Editing 1252: Increased Risk

{{comic
| number    = 1252
| date      = August 16, 2013
| title     = Increased Risk
| image     = increased_risk.png
| 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!
}}
==Explanation==
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.

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.

[[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.

[[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.

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.

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.

The caption clarifies Cueball's point, but without sarcasm.

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).

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==
:[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.]
:Ponytail: We should go to the north beach. Someone said the south beach has a 20% higher risk of shark attacks.
: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%'''''!
:Beret Guy: Oh no! This is our third trip!

:[Caption below the panel:]
:Reminder: A 50% increase in a tiny risk is '''''still tiny'''''.

{{comic discussion}}
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring Beret Guy]]
[[Category:Dogs]]
[[Category:Statistics]]
[[Category:Sharks]]