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.