound. Using ballistic
gelatin laced with an abrasive he fired bullets with their surfaces dyed into
it. The abrasive wore away the the dye only where the gelatin and bullet met.
For flat nosed bullets the only abraded region was the meplat, regardless of
how the nose was blended into the full diameter body. Semi-wadcutter, truncated
cone, or truncated round-nose, it did not matter: only the meplat contacted the
gelatin. Clearly, the assumption that the non-deforming bullets all acted like
full wadcutters and produced full diameter permanent cavities is in error.
Furthermore, the diameter of the PC for deforming bullets is also probably
not accurate. I do not want to belabor the point, but assuming that a .45 FMJ
produces a .45 inch dia. PC is not correct; it is possible to calculate where
the temporary gas cavity separates from the bullet's nose. It would probably
be much harder to determine where separation occurred for a deforming bullet
but even that could be done. Anyone want a Master's project? Ordinarily, it
would not be necessary but predictions are being made using this methodology,
predictions that others will be staking their lives on. You would like to know
that they were as thorough as possible and the predictions accurate. Methinks
the authors' want the most buck for the bang.

There are one or two more points. In the .40 S&W article listed above, Sanow
presents some predicted stopping percentages along with the PC and TC values.
The equations I listed above are the ones that he is currently using. They
predict the same percentages. He claims in that article, though, that the
regression equations are based on "6800 actual gunfights in other calibers
and loads", not on the 24 select loads and approximately 1800 shootings that
he claimed in the book. There is this nagging question of his integrity that
I cannot shake; I don't know which is the truth.

geoff kotzar   

From: gmk@falstaff.MAE.CWRU.EDU (Geoff Kotzar)
Subject: Handgun Stopping Power (Review Part-4 - LONG)
Organization: Case Western Reserve University

Handgun Stopping Power: The Definitive Study
by  Evan P. Marshall & Edwin J. Sanow

Part 4

The case reports that Marshall presents allow for some independent analysis.
First, two pieces of data that I know or at least I believe I know to be true.
Civilians engage 130% as many criminals in lethal combat as police [Ayoob],
According to Sanow in the Cor-Bon article the number is 3 to 1 in favor of the
civilians; also, only 20% of all handgun related wounds are fatal [sorry no
reference here]. With those two pieces of info I asked how representative were
the data in the 90 reports. In some of the reports more than one opponent was
engaged so there are more than 90 Fat/Non-Fat(NF). ?F=fatality undetermined.

     CTG.           # of reports  Pol/Civ  Fat/NF   shtng's

   .32 ACP               5         3 / 2    5 / 1    167
   .380 ACP             10         5 / 5    7 / 4    352
   .38 Spl               9         7 / 2    6 / 3   1571
    9 mm                12         9 / 3   10 / 4   1438    1-?F
   .357 Mag              9         6 / 3    9 / 2   1467
   .41 Mag               5         3 / 2    6 / 2    192
   .44 Spl               9         6 / 3    4 / 4    147    1-?F
   .44 Mag               6         5 / 1    6 / 0    256    1-?F
   .45 ACP              17        12 / 5    9 /11    780
   .45 Colt              8         6 / 2    3 / 5    202    1-?F
                       ----       -------  -------  ----    -----
                        90        62 / 28  65 / 36  6572    4-?F

I attempted to determine the impact points and the tissue damaged from the
case descriptions and wound up with the following:

     32A   380   38S   9MM   357   41M   44S   44M   45A   45C
UT    3     4     4     5     5     3     8     7     6     3
LT          1           1     2     3                 1
AB    1                                               1
TO          2     4     3     1           1           9     4
BK                      3     1                       1
SP          3     1     2     2     1     1           1     2
TH    1                 1
HD    1     1                       1

These are summarized below in the same order as above:

Upper Thorax          - 49 - 1 of which was a failure
Lower Thorax          -  8 - evenly split between liver and "stomach"
ABdomen               -  2
TOrso (non-specific)  - 23 - 7 of which were failures, 1 possible failure
BacK  (non-specific)  -  5 - 1 of which was a failure
SPine                 - 13 - 1 possible failure (officer downed, not-disabled)
THroat                -  2 - ***
HeaD                  -  3 - According to criteria no head shots included?                       ----
Total                  105

*** There was one additional success: an officer was shot with a sawed-off
    rifle in .22 LR. This was not included in any of the above or below.

There were a total of 9 failures described (5 in .45 ACP alone) and 2 that
were equivocal and thus unclassifiable.

You will also note the 3 head shots listed. According to Marshall's criteria
only torso hits were to be included in the study. Since Marshall does not let
the reader know explicitly how he classified a particular shooting, there is
no way to be sure if a particular shooting was presented anecdotally (as part
of a multiple opponent shooting) or if it was included in the study. Most of
the time it is obvious but there are a number of instances that leave the
reader uncertain.

There are three things that pop out of this easily. First, the distribution
of the shootings between police and civilians is out of kilter with the gen-
eral distribution. Second, the fatalities are much higher than in the general
population. If anyone knows of the reference that I am thinking of I would
like to hear about it, please. These make me wonder how representative either
the case studies are of the data base or the data base is of all handgun
shootings. Third is the distribution of the hits. Half (54) of the victims
were hit above the diaphram (high thorax); for all of those there was only
one failure logged. For those cases where the impact point was specified,
only 10% of the hits (and 10% of the successes) were in the lower 2/3's of the
target area. Even if we included all of the non-specified torso/back hits in
the below-diaphram group there would still be only roughly one-third of the
hits in the lower 2/3's of the torso. Not knowing what the global distribution
of shots is one cannot say how significant the distribution in Marshall's data
is but you still have to wonder if Marshall's data is distorted by examining a
sub-population that tends to aim higher than the general shooter. For example,
maybe police are taught to aim higher and these shootings dominate because
the police shooting records are more complete and as a result included in the
study. Or, as I pointed out earlier, it may distorted by excluding one-shot
failures by classifying them incorrectly as multi-shot successes - where the
additional successful shots were necessary because of low initial impacts.

The spinal hits also appear to distort things a little since any cartridge
with sufficient pentration to reach the spine would probably result in a
certain stop, at least this is what come to us from the hunting fields. Thus,
luck or marksmanship would be more important than any characteristic of the
bullet and cartridge other than penetration. All of the above makes me wish
that things had been broken out according to the structure or region hit. For
example, hits to the spine and head should have been examined separately; in
all probability we would have found that all cartridges performed about the
same. Furthermore, the torso and abdomen should have been broken down into
three sections: high thorax (above the diaphram), low thorax (below the
diaphram), and abdomen, at least as a first pass. Then we would have found
out if there was any real difference between cartridges and loads for less
than ideal bullet placement. If all of the hi-performance loads produce
uniformly good results in the upper thorax and uniformly poor results in the
abdomen, then we change where we aim; but if some loads are actually better
in the lower thorax and abdomen then those are the loads we want. Absurdly
obvious, right?

Also this aiming point issue may explain the adamant position of the Cooper-
ites. By the time you get to Cooper's "club" you are no novice and you may
be disciplined enough to place your shots effectively, hence the high success
rates they claim.

At this point my anger at the attempted flim-flam is spent, and my confusion
level is pretty high. I do not know what to make of Marshall's data. There
are just too many unanswered questions which I think we could answer or make
a serious attempt at if we only had the raw data. Sounds like we are right
back where we were months ago while awaiting the Definitive Study. At least
I am.

geoff kotzar   

Index Home About Blog