Editing 1252: Increased Risk

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| title    = Increased Risk
 
| title    = Increased Risk
 
| image    = increased_risk.png
 
| image    = increased_risk.png
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| titletext = You may point out that strictly speaking, you can use that statement to prove that all risks are tiny—to which I reply HOLY SHIT WATCH OUT FOR THAT DOG!
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| titletext = You may point out that strictly speaking, you can use that statement to prove that all risks are tiny--to which I reply HOLY SHIT WATCH OUT FOR THAT DOG!
 
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}}
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==Explanation==
 
==Explanation==
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The panel satirizes the common misunderstanding of the concept of percentage. Quoting a percentage change without mentioning the base probability that this ratio acts on is meaningless (outside of arithmetic for arithmetic's sake). Most everyday communication, however, succumbs to such incompleteness. In the aftermath of this ambiguity, people tend to conflate relative and absolute changes.
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{{incomplete}}
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The panel satirises the common misunderstanding of the concept of percentage. Quoting a percentage figure, without mentioning the base which this ratio acts on is meaningless (outside of arithmetic for arithmetic's sake). Most everyday communication however, succumbs to such incompleteness. In the aftermath of this ambiguity, people tend to conflate relative and absolute changes.
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If the probability of a shark attack at the North beach is 5 per million, then the probability of shark attack at the South beach is still not more than 6 per million. The difference between these values is not enough to normally justify choosing one beach over the other, even though a "20% greater" chance sounds significant when stated out of this larger context.
 
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[[Cueball]] parodies the concern by noting that by going to a beach three times instead of two, their chances of attack by dogs with handguns in their mouths (a ludicrous and unrealistic scenario as dogs cannot buy guns{{Citation needed}} and are not likely to pick one up off the ground) increases by 50%. If the chance of the dog attack is one per billion on each visit to the beach, then the chance of attack increases over multiple visits; regardless it's still one in a billion for any specific visit. This does not change the overall improbability of there ever being a dog swimming with a gun in its mouth.
 
  
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[[Beret Guy]] misunderstands Cueball's probability, exhibiting the {{w|gambler's fallacy}} by believing that since they haven't been attacked in their first two trips, the chance of attack by dogs with handguns is higher on this outing.
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If the probability of a shark attack at the North beach is 0.000001% (one in a million), then the probability of shark attack at the South beach is still 0.0000012% (1.2 in a million). The difference between these values is not enough to normally justify choosing one beach over the other, even though a "20% greater" chance sounds significant when stated out of this larger context.
  
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This is a common misunderstanding of statistics. While the overall probability of an attack in three trips would be higher than in a single trip, it doesn't change the fact that in each individual trip, the probability is still the same; whether or not they managed to avoid being attacked in their first two trips, the results of these trips do not factor into the probability equation of the third trip.
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[[Cueball]] parodies the concern by noting that by going to a beach three times instead of two, their chances of attack by dogs with handguns in their mouths (a ludicrous and unrealistic scenario) increases by 50%, which is simply on the basis that they will have three trips in which to be attacked rather than 2 (a 50% increase in the opportunities). If the chance of the dog attack is 0.000000001% (one in a billion) on each visit to the beach, then the chance of attack over two visits is 0.000000002% whereas in three visits it becomes 0.000000003%. This does not change the overall improbability of there ever being a dog swimming with a gun in its mouth.
  
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This also can be illustrated by coin flips: if one flips a "fair" coin ten times in a row, no matter what the result of each previous flip is (even if it were nine heads in a row), the odds of getting heads on the tenth coin flip theoretically remains 50%. In other words, past experience does not impact subsequent flips. In practice, if the odds on each flip were 50%, then the odds of nine heads in a row would be 0.2%, so after it might be worth considering the possibility that the coin has been bent or weighted to alter the odds, or even a counterfeit with "heads" on both sides.
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[[Beret Guy]] further misunderstands Cueball's probability, believing that - since they haven't been attacked in their first two trips, the chance of attack by dogs with handguns is higher on their third outing. This is also common misunderstanding on statistics: While the overall probability of attack in three trips might be 0.000000003%, it doesn't change the fact that in each individual trip, the probability is 0.000000001%; if they managed to avoid being attacked in their first two trips, these trips no longer factor into the probability equation of the third trip. The fault in the logic involves the lack of dependency of the events between successive visits, and is best illustrated by coin flips: if one flips a (fair, neutral) coin 10 times in a row, no matter the result of each previous flip is, the odds of getting heads on the next coin flip remains 50%. In other words, past experience does not impact subsequent flips (and specifically the probability of the results). By the same logic, the odds of getting attacked by dogs with handguns the same on the third trip than it had been on each of the first two trips to the beach. The "tripled" odds applied to the overall group of three trips; however now we have further information that the first two trips were uneventful, and take an independant look at the third trip.
  
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The caption clarifies Cueball's point, but without sarcasm.
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The title text discusses the argument that, if a tiny risk increased by 50% is still tiny, then since any probability can be reached by repeatedly increasing by 50%, then any probability is "tiny". [[Randall]]'s response to this is to mockingly warn of an impending attack by a dog holding a gun, implying that one who believes such an argument must believe that the probability of whatever occurance they are discussing is just as unlikely as the probability of a dog with a gun in its mouth shooting you, even though in reality the occurance being discussed is probably much more likely and believable. Alternatively, perhaps Randall actually sees a dog with a gun in the midst of his reply.
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Then again, the title text objects to this point (that a tiny risk increased by 50% is still tiny). If this 50% increment is done repeatedly, the risk can get arbitrarily high, while the statement says that it is still tiny. This can be compared to the {{w|Sorites paradox}} (the "paradox of the heap"), which involves a "heap" of sand from which grains of sand are removed individually. If one assumes that, after removing a single grain, a heap of sand is still considered a heap of sand, and that there are a limited number of grains of sand in the heap, then one is forced to accept the conclusion that it can still be considered a heap of sand even if there is only a single grain of sand (or even none at all).
 
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Being shot by a swimming dog with a handgun in its mouth is also specifically referenced in what if? 146, [https://what-if.xkcd.com/146/ Stop Jupiter].
 
  
 
==Transcript==
 
==Transcript==
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:[Cueball, Ponytail, and Beret Guy are standing around. Cueball and Ponytail have beach towels. Ponytail is looking at her cell phone. Beret Guy has his hands up to his face, looking distressed.]
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:Ponytail: We should go to the north beach. Someone said the south beach has a 20% higher risk of shark attacks.
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:Ponytail: We should go to the north beach. Someone said the south beach has a 20% higher risk of shark attacks.
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:Cueball: Yeah, but statistically, taking three beach trips instead of two increases our odds of getting shot by a swimming dog carrying a handgun in its mouth by '''''50%!'''''
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:Cueball: Yeah, but statistically, taking three beach trips instead of two increases our odds of getting shot by a swimming dog carrying a handgun in its mouth by '''''50%'''''!
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:Beret Guy: Oh no! This is our third trip!
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:Beret Guy: Oh no! This is our third trip!
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:[Reminder: A 50% increase in a tiny risk is ''still tiny''.]
  
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:[Caption below the panel:]
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{{comic discussion}}
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:Reminder: A 50% increase in a tiny risk is '''''still tiny'''''.
 
  
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{{comic discussion}}
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[[Category:Friday comics]]
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[[Category:Comics from August]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Cueball]]
 
[[Category:Comics featuring Ponytail]]
 
[[Category:Comics featuring Ponytail]]
 
[[Category:Comics featuring Beret Guy]]
 
[[Category:Comics featuring Beret Guy]]
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[[Category:Dogs]]
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[[Category:Math]]
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[[Category:Statistics]]
 
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[[Category:Sharks]]
 

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