DON'T BLAME THE MATH

a probability blog

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Tag: life

  • What’s the Weather Like?

    You look at your forecast. 30% chance of rain, that’s a bummer(unless you’re one of the rare people who like the rain). But what does this number really mean?

    Many assume this number means that 30% of the given town would rain or it will rain for 30% of the day, but what it actually means is far more interesting and uses a clever calculation not many are aware of. When the forecast shows 30% it means that there is a 30% probability(I love that word) that at least 0.01 inches of rain will hit any given surface in the town over a certain time period(usually one,twelve,or twenty four hours). So now that we know what a 30% chance of rain means, how is it calculated?

    The National Weather Service says the probability is calculated like this, where P=probability of rain, C=confidence of prediction, and A=percent area of town expected to receive rain:
    P=C*A
    I know its pretty surprising how simple that is, you were probably expecting some crazy formula, or applying Bayes theorem and finding the expected value, but no its just multiplying two values!

    So for example, if P=30%(I don’t know why I keep using that number), you could have the following extremes:
    1. You have small storms incoming on only a fraction of the area but the meteorologist is very confident that this event will occur
    2. You may get a large storm flooding your entire town but the meteorologist is not super confident this will occur
    These both will show the same number on your weather app but they are two very different types of storms and occurences.

    So next time you look through the rain probability always think what kind of confidence or area of rainstorm you could be encountering!

  • WORLD CUP!!!!! post 1

    Penalties. A “free” goal in a regular game, but in a tense shootout in the World Cup it could make or break your chances to win the trophy. So imagine this. You’re standing 12 yards from the goal, you need to make this or your team goes home, you have an entire country on your back, where do you aim?
    Now first instinct, the top corners, thinking its the hardest for the goalie to get to, but let’s break it down using statistics.
    This is a diagram made by me:

    red: minimal effort needed for save(red lines mark wing span of goalie)
    yellow: 50/50 requires good power to make, assuming goalie goes the right direction
    green: high probability of making(assume a make for calculation purposes)

    As you can see the corners, to no ones surprise are the best outcome, but which corner to aim at?
    I claim aiming for the bottom corners is better than aiming for the top, let’s break it down:
    When going for the top you have many things to worry about, for starters its common sense that shooting an aerial ball will be harder to aim than shooting a ground ball(because you have the “support” of the ground, and there is no force of gravity acting upon the ball). There is also the concern of hitting it too high or too low, when hitting to the top corners, let’s say this is your stats:
    50%: getting it in the box(score) expected score:1
    25%: hitting outside the goal(miss) expected score:0
    25%: hitting below or to the yellow side of the box(50/50) expected score: 1/2
    (these seem like bad stats, but remember it is much harder to shoot in the air rather than on the ground)
    Doing some math calculations(counting and probability is actually my favorite math subject) we see that the expected score is 5/8, meaning there is a 5/8 probability that you make it.

    This is not a great percentage in a high stakes game so let’s check out the other case, aiming for the bottom:
    Now for this case we don’t have to worry about hitting too low because unless your hitting into earth’s crust(which is an such an impressive feat that it definitely deserves a goal) there’s nothing lower you can hit, and since you are never taking the ball too high off the ground so we don’t need to worry about hitting too high:
    So let’s say these are your stats:
    85%:hitting in the box(goal) expected score:1
    10%:hitting outside of the goal(miss) expected score:0
    5%: hitting to the yellow side of the box(50/50) expected score 1/2
    Doing the calculations your expected score is 7/8 meaning there is a 7/8 chance of making.

    So let’s sum it up, a 5/8 chance of making(top corners), and a 7/8 chance of making(bottom corners), well the obvious pick is the bottom corners(these numbers will obviously vary slightly depending on the strength of the goalie and strength of the shooter)!
    Additionally, when picking which side to pick, you may want to go for the goalie’s non-dominant hand because he may have less power and/or control in that hand.

    Evidence, and a real-world example shows this. Harry Kane arguably the best current-day penalty shooter aims for the bottom corners the majority of the time!
    Summing it up, next time(if ever) you’re shooting a penalty, going for the bottom corner is the smartest choice.

    Thanks for reading, and enjoy the World Cup!

  • 8/13-first day of school-(the school scoop part one)

    Welcome to PART ONE of the “School Scoop”(i just thought of a random name that sounded kinda cool), in this series of blogs I will mainly be writing about school, and tracking my journey through it, depending on how this goes I may continue this chain of blogs until the 12th grade, so, if you want , follow along every Wednesday, and starting from next Wednesday posts will come at 8am!

    A lot of things become less of a deal every year, for example your birthday, but more significantly the first day of school. There are usually two types of people: people who never want summer to end, and people who despise school, OR people who just want to get back to school. I have never really seen anyone in the middle, just two very drastic sides. I personally, have almost always been the second option, if you have seen a previous post of mine called “boredom”, around a month ago, you would know that I tend to get very bored in summer, so in terms of the first day of school, it is very binary either a high or a low.

    One thing about going back to school as a 7th grader, is that it feels just wrong. To be more precise it feels wrong to see 300 6th graders pop into middle school, looking so lost, knowing that was me just a year ago. When you are so used to being the lowest and youngest grade, the moment you step up it feels so different. 7th grade is also like the middle child affect, you don’t get the just-out-of elementary freedom as a 6th grader, but you also don’t get the feel to be off to high school next year, so I guess 7th grade is unique like that. Anyways see you in the next one, and as always, thanks for reading!

    ~aaroosh

  • 7/31-how to describe yourself

    Daily writing prompt
    How would you describe yourself to someone who can’t see you?
    View all responses

    Originally I would think of how to describe me visually or how to describe my personality to answer this prompt, but if you think about it, I am sure there are many people who have darker hair, or who are sporty, so just saying vague things like that won’t really describe me/you precisely. What I would think about, is more like an about the author page. It gives you some details just about what you like, how old you are, and details like that. My English teacher used to call it the 5 W’s, Who, What, When, Where, and Why. These are the 5 basic things you need to know to learn about someone. Sure giving some adjectives would help, but that’s what the Who and What are for. Who tells you, who they are. What tells you, What type of person they are, When tells you their age, Where tells you where they come from, and most importantly Why tells you their purpose, why they do what they do. In conclusion, describing someone doesn’t have to be through visual or personality context, just something to think about! 🙂

    btw: i’ll most likely switch to posting every Wednesday due to school starting again .

    ~aaroosh

  • 7/24/25-what we know

    We know a lot, but how much do we not know? I have always wondered about this. Reading books about human evolution and inventions truly makes you marvel how far we have come, and how much we have achieved. How much of what we don’t know will we ever know? Is everything just waiting to be discovered? In recent human times, most of our inventions have just been a chain reaction of some other invention, to give you an example of what I am saying think about the invention of the smart phone. Because of the smart phone, so many companies and inventions have come to life. Like uber or doordash, they are both apps, if it weren’t for the phone, would they ever have happened. Its a trend in history that quite a few people have told me about. history simply states what happened, but never what would have happened. If the Wright Brothers never came up with the plane would we still be traveling by boat to cross vast oceans? If the Americans lost the revolutionary war would there ever be an America?! If humans didn’t evolve and dominate, would tigers rule the planet? These are all unanswered questions that we will probably never know. If we don’t know so much, so much of our world is simply just driven by belief. For example aliens(in this context any living organism outside of earth). In the vast universe it is hard to not think that there is some life out their but the truth is we are not 100% sure yet. The reason why so many are trying to invest in space exploration is because they believe that there is life out there. Overall, the main idea of this post is about how much we really know, how much we have progressed, and how much we will advance.

    thank you for reading!

    ~aaroosh

  • 7/17/25-repeatable things

    Everyone has that one thing. The most basic, yet oddly fun stress reliever. Something that is so random, something that everyone else would question. Something that just passes time. For me this happens to be throwing a foam ball off walls. Yes, I know, throwing something off of something seems like the most boring thing in the world but it’s just fun for me. My dad listens to a lot of podcasts and sometimes when I listen to a bit of them, a huge theme in many is that repeatable things result in repeatable outcomes, like if something is working, why change it? For me I do this throwing thing almost any time I have nothing to do, it just fills up the boredom, or “nothingness” and is something so mindless I can think of something completely different while doing this. To illustrate to you how much I do this, let me give you the exact details. It’s summer break for me, and it can’t be everyday that you meet a friend, or have a class, meaning much of the day is doing assignments and courses, You obviously can’t do this all the time(at least if you want to keep your brain from frying), so I have adequate breaks. During these breaks I read or throw my ball around. The total time I throw around is probably around an hour a day if not more. The walls in my room literally have black marks in the shape of circles from how much I throw. It’s just so easy, so oddly satisfying, and I’m sure that you have something like this, or you just haven’t discovered it yet. So next time you are bored think about what is something basic that makes you happy. 🙂

    Question: Do you have one of these “repeatable things” if so what is it? Comment your answer down below!

    ~aaroosh

  • 7/11/25-boredom

    It’s summer break for me. Every summer goes the same exact way. I start so excited to be off from school, but as the break progresses I realize I am extremely bored without school. My weekly schedule is generally the same on every week. Meeting up with friends(roughly 2 times a week),and taking courses/classes to speed up learning. Now I wanted to spice things up and as many say it is “better to be super busy than super bored”,I chose something that could have an element of uncertainty something that would be cool to try out. You guessed it, a blog! I never really cared about views or anything like that, I just wanted a place to put down my thoughts. However, I was stunned on how many views and likes I had got within 24 hours of my blog opening(sure, nobody is becoming mega-famous, or anything like that, but it is nice to know that people actually care for what I am writing). I realized that blogging is a very fun and easy thing to do, and could be used as a stress reliever when times get tough(important school tests, many events line up, competitions, etc.). So maybe being bored wasn’t all that bad, at least it got me into blogging!

    Question of the Day:
    If you are a student like me comment what you are doing over summer to pass the time, or if summer is actually super busy for you. If you are an adult think back to your summer breaks, and what did you do during those times)

    btw: I will post twice a day, one regular post(like this one),and one funny post(check out 7/10 funny post),hope you enjoy!

    ~aaroosh