Math/Statistical question

[TopOfTheCircle]

Hi, everyone.

I want to check my math/logic with a lot of you sports journalists, especially those who are good at mathematics.

Because I had a raft of people in the last month reach a major milestone victory (200th, 300th, etc.), I wanted to figure out what the odds were of reaching a milestone on any given day.

So, I assumed 1,950 coaches who average 18 games per season, which means that on average the coaches get nine wins per year (I didn't figure ties into the equation). The season lasts 12 weeks, which means 72 possible matchdays (every day except Sunday).

So, I get (1950 x 9)/72 = 243.75.

That means that, every day of the season, there are bound to be about 244 wins and 244 defeats. There is a 1 in 100 chance that any particular day, a coach's win total will end in 00, so I would guess that, in a perfect mathematical world, 2 to 3 coaches every day will hit some sort of milestone ending in 00.

There are, of course, real-world caveats. First, of course, is the possibility of a tie game. Second, some coaches accrue wins much faster than others because of the length of season and the success/failure rate of some teams. Third, a lot of coaches never get to 100 wins in the first place because the coach leaves after a year or to do something else.

Is the math right here? Is there something I am missing?

 

[Slacker]

We were told there would be no math here.

 

[Spartan Squad]

The flaw here, I believe, is that you can't assume on a given day there is a 1 in 100 chance someone's win will end in 00. The number is going to be skewed much differently. Some days will be an absolute zero chance because coaches will not be on _99 wins. In fact those days will far outnumber the days where a win total ending in 100 is a possibility. Some years the odds will be absolute zero because the number of wins a coach will require is greater than the number of possible wins in a season. Figure if a team does play 18 games and wins every game, it will take then 5.5 years to reach 100. If we were randomly drawing numbers, your 1 in 100 would be true. So saying on a given day 2 or 3 coaches will hit a 100-win milestone is wrong.

 

[TopOfTheCircle]

Thanks for pointing out the flaw regarding the accumulation of wins. I figured that would be a big reason you don't have a flurry of major coaching milestones in sports every year ...

 

[Spartan Squad]

Yeah I saw you threw in the caveats which are completely true. The numbers get weird and start to go over my head on a problem like this. I kind of want to send your problem to Numberphile and have them work out what the true odds are and how many coaches you might expect to reach a 100-win milestone on a given day. I just think the number is going to be at a far slower rate than 2 to 3 a day even in a perfect mathematical world where no coach gets fired or quits, we eliminate ties and odds of winning are even for all teams.

 

[justgladtobehere]

The number would be much lower if the median length of a coach's career is below the number of years it would take to reach 100 in a reasonable scenario. I'm guessing coaches aren't going to coach long enough to reach even 100, so every season a significant portion of the coaches have no chance to reach a number ending in -00. I guess one way to view it would be that career wins aren't distributed evenly over 0-99, but tend to bunch up in the lower numbers.

 

[TopOfTheCircle]

Thanks, everyone. Makes sense when you compare the world of math to the real world.

 

[jr/shotglass]

Well, I learned something from my 12-year-old granddaughter, and it was really jarring that I had no clue about lattice multiplication.

If you don't know what that is, look it up. It has to do with setting up a matrix, adding up numbers diagonally. And it works perfectly ... but I can't wrap my head around why it works perfectly.

578 * 823 = 475,694. Because this.

 

[waterytart]

I’ll take your word that it works. First reaction, though, is that it would take me longer to set up the lattice than to do the multiplication.

 

[jr/shotglass]

Yeah, but this is more fun.

But really, what makes this valuable, especially for kids, is that your multiplications are all single-digits. For instance, in the first row of that example, the calculations are 5X8, 7X8, and 8X8. And after that, it's all adding up the diagonal columns.

(And by the way, if your multiplication results in a single-digit number, you just put it in as "05," "09," etc.)

 

[Here me roar]

I'm just going to pretend I never saw any of that.

 

[2muchcoffeeman]

Seems appropriate.

 

[justgladtobehere]

Well, I learned something from my 12-year-old granddaughter, and it was really jarring that I had no clue about lattice multiplication.

If you don't know what that is, look it up. It has to do with setting up a matrix, adding up numbers diagonally. And it works perfectly ... but I can't wrap my head around why it works perfectly.

578 * 823 = 475,694. Because this.

View attachment 20786

It is just the table you would get doing it normally upside down with a right indent and what would be vertical lines are diagonal. I don't know its pedagogical value.

 

[jr/shotglass]

It is just the table you would get doing it normally upside down with a right indent and what would be vertical lines are diagonal. I don't know its pedagogical value.

I absolutely believe you, and I absolutely can't wrap my head around it yet.

 

[justgladtobehere]

I absolutely believe you, and I absolutely can't wrap my head around it yet.

If you do the multiplication table out completely without carrying over, you will see it.

 

[Brooklyn Bridge]

My daughter struggles in math, and when me or my wife try to help her, she says "that's not the math strategies my teacher told me to use," so we can't help her. Anything she has a question on, she has to go back to the teacher.

 

[waterytart]

I’m one of the Luddites who taught my kids the times tables because they didn’t learn something that exacting in school. They learned how to think about multiplication, not how to do it.

 

[Spartan Squad]

Well, I learned something from my 12-year-old granddaughter, and it was really jarring that I had no clue about lattice multiplication.

If you don't know what that is, look it up. It has to do with setting up a matrix, adding up numbers diagonally. And it works perfectly ... but I can't wrap my head around why it works perfectly.

578 * 823 = 475,694. Because this.

View attachment 20786

This took me a hot minute to resize what was going on, mostly you add numbers going from the bottom right corner and work your way to the upper left rather than the other way around.

I think I works because you are effectively doing the traditional multiplication but you aren’t using place holder values. It’s just a single digit number times another and add the single digits of the results (remembering to carry at the end).

So instead of
78
x23
234
1560
1794

You have a box
1/4|1/6
2/1|2/4
1794

That extra step of the place holders gets annoying when you go above two digit multiplication.