Choosing Your Health Insurance Plan – With Math!

A couple years ago my wife and I were procrastinating yet again on selecting a health care plan option. Specifically, which of two plans to select for her and our son that were offered by her company.  My health insurance is super simple: I’m fully covered, no premiums (ignoring dental and vision). But hers was hard! There’s a huge amount of information to consider, from premiums to deductibles to co-pays to co-insurance rates to tax-savings to traditional vs high-deductible plans to how much to put in your FSA or HSA…. Insane.

I got fed up with trying to eyeball this decision. So, I broke out Python! I managed to script up and plot a wide variety of scenarios, and as a result the decision finally became clear. I love Python and plots – I’m definitely an engineer to the core.

And when open enrollment rolled around this year, I just had to re-open the Python script, plug in a few updates to the numbers, and I got my answer! Beautiful.

What We Compared

We’d already ruled out the premium health plan in past years, via a much simpler analysis. And we weren’t considering a change to dental or vision plans. So, given that our son is on my wife’s insurance plans, our analysis specifically compared the standard and high deductible health plans for an “employee plus children” plan. If you’d like to compare other options, or your insurance plan options are structured differently, you’re welcome to modify the python script. If you do, it would be great to hear from you what changes you made – I’ll try to add any fundamental capabilities to the template. See “Conclusions” section below for more info.

Inputs

Below are the “inputs”, which are all the numbers that have an impact (big or small) on our decision. I provide values for the “employee plus children” option for both a standard plan and a high deductible health plan (HDHP).

Monthly Premiums:

• Standard: $93
• HDHP: $61

Standard plan office visit copays (not applicable for HDHP, as you pay those costs in full until you hit your deductible):

• Primary care physician: $30
• Specialist: $40

Note: well visits remain $0 for both plans.

Estimated Office Visit cost: 

• Primary Care Physician: $103.05
• Urgent Care: $165
• Specialist: unknown, probably highly variable based on type of physician

Note: As a result of not having a good estimate for all possible specialist office visits, did not assess specialists below, but we operated on the assumption that the Urgent Care rate was probably close to a conservative average rate for specialists.

Deductibles (in network):

• Standard Individual: $1000
• Standard Family: $3000
• HDHP Family: $3200 (note: for HDHP, must meet family deductible for individuals within family plan)

Co-insurance (percentage of medical expenses covered by insurance after deductible met, until you reach out-of-pocket max):

• Standard: 0.8 (80%)
• HDHP: 0.8 (80%)

Out of Pocket (OOP) max:

• Standard Individual: $4500
• Standard Family: $9000
• HDHP Individual: $6850
• HDHP Family: $10000

Company HSA Contribution (Annual): $1500

Max Employee HSA Contribution (Annual): Max $7100 total – $1500 company contribution = $5600

Max FSA Contribution (Annual): $2750 (2020)

Note: only available for Standard plan, just like HSA only available for HDHP plan – though very importantly, the FSA is use-it-or-lose-it every year, so quite stressful (unlike HSA)

Prescriptions:

• Standard Copay: $10
• HDHP Expected cost: $15

Note: with HDHP, you pay the full cost of drugs until deductible met, then insurance pays for 80% until max OOP, just like other medical expenses

Tax Savings Rate: 0.22 (top income tax rate) + 0.0765 (FICA)

Whew! That’s a lot of numbers. What do we do with all these numbers? We build plots of course!

Results

Comparing Out of Pocket Expenses for Individual Within “Employee+Children” Plan

What happens with each plan (Standard vs HDHP) if we start with zero dollars in medical expenses for an individual within an “employee + children” plan and slowly raise that number to $30,000? How much will you actually pay (out of pocket) for each plan?

Wow, the HDHP plan wins at every single value! My wife and I were shocked the first time we saw this plot. You can also see how much more the Standard plan is than the HDHP with the green “difference” line: over $500 at all times. (My apologies to those with color-blindness, normally I use different patterns for different lines to prevent confusion.)

Comparing Out of Pocket Expenses for Family Within “Employee+Children” Plan

What about medical expenses for the entire family (“employee + children” in this case)? 

Incredible, the difference is even larger! You save over $2000 at almost all expense levels by choosing the HDHP.

Comparing Out of Pocket Expenses for Primary Care Doctor Visits

What about doctor visits? Won’t you save money with the standard plan if you’re paying co-pays instead of the full cost for doctor visits throughout the year? Let’s first take a look for primary care physician visits (using the estimate provided for the full visit fee, and assuming no other medical expenses, which would tilt the answer toward the HDHP):

So at our estimated doctor visit cost of $103.05, it doesn’t matter how many times you visit the doctor throughout the year: you’ll always save money with the HDHP!  If you somehow go to the doctor every other week (26 visits), you’ll still save hundreds of dollars. Note that this plot is for an individual within a family plan.

Comparing Out of Pocket Expenses for Urgent Care Visits

What about expensive doctor visits: something like urgent care visits? Especially if you can get those for the same lower primary care physician copay of $30? And assume those cost the much steeper price of $165 for the HDHP?

We now FINALLY find a scenario where the Standard Plan comes out ahead of the HDHP: if you go to an urgent care clinic at least 20 times (every 2.6 weeks the entire year), then you finally start to see savings in the tens of dollars, ramping up towards about $100. Psh. Not compelling in my mind.

Investing HSA Funds

Something else I don’t account for: growth of the HSA funds as they are invested in a low cost index fund (based on historical market returns). In fact, some argue that HSA funds are the ultimate retirement account. 

Combining Factors

Also note that I only considered one factor at a time, instead of mixing medical expenses with doctor visits. But because the scenarios for medical expenses are always better for the HDHP, I believe mixing those with doctor visits will only shift the result further towards the HDHP being cheaper.

Conclusions

Overall, the combination of lower premiums, company contributions, and significant tax savings (because you can max out your HSA) leads the HDHP to be the clear winner for us. The above results are strong enough in my mind to conclude that we are almost certain to pay less overall with the HDHP. And what’s really crazy is that this remains true even for large EXPECTED medical expenses: major upcoming surgeries, having children, etc.

While the above plots might help you if your numbers are similar to ours, nominally I would encourage you to run your own numbers to make sure. One day I may create a web application (after I learn how to build a web app of course) that you can plug your numbers into and get an answer. But until then, here is the Python script I employed for our analysis. You’ll have to be able to run Python scripts on your machine, but otherwise you’ll just need to change the numbers in the top “User Inputs” section – no code modifications needed (unless your plan structure differs, or you’d like to compare more options, or you just want to!)

If you have questions or would like to discuss the numbers you’re seeing in your insurance policies, feel free to ask in the comments below or shoot me a note on the Contact page. I’m no financial professional, but I’ll try to help you see what the math says!

And if you do find that for your situation the standard plan is clearly the winner, please let me know! I’d love to better understand what scenarios make the standard plan cheaper. And of course if you find a bug in my code, I’d greatly appreciate hearing about that!

Note: This post was originally on a different site and some of the comments below are from that original post (thus the older comment dates).