Math Is Fun Forum

LCM9001

Novice

Registered: 2024-05-15

Posts: 2

Help Modeling Statistics Scenario to Support Claim

Context: I'm a salesperson that works for a company that has a product that helps to increase Influenced Hires, a company would want to hire more Influenced Hires because they have a 27% higher promotion rate than Non-Influenced Hires.

Based on the assumption that employees that are promoted are highly engaged employees, and studies show that highly engaged employees produce 21% more profit, I want to illustrate to clients the potential positive financial impact increasing their percentage of Influenced Hires could have on Revenue by investing in my company's product.

Some assumptions & inputs:
  - Company made 55 hires in the past year, if relevant/necessary we can assume the company will make 55 hires in each of the next 3-5 years (if longer timeline is helpful to proving statement that's fine)
  - Company had a 35% Influenced Hire Rate in the past year
  - Median Salary at company is $100,000
  - Organizational Value of each Employee is 2x their annual salary, meaning each employee is expected to generate $200,000 in Revenue
  - Profit margin stays constant year over year meaning the 21% more in profit mentioned earlier can be applied to revenue
  - Average promotion rate in the US is 10%
  - Influenced Hires have a 27% higher promotion rate than Non-Influenced Hires
  - Employees promoted are highly engaged & highly engaged employees produce 21% more profit

I've been running into issues doing the math and it showing that despite a 27% higher promotion rate, the expected number of promotions for Non-Influenced Hires comes out to be higher than the expected number of promotions for Influenced Hires.

I think that might be because I'm using the 35% Influenced Hire Rate when in order to support my claim, I'd need to be using a 50:50 split, but math is really not my strong suit so need confirmation if using a 50:50 split is ideal or not.

It could also have something to do with using too short of a timeline?

What would be the best way to model this out to support my claim?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: Help Modeling Statistics Scenario to Support Claim

hi LCM9001

Welcome to the forum.

I'm struggling somewhat here because of the business jargon.  I got a definition of 'influenced hire' from linked-in that seems to make sense.

What I'm getting is this: you've constructed a model and it's not giving you the answers you were expecting.  To go further I need to see the model, with live data.  Then I can 'mark your homework'. It could just be you've got a sum wrong somewhere but without the figures I'm completely in the dark.

Also 50/50 split ? What are you splitting?

And another thought based on the linked-in definition.  That seems to me to cover virtually all the ways someone might get a job. How else does someone get a job if they haven't "viewed a job or clicked Apply"; "opened an InMail (email?) etc; "Viewed an advert; "Clicked a Work with Us Ad, clicked a Recruitment Ad, engaged with a Sponsored Update, interacted with your viral feeds or other talent ads."

If someone gets a job by some other route I can only think it's because they already know the company boss, are maybe related. In which case their performance might well be superior.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

LCM9001

Novice

Registered: 2024-05-15

Posts: 2

Re: Help Modeling Statistics Scenario to Support Claim

hi LCM9001

Welcome to the forum.

I'm struggling somewhat here because of the business jargon.  I got a definition of 'influenced hire' from linked-in that seems to make sense.

What I'm getting is this: you've constructed a model and it's not giving you the answers you were expecting.  To go further I need to see the model, with live data.  Then I can 'mark your homework'. It could just be you've got a sum wrong somewhere but without the figures I'm completely in the dark.

Also 50/50 split ? What are you splitting?

And another thought based on the linked-in definition.  That seems to me to cover virtually all the ways someone might get a job. How else does someone get a job if they haven't "viewed a job or clicked Apply"; "opened an InMail (email?) etc; "Viewed an advert; "Clicked a Work with Us Ad, clicked a Recruitment Ad, engaged with a Sponsored Update, interacted with your viral feeds or other talent ads."

If someone gets a job by some other route I can only think it's because they already know the company boss, are maybe related. In which case their performance might well be superior.

Bob

I want to preface my response with, I'm not trying to manipulate the data to show anything it shouldn't, I don't want to do anything in the calculations that wouldn't make sense to do or would invalidate things, I don't come from a math background and I was never that good at math growing up, so I'm mostly thinking out loud and don't understand the consequences of changing something or trying something a certain way.

The idea here, which I think makes sense based on the assumptions shared is, companies should try to increase the number of Influenced Hires to potentially generate greater revenue.  I don't see why this wouldn't hold true if we accept the assumptions, but again, not very good at math.

I think where I've run into at least my first problem is, when trying to illustrate the higher likelihood of promotion, I used the company's previous Influenced Hire Rate of 35%, rather than an even playing field of 50% (this is what I was referring to when I said 50:50 split originally). 

However, I'm not sure if using a 50% Influenced Hire Rate, would break any rules of math or something like that.

Here is the math that I did previously using the 35% Influenced Hire Rate.

# of Influenced Hires: 55 x 0.35 = 19 # of Non-Influenced Hires: 55 - 19 = 36

Promotion rate for Influenced Hires= 1.27x

Expected # of promotions for Influenced Hires = 19(1.27x)

Expected # of promotions for Non-Influenced Hires = 36x

Total Expected Promotions = Expected # of promotions for Influenced Hires + Expected # of promotions for Non-Influenced Hires

Total Expected Promotions based on 10% promotion rate for 55 hires: 5 (rounded down)

5 = 19(1.27x)+36x --> 5 = 24.13x + 36x --> 5 = 60.13x --> x = 5/60.13 = 0.083

Expected # of promotions of Influenced Hires: 55 x 0.35 x 1.27 x 0.083 = 2
Expected # of promotions of Non-Influenced Hires: 55 x 0.65 x 0.083 = 3

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: Help Modeling Statistics Scenario to Support Claim

I'm still struggling a bit. You didn't answer my question

How else does someone get a job?

When mathematicians write out a calculation using x, they say what x stands for.  I'm guesing, based on your calcs that it is the promotion rate.

The ratio of influenced hires to non-influenced hires (let's abbreviate to IH:NIH)is 19:36. That's not far off 18:36 ie twice as many NIH.

Your promotion calcs end with a ratio of 2:3. So only 1.5 as many NIH.  So you have a sensible result.  IH are doing better but there aren't enough of them in the company to end up with the ratio tipping towards them fully.

So far I see no reason to use 50/50.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Help Modeling Statistics Scenario to Support Claim

I'm still struggling a bit. You didn't answer my question

How else does someone get a job?

When mathematicians write out a calculation using x, they say what x stands for.  I'm guesing, based on your calcs that it is the promotion rate.

The ratio of influenced hires to non-influenced hires (let's abbreviate to IH:NIH)is 19:36. That's not far off 18:36 ie twice as many NIH.

Your promotion calcs end with a ratio of 2:3. So only 1.5 as many NIH.  So you have a sensible result.  IH are doing better but there aren't enough of them in the company to end up with the ratio tipping towards them fully.

So far I see no reason to use 50/50.

Bob

What are your thoughts on statistics? In the United States, statistics is a separate branch of mathematics at most universities. In fact, it is often taught together with probability. I am not really into reading bar charts, or line charts, or dot charts or interested in population explosion surveys, etc.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: Help Modeling Statistics Scenario to Support Claim

When I did my age 18 A levels, stats wasn't part of the course.

But it was introduced later and I had to teach it.  Sometimes I have to look up the methods.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Help Modeling Statistics Scenario to Support Claim

When I did my age 18 A levels, stats wasn't part of the course.

But it was introduced later and I had to teach it.  Sometimes I have to look up the methods.

Bob

I know little about statistics. I like the formulas but dislike the graph reading and survey part of the course.