Response to Charnin: the grassy knoll probability problem

Charnin’s methods of calculating PN (joint probability) and PS are flawed, for several reasons.

Given the 500-word limit you’ve imposed, I’ll point out just one flaw. It has to do with the proposition the probability a witness was correct in hearing a shot from the grassy knoll was 0.42.

By way of perspective, it is true the probability of drawing a Queen from a deck of 52 is 4/52, or 1/13, or 0.0769. Note that here we know there are four Queens in the deck.

Charnin posits 51 witnesses said they heard grassy knoll shots; 32 witnesses said they heard TSBD shots; and 38 heard shots but had no opinion of their origin. This information is no basis whatsoever for saying there is 0.42 probability the 51 witnesses were correct — for saying there is 0.42 probability a shot came from the grassy knoll. All one can say from this information is that 42 percent of the witnesses said a shot came from the grassy knoll. That is ALL the information we can glean. We cannot by any logic bootstrap “42 percent of the witnesses said they heard a shot from the grassy knoll” into “there is a 0.42 probability a shot came from the grassy knoll.” The 51 witnesses could all be correct or incorrect; some could be daffy or deceitful; some could be swayed by another’s opinion. We don’t know.

The 51 witnesses are like the four Queens in the deck of 52. We know the probability of picking one of those witnesses out of the group of 121 total witnesses (probability = 0.42).  But that’s all we know from the law of probability.

I guess I’ve got room to address Charnin’s calculations of PN and PS. The calculations make no sense whatsoever inasmuch as they’re based on the flawed notion that there was a 0.42 probability of a grassy knoll shooter.

A case of garbage in, garbage out.”

63 thoughts on “Response to Charnin: the grassy knoll probability problem”

  1. Gang I want to share a few observations with you having just returned home from Dallas .
    I went to Dealey and walked around it for 4 hours one afternoon and 3 hours the following day. What I came away with was pictures and video from at least 50 different possible shot locations taking into account the angle of the limo and the width of the windshield etc.
    The most startling thing is this there are any number of shots that are/were VERY make able being a long time hunter and having shot everything from a 22 to a 30’06 there are very few angles that would have provided any real resistance to anyone with regular shooting experience. In fact I could make the shot from the corner of the fence by the walkway with my Compound Bow!
    I will tell you this from up in the sixth floor museum it is very clear that it would take an incredible gifted shooter to hit a moving target once much less twice!
    Bottom line No way didn’t happen period!

  2. Jean, the single sentence you have lifted from Julia Postal’s testimony regarding what she heard the police officer say in and of itself might serve your argument; however, when read in full context, the officer’s statement takes on a different meaning:

    Postal: ” …..well, that is when I first heard Officer Tippit had been shot because some officer came in the box office and used the phone, said, “I think we have got our man on both accounts.” “What two accounts?” And said, “Well, Officer Tippit’s,” shocked me, because Officer Tippit used to work part time for us years ago. I didn’t know him personally.”

    The officer’s full comment suggests that Oswald was already suspect in two accounts, but that Tippit’s was the SECOND account, not the initial one. Doesn’t that mean that the DPD was already en route to …. where? The Theater? and or then the site of Tippit’s murder? or Oswald’s boarding house, or Ruby’s place? I thought the argument has long been that Oswald was arrested at the theater because of the Tippit murder, that Oswald was charged for his murder, and that only hours later was he charged with the assassination of President Kennedy.

    The time gap certainly allowed ample time to align all of the ducks … the rifle (which rifle?) the shells, Oswald’s position on the 1st Floor, or en route to or from the coke machine, holding a soda, or not holding a soda, coming from the 6th Floor, on the stairwell or not, catching a bus, a cab, en route to his room, en route to someone else’s house, to the theater, one wallet, two wallets, etc. It was a very complicated few hours, wasn’t it?

    Regarding Truly’s contribution of Oswald’s address … you site the testimony of Captain Fritz, but you don’t refer to Truly’s own testimony. A new student of assassination research will do well to study Truly’s questioning by the WC in depth, in particular pay attention to those questions posed by Mr. Ball. If ever there was an example of leading a witness in the Warren Commission records, this is a prime one. Truly initially asserts that he provided an address for Oswald within 20 minutes of the assassination (time for the DPD to head toward Irving?), but by the time Truly is finished – or by the time Ball is finished with him – that episode occurred long after 1 o’clock.

    If the description of Oswald was relayed based solely on Howard Brennan’s eyewitness account and not Truly’s, and the officer(s) at Texas Theater suspected they had their man on two (both) accounts, clearly they were relying on eyewitness testimony … Brennan’s and separately Bentley’s at the shoe store, right? If Truly’s identification that Oswald was missing occurred later, what other reason did they have to suspect Oswald … your other arguments apply only after the fact: the officers at the theater didn’t yet have confirmation that the rifle was tied to Oswald and the 6th Floor; they had wallets / conflicting ID at the site of the Tippit murder and or allegedly on Oswald’s person inside the Texas Theater (depending on which version you use in your argument) … so it seems to me that Brennan was the pivot in that first hour linking Oswald to the Dealey Plaza murder. Why were the police banking on this brief, very limited description by one witness; why were they so certain it was the same person alleged to have been at the Tippit murder scene, and why were they then so certain that both crimes had converge with the arrest of Oswald at the Texas Theater within an hour and a half of the assassination.

    Would that the Dallas Police had been as efficient during the brief hours that Kennedy was alive in their city.

    1. Leslie,

      The “two accounts” were (obviously) JFK’s murder and Tippit’s, and it was natural to connect the two. The President’s killer was still at large when a policeman was shot in a nearby neighborhood, and the descriptions of the suspects were similar. No one said the cops were “certain” the two were connected — a single policeman expressed that OPINION. (“I think we have our man…”)

      Oswald was arrested for the Tippit murder only because Johnny Brewer pointed him out as the man who’d been acting suspiciously in front of his shoe store and then sneaked into the theater, which wasn’t far from the Tippit murder scene. After Postal called the police and described him, they went to the theater to check it out (as they’d checked out other leads that day).

      Truly initially said he talked to Fritz in the NW corner where the rifle was found “20 minutes after the assassination.” But Fritz wasn’t in that area then, had no reason to be there until the weapon was discovered at 1:22. So Truly’s time had to be wrong. Ball tried to clarify that.

      The description of the TSBD sniper was broadcast at 12:33, when Truly was likely still headed for the roof with Baker. No one went to Irving until around 3 P.M.

      You’re suspicious of Truly, but not the guy who was where the sniper would’ve probably been around 12:32, just off the back stairs? Of all the places for him to be, why there? Just a weird coincidence, you think?

      1. Jean, why did Truly’s time have to be wrong? Because it did not match the testimony of Captain Fritz. His easy acquiescence to Ball’s questioning is indicative of servitude; Ball’s questioning was indicative of a style of interrogation that permeated the WC.
        I stand corrected that Truly did not provide the Oak Cliff address. However, I speculate Truly was a very good soldier just as when he was seconded to North American Aviation during WWII and then returned to the depository business in Dallas.

        Fritz is a subject in and of himself; word count does not permit the pursuit so many of your arguments will go virtually unchallenged which is unfortunate for the new student of the assassination.

        you state: “it was natural to connect the two.” and “Oswald was arrested for the Tippit murder only because Johnny Brewer pointed him out …. which wasn’t far from the Tippit murder scene.”

        You argue this from a post-arrest perspective that gives the impression that you know precisely what happened because the Warren Report told you what happened. An unbiased researcher relinquishes prejudice, gets inside the moment as if one had no prior information, and considers the testimony, both in tone and content.

        you state: “The “two accounts” were (obviously) JFK’s murder and Tippit’s, and it was natural to connect the two.”

        ‘Obviously’ is conjecture, and ‘natural to connect’ is opinion.

        The officer’s statement indicates to me that the DPD went into the Texas Theater knowing that they were going there to arrest someone on charges of assassination of the President of the United States.

  3. You need to go to the Wikipedia pages that reference John McAdams survey and edit those pages so readers do not think that the John McAdams survey is the definitive survey. It is not.

    However , not anyone can edit those Wikipedia pages. You have to be able to reference some other study.

    You have that ability. You can edit the Wikipedia page and alert readers to other interpretations and reference your data.

    Here is a link to such a page. Look for Dealey Plaza Ear Witnesses in footnotes…

    1. Mike, I suggest you do it. I tried once to edit Wikipedia on witness deaths. The moderator told me I was not “peer-reviewed” so he wouldn’t let me add the info.. Anyway, since then, I have been cited in Belzer’s “Hit List” and Marrs “Crossfire”.

      But back to the Dealey Plaza witnesses. My latest post exposes McAdams survey as a sham. You can post a summary on Wiki. I would do it but Wiki will probably put the kabosh on it just like the last time.

      Here is the latest spreadsheet:

      Survey… Feldman McAdams Galanor Adjusted
      Total Witnesses 121 241 216 223

      Witness Opinion.83 100 109 132
      Grassy Knoll….51 34 52 81
      Book Depository.32 61 48 40
      No Opinion……38 69 37 36
      Both TB and GK..0 2 5 7
      Other locations.0 3 4 4
      Not asked…….0 72 70 55

      Percent of opinions:
      Grassy Knoll….61% 34% 48% 61%
      Book Depository.39% 61% 44% 30%
      GK / (GK+TB)….61% 36% 52% 67%

      1. I would just point out that McAdams ear witnesses data is not peer reviewed yet it exists as reference on many Wikipedia pages.

  4. I just posted this:

    An analysis of four surveys of the source of the shots at Dealey Plaza yielded surprising results. Three surveys indicate that a majority of witnesses (52%, 61%, 61%) observed shots from the Grassy Knoll area.

    The fourth survey by prolific Warren Commission apologist John McAdams indicates that 62% of 99 witnesses claimed the shots came from the Texas School Book Depository.

    The witness data has been added to the JFKCalc spreadsheet:

    1. He also claimed that JFK yelled out “My God, I’m hit!”- even claiming to hear JFK’s Boston accent.
      Unfortunately the characteristics of the neck shot make it impossible for JFK to have said anything.

      1. You forget that JFK was first hit in the BACK (5.5 inches BELOW the collar) by a DOWNWARD trajectory gunshot and could have cried out. THE BULLET DID NOT EXIT. But the MAGIC BULLET FAIRY TALE claimed that it CHANGED direction and exited his throat, causing SEVEN wounds to JFK and Connally. And emerged in PRISTINE condition at Parkland Hospital. And we have another FACTOID that you cannot explain: ALL Parkland doctors that the throat wound was one of ENTRANCE. BYR-BYE SBT.

        1. Actually the doctor who examined the throat wound most closely and did the tracheostomy (Perry) said that it could have been either. He was so disgusted by the claims after the initial press conference that he didn’t want to speak to the press afterward for fear of again being misquoted by medically ignorant reporters.
          The bullet that caused the back wound clearly passed through the neck. Even a weak round like a .22 short would have traversed the tissue equivalent of two boneless chicken breasts; if it had not where was it on the postmortem radiographs?
          If you assume that the throat wound was an entrance wound, the shooter would have had to be on the floor of the limo in front of Connolly’s jumpseat .
          What is the probability of two shots fired simultaneously from 2 different directions tens of yards apart simultaneously hitting a moving target exactly opposite each other shot’s point of entry?
          I am still waiting for the probability of thousands of flying saucer witnesses being should be able to come up with a real figure.

    1. No, I am simply right: Andrew Mason on the applicability of witness evidence.
      One need not start with the belief that witnesses are reliable at all. Provided there are several independent witnesses, determining a witness’ reliability is simply a matter of seeing how their recollections fit with the rest of the evidence. Subjective techniques for assessing witness accuracy and trustworthiness are fraught with uncertainty.

      It is very important to distinguish between the fallibility of a single witness and that of a group of witnesses who independently report observing the same fact. If the witnesses are independent, they will either independently agree on a fact because they observed it or they will be independently mistaken. Where there is more than one way to be mistaken, independent errors will be distributed over the range of all incorrect possibilities.

      Dishonesty is an inherently random factor unless there is collusion between witnesses.The testimony of the independently mistaken or dishonest witnesses will necessarily fail to converge on a common explanation. Conversely, the convergence of consistent witness evidence on a particular detail can have only one of two rational explanations: either they all shared a common observation or they are not independent.

      This use of corroboration as a technique for assessing reliability does not require subjective assessment of the witness’ demeanour or appearance of trustworthiness. It is not the witness recollection per se that is important. It is the fact that the same witness recollection is produced by multiple independent sources that is key. Juries intuitively understand this and, generally, do not need to have the probabilities quantified. They apply common sense to conclude how unlikely it is that multiple witnesses will independently have with the same recollection of something that they did not actually observe. The mathematics of probability supports our common sense.

      1. No, you are simply wrong. Your follow-up statement is full of self-contradictions and unfounded assumptions.”It is the fact that the same witness recollection is produced by multiple independent sources that is the key.” That assumption is clearly erroneous and destroys the basis for your entire “statistical” theory.
        As stated before, what is the statistical probability based on witness statements that flying saucers exist? You can make the same argument to “prove” that flying saucers exist, that ghosts exist, that the Germans bombed Pearl Harbor. The unfortunate thing is that the vast majority of Americans know nothing about statistics and how you completely mislead the ignorant. They cannot see the difference between a t test and a t shirt.

        1. No you are wrong. You are generalizing an incident specific analysis to a sociological one. Like saying the analytic results of fossil dating can’t be true because the majority of the world believes the dates in Genesis. It’s a ridiculous basis for disputing the results. You seem smarter than that, but…maybe not.

  5. The number of Book Depository employees on the street who were afraid to return to the building because they thought a crazed gunman was in it: ZERO.

    1. The crazed gunman was on a bus within 10 minutes after the assassination – and the only unexcused male not present for a roll call.

      1. What does that have to do with my point? And he was not the only missing male (Charles Givens was another), let alone the only missing employee. Many could not get back into the building after it was sealed off.

          1. Uh, no. According to my research, the roll call happened somewhere between 1:05 and 1:15. The police radioed to pick up Givens at 1:46pm, and he was encountered by Jack Revill (who knew him from his narcotics background) at the TSBD shortly after 2pm.

        1. Why is it that for thirty years or more conspiracy books have said “Oswald wasn’t the only one missing” (the WR didn’t claim that he was), yet they never seem to point out this more important and relevant fact:

          Oswald was the only TSBD worker *who was inside the TSBD at the time of the shooting* who left before the building was sealed off.

          Why do these books repeatedly trot out Givens, who was outside with other people when JFK was killed and therefore couldn’t have been the shooter?

          1. Really, Jean? Only conspiracy books have claimed that? Here’s the Washington Post 12/1/1963: “The suspect was the only employee of the school book building who was missing at a 1:15 checkup. It was at this point that Oswald was named in a police radio lookout.”

            And did the police immediately know the exactly location of every TSBD worker at the time of the assassination? I don’t think so.

          2. Jean Davison writes:
            “Oswald was the only TSBD worker *who was inside the TSBD at the time of the shooting* who left before the building was sealed off.”

            I don’t know anyone who believes that Oswald was simply an ordinary citizen who just happened to be the convenient scapegoat. After all, some very powerful people believed that the unaffiliated, friendless stumble bum could ignite World War Three!

            So Oswald left the building . . . and nobody knows his rationale. Perhaps it was an escape or a rendezvous. It was pretty easy. He just walked away after helpfully directing a newsman to a telephone. True, the fact that Oswald left the TSBD and Dealey Plaza is a little piece of evidence that suggests guilt. Just as the negative paraffin cast is a little piece of evidence suggesting innocence.

            It’s hard to piece it all together . . . especially since the government never tried to pursue an honest, open, unbiased investigation.

            Incidentally, the originator of this thread is correct. The percentage of witnesses does not skew the odds.

          3. TLR, which begs the question, who held the roll call, drew attention to Oswald’s absence and provided his address; the same individual that had already identified Oswald in person to a police officer some minutes before. Or am I mistaken? If not, why wasn’t Truly conflicted by that? Why didn’t he qualify … “but we just saw Oswald.”

          4. TLR,

            I didn’t say only conspiracy books have claimed that. The media made a lot of errors in the first few days, but that has nothing to do with my point, and neither does what the police knew and when.

            Oswald was not the only employee missing, but he was the only one missing WHO COULD’VE BEEN THE SHOOTER.

            Truly happened to notice that Oswald wasn’t still there (he’d seen him right after the shooting upstairs). He didn’t report this right away and by the time Fritz gave the order to look for him, Oswald was already at the police station under arrest. The police were never “on the lookout” for Oswald specifically.
            (You’d never know this from reading Rush to Judgment, which has a whole chapter called “Why Oswald Was Wanted.”)

            Truly knew that Givens hadn’t been inside during the shooting because he’d seen him walk away from the building right before the motorcade arrived. See his testimony:


          5. Jean, so Oswald was arrested solely on the basis of his alleged involvement in the Tippit murder. However, how do you square that Texas Theater employee Julia Post testified that she heard a police officer declare that they “had Oswald …. a suspect in both murders.” (paraphrasing)

            If Truly’s information didn’t send the DPD to Oak Cliff, how did this officer at the Texas Theater know that Oswald was suspect in the assassination of JFK as well?

            Beyond that, I still wonder why Truly didn’t pause, even if for a moment, to wonder why he and DPD Baker had encountered Oswald in the location they had only minutes, perhaps seconds, after the shots from the 6th floor, and yet Oswald went missing … Truly: and by the way here’s his address. Oswald had to be allowed to leave the building, had to be en route somewhere when the Tippit murder occurred. Then conveniently Truly pegged Oswald as missing.

            He couldn’t do so earlier – Baker was by his side – because Oswald was NOT missing, in fact he was drinking a soda inside the building.

            If Truly was not playing out a role, why wouldn’t he have paused and speculated …”but we just saw Lee, in fact when we saw him it was obvious he could not have been involved … he was drinking a soda for God’s sake …” which was precisely why he and Baker did not intervene immediately, and I would speculate further that Truly knew not to nail Oswald while inside the building. He had his compartments, and he stayed within them.

            Sounds to me like the timing was a bit off … which would be the case in an intricate operation. Unfortunately for Oswald, the gods aligned with the magicians behind the assassination supported by a fumbling press. Truly et al didn’t know what “hit” them.

          6. Leslie,

            Julia Postal testified that a policeman said, “I think we have got our man on both accounts.”

            That was a natural assumption, since Tippit was shot less than an hour after the assassination, and someone had asked over the police radio,”Is there any indication that it has any connection with this other shooting?” The dispatcher replied, “Well, the descriptions on the suspects are similar and it is possible.”

            (police radio transcript here:

            Truly didn’t have Oswald’s Oak Cliff address. Fritz said Truly gave him the Irving address after the rifle was found (after 1:22).

            Baker and Truly testified that Oswald was NOT holding a Coke when they saw him. Baker spotted Oswald just as he was going into the room where the Coke machine was. A secretary saw him afterwards with a “full” bottle, she said.

            Truly’s seeing Oswald near the back stairs when he did was not an indication of innocence. Quite the contrary. Reconstructions of the “lunchroom encounter” showed that if Oswald had fired the shots, ditched the rifle and gone downstairs immediately, the second floor stairway area was *exactly* where he would have been.

            Nothing suspicious about that, though, right?

  6. What is the probability of the thousands of flying saucer witnesses being mistaken?
    There is no medical evidence for a Grassy Knoll shooter- what is the probability of 30 forensic pathologists being wrong about that conclusion?
    This pseudo-statistical exercise is quite entertaining to those I us who have actually been involved with statistics and statistical reminds me of the Drake Equation from a few years back that Carl Sagan loved. That equation came up with the probability of thousands of advanced civilizations in our galaxy, without anything but repeated assumptions that could not be proven.
    The prior tests that were used to establish the accuracy of estimating the direction of shots in Dealey Plaza could never reproduce the confused and unsure perceptions of Nov. 22, when nobody was expecting any kind of disturbance . Those tests are not a basis for any real evaluation of witness accuracy for the actual event, which renders this hypothesis completely invalid from the start.

    1. Photon, read this and please stop claiming that the medical evidence is a settled matter:

      I’m pretty sure I’ve asked you before which investigation we are supposed to believe in (WC/Clark Panel/HSCA) – was JFK’s rear wound in his neck, shoulder or back? Was there a bullet hole low on the back of the head near the occipital or four inches higher? Where was the exit wound – right-front, right-side, top…? Each investigation has moved Kennedy’s wounds around repeatedly. Have you ever heard of such a thing?

      1. Gary Aguilar may be an excellent ophthalmologist but I would bet you a year’s pay that he hasn’t done a physical exam since his internship and knows virtually nothing about forensic pathology. The repeated claims of movement of wound positions is nothing but a Red Herring put out by people with no medical background completely ignorant about autopsies, medical procedures and medical records . A panel of 9 board-certified forensic pathologists hired by the HSCA stated that only two wounds were found on JFK and both came from the rear. There was absolutely no evidence whatsoever of any shot coming from the front striking JFK or Connolly. None. Now who is more competent to judge wound direction and origin- 9 board certified forensic pathologists with over 100,000 autopsies done or an ophthalmologist who removes cataracts and hasn’t held or used a stethoscope in 30 years?

        1. In other words, you can’t be bothered to read that lengthy essay and refute any specific point in it. The moving wounds is not a red herring, and you don’t find such a phenomenon in any other prominent murder case.

          Dr. John Lattimer is frequently used by lone-nutters to defend the official story, and he was a urologist.

          1. So you accept the conclusions of an ophthalmologist and and his expertise in evaluating the autopsy results over the judgement of 9 board certified forensic pathologists with 100,000 autopsies performed collectively ?
            Is that a joke?

          2. Photon, the joke is that you won’t actually read the article and try to refute anything in it. It doesn’t matter whether it was written by an opthamologist or a car salesman. The facts are what matter.

            I don’t know why you aren’t the least bit skeptical of a military-run autopsy performed by people with little experience at forensic pathology. The constantly changing descriptions of Kennedy’s wounds are a sign that something is seriously wrong. The testimony and documents released by the ARRB was further confirmation that the HSCA played games with the medical evidence.

        2. S.R. "Dusty" Rohde

          “The repeated claims of movement of wound positions is nothing but a Red Herring put out by people with no medical background”…

          This is an excellent example of deception couched in truth. The author (Photon) doesn’t state who was responsible for or where the movement of wounds originated, although merrily referring to them in demeaning and derogatory terms. Some might mis-take Photons comments as a reference to the research community, which it is not. How can it be? It was commitee members who decided the wound was higher….placing the wound near the “cowlick” or top-center back of head, contrary to the Doctors identification of two wounds lower on the back of head. How did this happen? A simple error has been made by many people. Mistaking a frontal forehead view (Anterior-Superior view) for a Posterior-Superior view. In doing so, a frontal exit wound maigically became a back of head wound much higher than Doctors identified.

          “A panel of 9 board-certified forensic pathologists hired by the HSCA stated that only two wounds were found on JFK and both came from the rear.”
          …This is a misrepresentation of known evidence. Bethesda Doctors themselves identified a minimum of three wounds and indirectly four. Doctors marked on the back of a skull (near middle right) two wound locations they confirmed. But, this did not include the throat wound, back wound or the bullet wound described by Doctors located in the lower right (back of head) at the hairline. The two wound reference is false.
          “There was absolutely no evidence whatsoever of any shot coming from the front striking JFK or Connolly.”
          …There is absolutely no truth in your statement.

          1. There is nothing but truth In that statement. Please post any statement from any pathologist who has reviewed this case clearly stating that any wound on either man came from the front.
            As you have never seen an autopsy, nor participated in one, nor reviewed how individual pathologists make personal notes during the procedure, your conclusions are simply not valid.
            Give us some proof that you know more than the nine world renowned forensic pathologists retained by the HSCA about wound placement and ballistics. I will always accept the opinions of Medical school graduates who have completed formal pathology residencies of many years with further fellowship training in forensic pathology and the experience of performing tens of thousands of autopsies over the opinion of an E. M. T.

  7. Discussion about inferring the number of shots fired from ear witness accounts is more than a little esoteric. There is ample documented evidence of there being more shots fired than the Warren Commission’s mythical three. There is both photographic and other evidence of multiple shooters. The medical evidence as shown by Mantik, Horne and others is evidence of multiple shooters from different locations. And none of the acoustic discussion takes any account of the possibility/probability that one or more of the shooters had a silenced weapon. In the light of this evidence it does not really matter what the statistical odds are of a, b or c.
    There were multiple shots fired by multiple shooters, result, one dead President, and a massive coverup that extends to this day.

  8. Mike Rago gets it. To those who claim that the individual witness probability based on the percentage mix of observations is invalid, I ask: What estimate would you use?

    This is not a case of “garbage in-garbage out”. The data is the best evidence of witness observations based on sound, sight and smell in the area of the Grassy Knoll. The simple probability calculations of the independent observations only confirm the acoustic, medical and ballistic evidence of at least one grassy knoll shooter.

    I have just updated the JFKCalc spreadsheet by consolidating Table 1 and Table 2 (Galanor’s) into Table 3. Approximately 180 witnesses were asked where the shots came from. Of the 143 who had an opinion, 87 (61%) said the Grassy Knoll; 49 the TSBD; 3 from both locations; 4 said elsewhere.

    The probability that a given witness who said shots came from the Knoll would be MISTAKEN is P= 1-.61 = 0.37.

    The probability that ALL 89 witnesses would be MISTAKEN is
    0.37^87 = 2.7E-38 or 1 in a trillion trillion trillion!

    In a court of law, less than 1 in 100 is considered beyond a reasonable doubt.


    The probability that a given witness who said shots came from the Knoll would be MISTAKEN is P = 1-.61 = 0.39.

    The probability that ALL 89 witnesses would be MISTAKEN is
    0.39^87 = 2.7E-36 or 1 in a trillion trillion trillion!

  9. Everyone,

    If a shot was fired from the grassy knoll (given information for purposes of this example), the probability a shot was fired from the grassy knoll is 1.0. Certainty.

    If in this situation (situation being one shot from anywhere, but certain knowledge it was fired from the grassy knoll) 42 percent of witnesses report hearing a shot from the grassy knoll, we can say there is a 0.42 probability a witness will correctly determine the source of the shot.

    If in this situation 51 (or whatever number) of witnesses report hearing a shot from the grassy knoll, and 51 witnesses represent 42 percent of all witnesses, then again there is a 0.42 probability a witness will correctly determine the source of the shot.

    All of probability theory is based on (a) a base of possibilities, all having equal chance of occurrence, and (b) a posited outcome from the base of possibilities.

    Probability theory is not based on guesswork or supposition. It is a rigorous mathematical theory.

  10. We know the results from an actual hearing test that was conducted at the time of the test shots in 1978.

    Two observers were asked to determine the source of a shot.
    Combined they were able to correctly identify the source of the shots 82% of the time when the shots were from either the Grassy Knoll or the TSBD.

    We also know from the test shot acoustical recordings (recorded in 1978) that there were no significant echos from the Grassy Knoll area.

    The following image identifies the location of echos for one of the test shots from the TSBD. There were no significant echos from the Knoll area.

    It should not be surprising that there is no problem discriminating the origin of a shot between the knoll and the TSBD.

    However, it would be a problem for listeners if they were trying to discriminated between a shot from the TSBD and the DALTEX or Criminal Records Building.

    If we use the results from the acoustical “loudness” test, of 82% as the probability that a witness will correctly identify the location of the origin of a shot then the probability that all 33 grassy knoll witnesses were wrong is (.18) to the 33rd power = 2.5 x 10 to minus 25th power. Using that number the probability that all 33 knoll witnesses were wrong is zero.

    But lets say that 82% is too high a number to apply to all the 33 witnesses. The witnesses were scattered throughout the areas, had different abilities , heard different echos.

    Lets arbitrarily drop the probability to 50%. Using 50% the probability that ALL of them misidentified an echo as as shot is (.5) to the 33rd power = 1.164 x 10 to the minus 10th power. Again, the probability that ALL of them were incorrect is so close to zero we might as well call it zero.

    Lets arbitrarily drop the probability again. This time lets drop it to 20%, meaning the probability that a witness could correctly discriminate an knoll gunshot from a knoll echo is 20%. The probability that all 33 were incorrect is (.8) to the 33rd power = .00063. The probability that ALL were incorrect is .00063 which means that the probability that at least one witness correctly identified a gunshot from the knoll is 1-.00063 = .99936.

    Lets do it again. Lets drop the probability to 10%. So the probability the knoll witness was incorrect is (.9) to the 33rd power = .0309. So there is a 3% chance that all 33 witnesses were incorrect and there was no shot from the knoll. Of course, this means that the probability there was a shot from the knoll is 97%.

    While some may say that 82% is too high a probability to assign to the 33 witnesses it is also reasonable to assume that 10% is too low a probability to assign to them.

    What has been shown that for all reasonable probabilities that one would assign to a witness the probability that ALL 33 witnesses would be incorrect is very small.

    The reason the probabilities are not important is because too many people reported a shot from that location. It is the 33 witnesses that is the significant metric. Any reasonable probability raised to the 33 power will result in a conclusion there was a shot from the knoll area.

    Mike Rago

  11. I believe the poster is probably correct.
    I am not sure of the validity of the characterization of the number of witnesses who heard shots from where–I know several have studied that question. Suffice it to say that a large number reported shots or a shot from the grassy knoll and a large number heard shots or a shot from the TSBD.
    Where I stronly DISAGREE with this poster is when he says that the 51 witneses who heard shots from the knoll could ALL be wrong. I think that is at least intuitively incorrect. And look at it this way: what if all but ONE was incorect? That still establishes a shot from the knoll
    The same reasoning applies to those whio heard shots from the TSBD. Not likely every single one was wrong.
    Logic says that at least ONE witnesss correctly heard a shot from the knoll aand at least one heard a shot from the TSBD.
    That being the case it is thus at least highly probable that there was at least one shot from the grassy knoll and at least one from the TSBD.
    This of course was also the conclusion of the HSCA accoustics panel.
    Bottom line: there was a knoll shot unless every single one of the (51?) knoll shot witnesses was wrong. Why complicate it any more than that?
    Tim Gratz

    1. The vast majority of witnesses who expressed an opinion about where the shots came from cited only one location — either the TBSD or the GK area. Not both. Only 4 or 5 witnesses, a much smaller group, said shots came from more than one direction, according to lists from both sides of the debate.

      The “GK witnesses” in that larger group didn’t say “a shot” or “some shots” came from the knoll. They said “THE shots” came from there.

      For example, from Josiah Thompson’s list of knoll witnesses in Six Seconds in Dallas: Victoria Adams, Danny Arce, Mrs. Baker, O.V. Campbell, James Crawford, Harold Elkins, Ronald Fischer, and so on down the list, all said that they heard a total of three shots and that they thought these shots came from the GK area.

      What are the odds that only the 4 or 5 who said shots came from more than one direction were right and everybody else was wrong? Or does it matter?

      1. More than 4 or 5 thought the shots came from more than one direction, but they ended up in the “not” sure category.

        Harry Weatherford is one example here is what he said
        Here is what Harry Weatherford stated

        “I heard a loud report which I thought was a railroad torpedo, as it sounded as if it came from the railroad yard. Thinking, this was a heck of a time for one to go off, then I heard a 2nd report which had more of an echo report and thought to myself, that this was a rifle and I started towards the corner when I heard the 3rd report. By this time I was running towards the railroad yards where the sound seemed to come from.”

        So Harry Weatherford was not sure if the shot came from the Railroad Yard or the Depository.

        There are over 35 people in the “Not Sure” Category.

        There were many people who could not or did not offer an opinion.

        The people who were confused were the people who were not sure and/or did not offer an opinion.

        With respect to the people who did offer an opinion they gave as the direction the direction in which they had the most confidence. They singled out two primary directions.

        Finally, there were many witnesses who described the last two shots as nearly simultaneous. The Knoll shot was part of that nearly simultaneous pair of shots.

      2. Jean, your use of the term “Opinion” is disconcerting; you frequently argue that witnesses cannot be trusted, and in this instance you have reverted to the claim that it was little less than Opinion that later required witnesses to testify before the Warren Commission; are you suggesting that the Warren Commission called these witnesses to solicit their Opinion? Witnesses that insisted that the shots came from a location other than the 6th floor of the depository. Surely the WC had better things to do than invite “Opinion,” or perhaps not.

        Webster defines: OPINION: a belief, judgment, or way of thinking about something : what someone thinks about a particular thing.

        Are you suggesting that these witnesses had an OPINION about the assassination … that their eyewitness experience should be discounted because you have determined after the fact (not having been present in Dealey Plaza yourself) that they later formed nothing other than an Opinion about what they experienced/what they saw/heard/sensed? They swore under oath what they witnessed, but you seem to assert that their statements were nothing but an OPINION of their experience that day. This is an intellectually offensive argument in 2014; it may have passed muster on various forums over the years, but it will not survive scrutiny among those paying attention today.

        Would you not be more responsible to use terms such as “observation” or “witness” when addressing the testimony of one or more of those who were present during the assassination rather than reducing their experience to an opinion? If we are seeking a level playing field, is it wise to insert hierarchical thinking into the equation?

        OBSERVE:: to watch and sometimes also listen to (someone or something) carefully
        : to see and notice (someone or something): to make a comment about something you notice

        WITNESS:: a person who sees something (such as a crime) happen ….law : a person who makes a statement in a court about what he or she knows or has seen: a person who is present at an event (such as a wedding) and can say that it happened

        Full Definition of WITNESS: attestation of a fact or event : testimony 2: one that gives evidence; specifically : one who testifies in a cause or before a judicial tribunal
        3: one asked to be present at a transaction so as to be able to testify to its having taken place 4: one who has personal knowledge of something 5a : something serving as evidence or proof : sign

        1. Leslie,

          I don’t understand your objection to the word “opinion.” Witnesses testified about where they believed the shots came from.

          Witnesses can be honest, intelligent, and certain — yet still be wrong.

          The first article at that link, e.g., says:

          “…forensics can now support psychologists in their claim that memories and individual perceptions are unreliable; being easily manipulated, altered, and biased.”

          Google has many articles on eyewitnesses in law and psychology journals, like this one:

          1. Jean, I’ve cited the discrepancy between a person expressing an opinion vs. their testifying under oath regarding what they witnessed.

            A witness heard or saw someone in the region of the grassy knoll; he or she took an oath and testified to that affect. Then others testified similarly.

            Opinion enters into this examination only when these witnesses are asked to extrapolate beyond what they heard or saw. For instance, “does this mean that you think that more than one person was shooting at the president in the motorcade?” That question would extract an opinion. That would not however compromise their testimony as witnesses to what they saw or heard in Dealy Plaza. You are attempting to compromise testimony.

            Further: I heard the birds singing in my garden this morning. It is not my OPINION that they were singing. The birds were singing, I heard them singing, and I would testify under oath that I heard them singing, and in fact I saw them in the trees that were positioned in the same direction that I heard them singing.

            My OPINION might be that Spring is nigh; others might argue that Spring is not nigh, that the birds are confused (by Climate Change?!); but they cannot argue that the birds were singing unless they were where I was when I heard the birds singing and in a position to point out to them the trees in which said birds were singing, and able to prove to me that the birds were not singing. (I trust you won’t introduce the argument that perhaps I was merely “hearing things.”)

            Can you prove that no one was shooting at the president from the direction of the grassy knoll?

          2. Leslie,

            Jean Hill testified under oath that she heard 4 to 6 shots coming from the knoll. S.M. Holland testified to 4 shots, only one from the knoll. Others said 3 from the TSBD. And many other variations.

            They’re all correct?

          3. Jean, you make my point for me. There were shots from both directions, and the number is in dispute only because of the position the various witnesses held at the time/intervals of each shot. Why is that so unreasonable? And why are you so inclined to believe the shots came from the TSBD but not the Knoll? You must surely base that on one or two eyewitnesses that you have selectively chosen to trust. Following that, I can predict you will argue that a rifle was found on the 5th floor, but a rifle was not found at any other location identified by witnesses as the source of other shots. Ergo, the facts you rely on exclusively are those that existed inside the depository and the fact that an eyewitness supports that theory is all the better. That is cherry picking to borrow a popular phrase, but more significantly it is indication that the set up of Oswald was ingenuous.

          4. Leslie,

            You say, “Jean, you make my point for me. There were shots from both directions, and the number is in dispute only because of the position the various witnesses held at the time/intervals of each shot.”

            Don’t look now, but that’s merely your OPINION, not what the majority of the witnesses testified to.

            And you say that all the evidence against LHO is “an indication that the set up of Oswald was ingenuous.” The more guilty he looks, the more innocent he is?

          5. Jean, my response was not posted; perhaps it was overlooked.

            leslie sharp
            Your comment is awaiting moderation.
            February 22, 2014 at 2:21 pm
            Our disagreement on this issue began with the term OPINION as you applied to the statements/testimony of eyewitnesses. You then referred to varying degrees of testimony relating to number of shots and the direction of those shots. I then pointed out that said eyewitness testimony indicates there were shots from two directions, the number remains in question. That is not my opinion, that is restatement of witness testimony. Opinion entered into this discussion and remains there because you are expressing yours that 1) witnesses develop opinions but seldom relay accurately what they have experienced and 2) that when you combined their testimony, your opinion is that they cannot be trusted because they do not all agree on the number of shots.

            Opinion is defined: a view or judgment formed about something, not necessarily based on fact or knowledge.

            These people were present in Dealey Plaza, their testimony should be viewed as possessed of fact or knowledge, ie eyewitness and observation, NOT opinion. I believe that you simply chose the word unwisely.

          6. Leslie,

            You said:
            “I then pointed out that said eyewitness testimony indicates there were shots from two directions, the number remains in question. That is not my opinion, that is restatement of witness testimony.”

            The vast majority said either one direction or the other — not both.
            You “restate” this as, “There were shots from both directions.” That’s your opinion about what their testimony means, not what their testimony actually says.

          7. Jean, we’ll have to disagree on the semantics. Their testimony, when considered in the collective, indicates shots from both directions, not simply one or the other. I dislike football metaphors, but: The quarter back testifies that he threw the ball, and the tight end testifies that he received the pass; the testimony in its entirety describes the play. That is not opinion.

        2. Likewise your opinion of the witness testimony is your opinion.

          In your opinion all 33 of the witnesses who said a shot came from the knoll are wrong. That is your opinion and as has been shown the probability that all 33 were wrong is very small. For your opinion to be correct all 33 have to be wrong.

          You come to this very unlikely conclusion because you misinterpret the meaning of only 3 or 4 people stating the shots came from both directions.

          In probability theory when the intersection set of two events is empty it does not mean that only one of those events occurred. It means that the two events are independent events.

          Also, the study on which you rely is not accurate. But that is a different issue for an different time.

          1. Mike,

            When I reported what the witnesses said, that’s not stating my opinion.

            You wrote: “In your opinion all 33 of the witnesses who said a shot came from the knoll are wrong.” But that’s not what 33 witnesses said. Most of the “knoll witnesses” (no matter whose number you use) said *THE* shots came from the knoll, not *A* shot.

            Jean Hill testified that she heard 4 to 6 shots from the GK and nowhere else. Surely you don’t agree with that?

            You and Ms. Sharp seem to think that some witnesses heard only shots from the GK area while others heard only shots from the TSBD area. A kind of “selective deafness,” so to speak. This disagreement didn’t depend on witness position. In some cases, people standing next to each other picked opposite directions.

            Suppose there was a sudden loud explosion somewhere and witnesses pointed in two different directions, saying that’s where “it” came from. What’s the most likely explanation for that? Is it that there were really two explosions, and some heard one while others heard the other? Or that people were confused about where the sound came from?

      3. Mike,

        As you probably know, Weatherford was standing in front of the sheriff’s office on Main St. with Allan Sweatt and other deputies. Sweatt’s report says they were “about 30 feet east of the corner of Houston and Main” and that after hearing shots they “ran around the corner and towards Elm Street and Houston.” IMO, that’s the corner Weatherford indicated he “started towards” — Main/Houston, not Elm/Houston.

  12. I agree completely with the above comments. On the topic of the number of shots fired, I strongly recommend Donald Byron Thomas’ book Hear No Evil. He is a respected scientist and he vigorously defends the findings of the original dictabelt analysis which was done for the HSCA. He then goes further to show how the HSCA essentially watered down the report, for political reasons.

    1. Thomas’s work is worth a close look if one is to have a more complete understanding of the evidence. His original paper, written in 2000, was largely a critique of the statistical methodology used in the dictabelt analysis and he essentially provides the correct numbers. His data has come under fire from those who support the LNH but he makes a very cogent argument for his case.

    2. Don Thomas’s interpretation of the acoustic evidence sanctions the Single Bullet Theory.

      What this means is that if you accept Don Thomas’s acoustical interpretation(I do not) then you are accepting the validity of the Single Bullet Theory.

      1. No it doesn’t, Mike Rago, that’s nonsense. I for one accept Thomas’s analysis of the dictabelt but I most certainly do not agree with the SBT. All that’s important is that his analysis places shots at approximately Z-175, 204, 225, 313, and 327.

        A logical interpretation of this would be shot one (at 175) misses; shot two (at 204) hits JFK in the back; shot three (at 225) strikes Connally; shot 4 (the knoll shot at 313) strikes JFK’s right temple; and shot five (at 327) enters the back of Kennedy’s skull.

        That’s a plausible scenario based on the acoustics that does not include the SBT. You need to learn to separate the data from the author’s conclusions.

        1. I did make a mistake.

          It is Josiah Thompson who has adopted an interpretation of the acoustic evidence which sanctions the single bullet theory. For some reason I thought Josiah adopted the Don Thomas interpretation but he did not. I am not sure whose acoustic interpretation Josiah Thompson has adopted.

          The Don Thomas interpretation does not require acceptance of the Single Bullet Theory.

          Scroll to 18 minutes and 25 seconds in the following video to hear the acoustic interpretation accepted by Josiah Thompson merged with the Zapruder film.

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