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Shark bite statistics can lie, and the result is bad policy

The mathematics of shark bites look pretty simple: the more incidents, the worse the situation. That said, no amount of scientific explanation can fully address the tragedy of people being injured or killed…

Shark bites on humans are best viewed as random acts of nature rather than deliberate attacks. Mogens Trolle/www.shutterstock.com

The mathematics of shark bites look pretty simple: the more incidents, the worse the situation. That said, no amount of scientific explanation can fully address the tragedy of people being injured or killed by sharks.

Western Australia is currently dealing with such a situation. After a decade with few shark fatalities, seven people have now lost their lives in the past three years, prompting the state government to endorse using baited drumlines near popular beaches. The terrible numbers appear to speak for themselves. But there is an important problem that the public should know about when looking at these data.

The problem is that shark bite numbers can lie.

They lie in three ways. First, shark bites are discrete, random events that do not look random. Second, clusters of shark bite incidents are misleading. And third, we only count when human-shark interactions occur, not when they don’t. These points do not make these tragic situations any better but they can help in understanding how government policies can make them worse. And if governments are going to spend money on the problem, they need to be able to prove to the public that it will actually help.

Random events

Shark bites fall into a special statistical category known as “random, independent events”. This means that the likelihood that a shark bite will happen at a given time and place does not depend on when or where the last one happened. Just like a like a coin toss, if you get heads on the first time, you still only have a 50-50 chance of heads on the next flip.

Yet shark bites often do not look independent or random. Their nature makes them look like intent-based incidents. Any increase in frequency can also look like part of a new pattern, despite these events being independent, random and rare. As a result, the public understandably wants these vivid and frightening incidents stopped, and the government wants to diagnose a problem so it can come up with a solution.

It can be troubling for politicians and society to think of traumatic shark bites as random, unexplained events in nature - especially when they appear to come in clusters.

The impossibly hard situations following shark bites are made harder because beach-side communities can go through long periods of relative calm followed by a short spate of tragic deaths. This scene repeats itself around the world in other places like Hawaii and Reunion Island. But these clusters are misleading, and the coin-flip analogy helps to show why.

There may be times when you flip a coin and get five tails in a row. This doesn’t mean the odds have changed; sometimes these clusters just happen. Statisticians call them “Poisson bursts”, and this distribution was discovered after an analysis by Ladislaus Bortkiewicz in 1898 that included a review of a sudden spate of deaths among Prussian soldiers, all from the same unit, who were kicked by horses.

The late shark biologist Aiden Martin noticed that shark bites follow the same pattern. “They can seem to occur in clusters… but the likelihood of any one individual being attacked by a shark at a given time and place and the average interval between any two attacks remains constant,” he wrote.

Challenging thinking

In other words, the odds of having one shark bite incident followed by none for three months are the same as having a group of them occur. Yet when a cluster does happen, the inclination is to look for some new factor that explains the apparent trend.

A cluster of shark bites in Florida in 2001 provides a good example. As Pennsylvania State University mathematician David Kelton commented at the time: “It really does seem that there is indeed something odd going on with the ocean currents, temperatures, food supply, or water chemistry. However, even if such attacks were purely ‘random’ and independent of each other, it is not surprising that they seem to occur in ‘clumps’… and then not at all for a long time.”

This suggests that we should revise our traditional thinking about clusters of shark bites. In the 1950s, some people held the view that one lone shark, intent on biting people, was responsible for all shark bites in a region and that hunting this “rogue” shark was the answer. But a more deliberative analysis leads us to the view that shark bite clusters are statistical accidents of nature. Or put another way, I often tell people that “we’re in the way, not on the menu”.

For another angle, look at it the other way around: there are thousands of times when humans and sharks share the water and bites don’t occur - including, according to a 2009 New South Wales government report, those months when sharks migrate in their highest numbers along the coast. The coin is tossed all the time, but we only count the tragedies.

A word to Western Australia

Shark bites are random events but they are not perceived that way. Clusters make it look like we need to take action to stop a threat, such as the WA government’s new culling policy. But equally, the long gaps between clusters of shark bites could statistically make it look like a policy has succeeded even if it has no effect at all on the underlying risk of a bite.

As a result, the WA government has a duty to demonstrate to the public how its policies will genuinely safeguard them - particularly when the policy will harm ecosystems, as scientists suggest WA’s drumlines are likely to do. Presently, it is far from clear what effect the drumlines will have on public safety.

Shark bites are tragedies for families and communities, and very difficult for politicians. Reacting to these events is not easy, but numbers alone can tell a false story, or even lie. Approaching them with eyes wide open and a grain of salt can help with public education and public policies.

Join the conversation

47 Comments sorted by

  1. Nick Kermode

    logged in via email @hotmail.com

    Thanks very much Chris, great article and perspective.
    It is easy to fall into the trap of not thinking about this the other way around as for most people sharks are out of sight, out of mind until they hit the MSM. Then they are bombarded by articles that are almost universally full of inaccurate, sensationalist, fear driven hyperbole. It's no wonder it is hard for people to make informed judgements on the issue. The trouble is, the title " SPECIAL REPORT: No beach-goers were bitten by a shark today, same as yesterday, and the day before and the etc etc" is not going to sell many papers or make people tune in to the news. Combine this with the fact that statistics, as a subject, is so misunderstood by nearly everyone that it is really easy to draw incorrect conclusions and trick yourself and you have the recipe for the misunderstanding that you highlight well.
    Once again thanks.

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    1. David Harris

      Retired engineer

      In reply to Nick Kermode

      The importance of a good understanding of maths - especially probability - in making meaningful meaningful policies is, I'm afraid, beyond us. The few who understand are not in politics, and, of course, the media see this sort of understanding as the realm of fact-wonks. This is why there are such media frenzies over things like houses burning down, and no reporting at all of houses which didn't burn, even if they didn't because the owners took effective steps to prevent it. Our locals have just re-instituted aerial shark patrols. They cost heaps and achieve nothing but it makes people feel good.

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    2. Wade Macdonald

      Technician

      In reply to Nick Kermode

      What makes me laugh Nick is the comments by others on here and especially in social meedja about sharks attacking swimmers. If you look at statistics most are not swimmers at all but abalone divers, surfers, spear fishers etc etc.

      If we were to fearmonger the dangers of swimming then we would pick on rip tides as they account for 21 deaths per year in Australia.

      I liken the public perception on this topic to that of the rubbish conservation groups push to the public about rec fishing.

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    3. Nick Kermode

      logged in via email @hotmail.com

      In reply to Wade Macdonald

      Hi Wade, figures show that from 1970 to 1989 swimming actually was the leading activity involved in shark incidents. The last two and a bit decades are different though and the percentage has dropped a little, while surfing incidents have increased. Swimmers do still rank second though. However these recorded swimming incidences are all classified as deep water, quite some distance from shore and the comments floating around which I am sure you are referring to suggest shallow water near to the shore…

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    4. Wade Macdonald

      Technician

      In reply to Nick Kermode

      Hi Nick,

      I agree with your response. Just on attack statistics I was referring to fatalities not incidents as perhaps should of made myself clearer in the first instance.

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  2. David Roth

    Postgrad History Student

    At last, some rational thinking on the issue.

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    1. Nick Kermode

      logged in via email @hotmail.com

      In reply to Robert Tony Brklje

      Robert, Great Whites weigh about as much as a four wheel drive, have up to 300 razor sharp teeth, can travel at up to 50 km/h in bursts, hit prey with an impact upwards of 30 g's, have perfect camo to prevent detection, can detect half a billionth of a volt and have a bight force more than capable of ripping a human apart with ease. Do you really think they "fail" against a defenceless 80 kg human splashing about unaware of it's presence? If so could you explain to me how they could fail?
      Also the only disappearances in the ocean in the last two decades I am aware of that were of an unknown reason and bodies not recovered are listed in the ASAF as a "presumed shark attack victim" so not sure where you are getting "missing, presumed drowned" from. I am very interested in this topic and would appreciate a link to your information.

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    2. David Roth

      Postgrad History Student

      In reply to Nick Kermode

      Nick, I think that Robert's use of 'fail' meant that the shark had not succeeded in eating the attacked person, i.e. the victim was recovered.

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    3. Nick Kermode

      logged in via email @hotmail.com

      In reply to David Roth

      "fail"

      'To be unsuccessful in achieving one's goal.'

      "succeed"

      'Achieve the desired aim or result'

      If an animal completely ill designed for the ocean 'escapes' one of the most perfectly designed predators in all life on earth it certainly does not reflect a failure on the predators part. It is a reflection that eating a human is not the goal, investigation and curiosity is. The fact most take a relatively gentle (although horrific to our flimsy, vulnerable bodies) nibble then leave means they have actually achieved their goal (succeeded) and have not failed at all. If their goal was "eating the attacked person" the mortality rate would be more like 100% rather than 10.

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    4. David Roth

      Postgrad History Student

      In reply to Nick Kermode

      I do know the definition, Nick. But from the point of view of the victim, if they survive, the shark has failed.

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    5. Nick Kermode

      logged in via email @hotmail.com

      In reply to David Roth

      I think we will have to agree to disagree then David, but it is a silly point to get tied up on anyway really isn't it :) I replied to Robert as he was using factoids to obfuscate what Chris presented well in the article and I was interested in some supporting evidence or clarification of some pretty loose language.
      Apologies if I came over snappy, I have had some anger management issues lately over this situation ;)

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    6. David Roth

      Postgrad History Student

      In reply to Nick Kermode

      Yes, it's just semantics and no big deal. I agree that Chris's article is a breath of fresh air. I am also p*ssed off that people like Buswell are in positions of responsibility and ignore the advice of the experts.

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    7. Robert Tony Brklje
      Robert Tony Brklje is a Friend of The Conversation.

      retired

      In reply to Nick Kermode

      Consider the learning exercise for a shark, what to eat and what not to eat, how to test and how not to let the test subject get away.
      Obviously the first lessons are pretty rude and painful, requiring regurgitating of the undesirable meal. So the shark learns to taste new prey first. So now it learns the second lesson, just tasting new prey often allows it to get away with just a wound.
      So the shark refines it's attack for new prey, it swims in hard and fast, try to inflict a massive wound sufficient…

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    8. Nick Kermode

      logged in via email @hotmail.com

      In reply to Robert Tony Brklje

      Hi Robert.
      Your comment takes some of the limited knowledge of the great white shark and adapts it to a narrative that fits your argument. Hence your comment has some truth to it but an underlying misunderstanding of the animal and it's ecology.
      I have spent time in and out of the cage with whites and if you had witnessed one swimming in "hard and fast" you would understand, like others who have witnessed it, why a human could not survive that. It is true in some situations they…

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  3. Karl Lusdig

    Private sector

    Just kill the bloody things and eat them. I love a bit of battered shark. Just thinking about it makes me want some fish and chips for dinner.

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    1. Steve Phillips

      Nurse Practitioner

      In reply to Karl Lusdig

      Cant eat Tiger sharks or Great Whites Im afraid. They contain too much ammonia and taste like s&!t.
      Bronze Whalers now, they ARE tasty but aren't bothering us.

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  4. Steve Phillips

    Nurse Practitioner

    Quite right!
    Sharks are dangerous but we are ration creatures who CHOOSE to put ourselves at risk when entering an environment that is not natural to us.
    I expected better from a Liberal Govt, Colin is wrong to promote this 'knee-jerk' response to shark deaths.

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  5. Geoff Clark

    Senior Lecturer at University of Tasmania, School of Architecture and Design

    Yet more support to Albert's assertion about infinite things and human capacity for stupidity.

    Some things are right and some things are wrong. Are we not slaughtering species already, "inadvertently", at a high enough rate to make us feel like we are all-powerful and in complete control, to satisfy our egos?

    Perhaps more of a concern is the utterly mind-blowing ability of our governments to, again and again, produce bad outcomes. Can anyone suggest that less sharks is a good outcome?

    And, of course, we look to the all-powerful science to help us to (fail to) make timely decisions that simply need the application of common sense, and about 30 seconds.

    Honestly, the WA government's decision is moronic.

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  6. Julie Fechner

    Retired (Grumpy old woman)

    Chris, thanks for a great article. As a person very concerned for dingo conservation I read your article and substituted dingo for shark. These two top predators have so much in common in terms of Government attitude policy and management strategies., the WA Government has implemented strategies to remove these (sharks) essential predators, as other Governments are doing to the dingo. As you say these are difficult decisions, but the growing body of science that demonstrates the positive aspects of both the dingo and the shark must be accepted by Governments. Only then can we begin the devise and implement sustainable strategies to minimize interactions. Living in Victoria I was so pleased to see the number of West Australians who came out in the support of the shark.

    And if governments are going to spend money on the problem, they need to be able to prove to the public that it will actually help.... so so true.

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  7. Lynne Black

    Latte Sipper

    The movie "Jaws" didn't help, either. It resulted in many people being apprehensive every time they went into the water. Decades (and many reruns of the movie on late night television) later, it is still there lurking in our subconscious.

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    1. David Roth

      Postgrad History Student

      In reply to Lynne Black

      Yes, many people seem to think that 'Jaws' is a documentary.

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    2. David Roth

      Postgrad History Student

      In reply to Julie Fechner

      More like Ibsen's 'Enemy of the People' wrt the sheriff than Azaria.

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  8. Russell Hamilton

    Librarian

    "I often tell people that “we’re in the way, not on the menu”."

    Some might answer that they prioritise themselves over sharks and would like a few spots where they feel safe to swim, so too bad for any sharks who stray into those spots.

    "Yet when a cluster does happen, the inclination is to look for some new factor that explains the apparent trend." I would have thought that would be a good response - take that cluster of cancer cases that happened at (IIRC) an ABC workplace a while ago ... should people not have looked for a responsible factor? Should they have just thought "ah well, clusters happen, just chance, nothing to worry about" ?

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    1. David Harris

      Retired engineer

      In reply to Russell Hamilton

      It's not a case of "...nothing to worry about". It is a case of seeing if this cluster could reasonably be explained by chance. It could still be worth investigating, for PR purposes if nothing else, but if we already know that the maths show that chance is a likely explanation, don't be surprised if an investigation reveals nothing more. And before you rush off to make policy on the base of the cluster, check whether chance is a likely explanation and assume it is the right one until and unless an investigation shows otherwise.

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  9. David Arthur

    resistance gnome

    Science News
    New Study Finds Extreme Longevity in White Sharks
    Jan. 9, 2014 — http://www.sciencedaily.com/releases/2014/01/140109004145.htm

    Great white sharks -- top predators throughout the world's ocean -- grow much slower and live significantly longer than previously thought, according to a new study led by the Woods Hole Oceanographic Institution (WHOI)
    ...
    Journal Reference:
    Li Ling Hamady, Lisa J. Natanson, Gregory B. Skomal, Simon R. Thorrold. Vertebral Bomb Radiocarbon Suggests Extreme Longevity in White Sharks. PLoS ONE, 2014; 9 (1): e84006 DOI: 10.1371/journal.pone.0084006

    ie Great white population may be more sensitive to culling than WA Premiers might realise.

    Human disturbance of ocean trophic chain appear to be favouring jellyfish - are they good to eat?

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  10. Christopher Neff

    Lecturer in Public Policy at University of Sydney

    Thank you very much for your the comments. I always appreciate the feedback and especially the critiques. I try to be very careful to follow the data and let the data make the argument. Thank you again! Chris

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    1. John Brady

      logged in via Facebook

      In reply to Christopher Neff

      In which case, Chris Neff, PLEASE ADDRESS THE SERIOUS ERRORS IN YOUR OTHER ARTICLES that I have commented on.

      Policy makers need to know if recent attacks are Poisson bursts or indicative of recovering prey populations. The un-rigorous bias you have show in your other articles on The Conversation suggest you are an unreliable source.

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  11. Edward Cannella

    Zoologist

    Please Chris, don't confuse the issue with facts. "Vengeance is mine" says Emperor Barnett. It is purely a political populist policy to try and bolster his somewhat less than adequate governing skills and divert public attention from other issues in this State.

    Unfortunately, you will just be labeled as someone working against the safety of "children" (I think that was his last heart-string-tugger attempt). Yet another greenie who, apart from not being from WA, is someone not from WA telling us what to do.

    Sorry for the cynicism but, unfortunately it is all too predictable. The cliched, standardised responses by our politicians in this country lacks any intelligence or factual basis.

    PS thank you for explaining the probability theory behind the data. This article will be shared.

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    1. Paul Prociv

      ex medical academic; botanical engineer at University of Queensland

      In reply to Edward Cannella

      You're absolutely right. It's all about emotional knee-jerkism and politicians grandiosely flexing their muscles, just as we're seeing in Queensland in regard to flying foxes, who also share a poor and unjustified media image with sharks. Far more swimmers, surfers and skindivers die on the roads than by the teeth of a shark; even way more people are killed by horses than by sharks. If this were truly about protecting human lives, then we should be selectively culling cars and horses.

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    2. Edward Cannella

      Zoologist

      In reply to David Roth

      PS. I need to let you know that I have a phobia about sharks and haven't been in the water for at least a decade. However, I have no issues swimming in creeks and rivers (some with salties) - but that is my decision to make based on the risk assessment I make.

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    3. Nonie Jekabsons

      Tree Spotter at -

      In reply to Paul Prociv

      culling is not the answer. Recognising that the drive to the beach is more hazardous than being there will start us on the journey to reality.

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    4. Christopher Neff

      Lecturer in Public Policy at University of Sydney

      In reply to Edward Cannella

      Hi Edward - just wanted to say thank you for your note. You are definitely right about the "children" argument - that is the leading critique I get from Barnett Government staff - that I don't appreciate the concerns of parents regarding their children. The whole situation is a shame and I'm hopeful that there will be a discourse about what can really be done to reduce risk, not just the perception of risk.

      Thanks again, Chris

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    5. David Roth

      Postgrad History Student

      In reply to Edward Cannella

      Sorry Edward, I overlooked your reply. I understand your phobia about sharks, but my comment about swimming between the flags was more to do with the tragic number of drownings at the coast, a much higher figure than shark fatalities.

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    6. Edward Cannella

      Zoologist

      In reply to David Roth

      David, I thought your comment was spot on. It is all about responsibility and risk reduction by the individual, in the first place. We cannot control everything in this world but if we take care then we are less likely to suffer dire consequences. You are correct, more people die every year of drowning off our beaches than have ever been taken by sharks. There are thousands who die on our roads due to irresponsible behaviour. And there are many more examples. So, if we wish to to live closeted in cotton wool protected from ourselves and everything else that is out there, why bother living at all?

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  12. Richard Gun

    Retired doctor

    The same clustering phenomenon occurs in the occurrence of cancer. Many people have personal experience of a seemingly excess number of cases of cancer in their street or their country town or their workplace, and think that there must be some chemical or radiation exposure responsible. The fact is that wherever there is random distribution clusters will occur. If you randomly distribute 64 coins on a chessboard you won't find one coin and one coin only on each square. Cancer being a very common disease, cancer clusters occur by chance, and occur commonly.

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  13. Chris Gillham

    Journalist

    WA hasn't had seven shark fatalities in three years after a decade with few shark fatalities. It's had 13 fatalities in 18 years following seven decades with just two deaths.

    The increased fatalities will continue, mostly between May and November, because greater numbers of great whites are being lured close to the WA coast by a huge increase in their favourite food - migrating whales which among humpbacks have increased from an estimated 600 adults in 1963 to a current population above 30,000…

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    1. Paul Prociv

      ex medical academic; botanical engineer at University of Queensland

      In reply to Chris Gillham

      That sounds a most reasonable explanation for what's going on. Humpback whale populations are also expanding rapidly along they east coast, so I wonder if eventually we'll see more great white shark attacks here? I remember vividly, many years ago (1970s) while visiting the whaling station in Albany, WA, sharks being winched up on the flensing deck by hanging onto the dead, heavily chewed sperm whales, but I suspect these were blue pointers rather than great whites. They sure were attached to their whale meat! And, in the Abrolhos Islands, I saw a bunch of tiger sharks pulverising the floating carcass of a young humpback.

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    2. Edward Cannella

      Zoologist

      In reply to Chris Gillham

      Fatuous causality. Great whites primarily feed on seals and large fish and follow the whale migration to attack sick whales and calfs. The follow the currents. Currents can come closer to the coast, they don't follow a set route. Albany was a hotbed of shark activity during the whaling years but people took care and shark attacks were mostly avoided. People take a risk whenever they go into any environment whether it be in the ocean or driving on a road. You assess the risks and take the precautions…

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  14. Gary Kloepfer

    logged in via Facebook

    These are only random events that occur with no predictable frequency.Probability depends in large part on location which in certain parts of the globe such as Australia there could be be a higher event risk.Its important to remember that Sharks do not intentionally attack humans. If you happen to be in the water sitting on a board with your legs dangling on the sides you resemble one of there favorite treats and your probability of being bitten will be higher .The oceans are there world and when humans visit it a possibility of an event exists and the probability of that event occurring are for the most part random. Any anomaly reported needs to be investigated as to what is happening to skew statistical outcome.

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  15. Andrew

    logged in via Twitter

    The statistics aside, the people (while unfortunate and tragic) who have been killed by sharks in W.A. have either been surfing in remote surf breaks far off the coast, diving with bags of (bloodied) fish in catch bags, or in the dawn or dusk patrol.

    The numbers of swimmers killed at Perth's family friendly swimming beaches? 0. It's a massive scare campaign and one that our local government is using to cover up the rest of their mess.

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  16. Daniel Duongasaur

    logged in via Facebook

    A coin toss remains to be 49.999% chance of either side landing. Regardless of the results.
    Shark bite chances do NOT remain the same. Simply because the variables change.

    Three close incidents are not like 5 tails in a row. It's more like 50 tails in a row and I would definitely think something is up.

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