Too Many Choices? — (mostly) A Study of the ORCA Card
Truth be told, I really just wanted to write about solving this question that has bugged me for a little while. However, on day one, I explicitly said I would avoid posting “Discussion of topics outside the scope of design.” So, I tied up my ORCA math with a little connection to design at the end.
I only recently started consistently using public transit when I moved to U-District this September, after previously using cars for the rest of my life. For consistent bus riders in the Seattle area, it’s usually worthwhile to get an ORCA card, so I read a little bit online, and decided I should get a monthly pass. I was confused to to learn that the monthly pass options are as follows:
I was confused — the price of every bus I’ve ridden to date has been $2.75 to me, so why would I buy anything other than the $2.75 PugetPass? For the record, the way the pass works is that whatever value you purchase from the left column is automatically deducted from your fare — if your fare is ≤ the value of your pass, it will be entirely covered. I first quickly checked the math on no pass or a lower-valued pass, and with my transit schedule, $2.75 was definitely the best option. I also imagined that, for any other transit fare, buying the equivalently-valued pass would be the best option, but I had no idea what other fare values existed. Elsewhere on the ORCA product list it says “Passes are valid on Community Transit, Everett Transit, King County Metro, King County Water Taxi, Kitsap Transit, Monorail, Pierce Transit, Seattle Streetcar, and Sound Transit,” so I did an exhaustive search of all of these transit services to figure out if every fare on the list above was represented somewhere. Here are my findings, and I only listed one unique item for each fare value.
Legend
Youth — children 6–18; LIFT — household income < 2x federal poverty level; Reduced Fare (RF) — age 65+ or disability or Medicare card holder; Access —disability option for King County Metro; Adult — everyone else 19–64.
$0.50 — Everett Transit(RF)
$1.00 — King Country Metro(RF)
$1.25 — Community Transit Local/Swift(LIFT, RF)
$1.50 — Everett Transit(Youth)
$1.75 — Community Transit Local/Swift(Youth)
$2.00 — Everett Transit(Youth)
$2.25 — Seattle Streetcar(Adult)
$2.50 — Community Transit Local/Swift(Adult)
$2.75 — King County Metro(Adult)
$3.00 — Community Transit Commuter(Youth)
$3.25 — Sound Transit Link Light Rail(Adult); fare varies by $0.25 increments from $2.25 to $3.25 depending on path
$3.50 — Sound Transit Sounder Train(Adult); fare varies by $0.25 increments from $3.25 to $5.75 depending on path
$3.75 — West Seattle Water Taxi(LIFT, Youth)
$4.00 — Community Transit Commuter(Adult)
$4.25 — Sound Transit Sounder Train(Adult); fare varies by $0.25 increments from $3.25 to $5.75 depending on path
$4.50 — Vashon Island Water Taxi(LIFT, Youth)
$4.75 — Sound Transit Sounder Train(Adult); fare varies by $0.25 increments from $3.25 to $5.75 depending on path
$5.00 — West Seattle Water Taxi(Adult)
$5.25 — Sound Transit Sounder Train(Adult); fare varies by $0.25 increments from $3.25 to $5.75 depending on path
$5.50 — Sound Transit Sounder Train(Adult); fare varies by $0.25 increments from $3.25 to $5.75 depending on path
$5.75 — Vashon Island Water Taxi(Adult)
This means that the only values I couldn’t account for in my search were the $0.75 and $10.00 passes, but given my success in finding every other value on the list, I imagine they are used somewhere and that I just couldn’t find them.
This means that my initial hypothesis — that there were too many niche options, causing unnecessary clutter — is wrong, since I believe every option actually represents the value of some possible fare that can be consistently paid using an ORCA card. Instead I believe the problem lies elsewhere, but before I make a claim, I want to do the math that confirms that the equivalent-value option is the best choice.
Some Math
I am currently enrolled in Bellevue College’s Calculus IV, so I am probably missing some of the best tools to conduct this analysis. I will make do with mostly algebra and possibly calculus, plus logic, which should be enough to correctly arrive at a claim without a flawless proof, which I imagine would require skills I don’t possess.
The price of every pass is 36 x the fare discount. A $0.50 monthly pass requires a one-time purchase of $18, a $1.00 pass requires a one-time purchase of $36, and so on. This means that each $0.25 increment increases the one-time cost paid by $9. Since there is a flat rate (y-intercept), this means that we can conclude basically right away that if you’re going to ride the bus very few times in a month, probably fewer than 36, it’s not worth purchasing a pass.
To confirm this, we can create equations for each fare as a function of x, the number of rides take in a month. Let f(x) = 2.75x represent the cost of taking x rides with no pass, and g(x) = 99 to represent the cost of taking any number of rides with the $2.75 pass. (I chose $2.75 arbitrarily because this is the pass I use). Algebraically, we can now solve for when 2.75x = 99, which we know to be 36. So what happens around this point? Very basic calculus tells us the answer, but it’s probably just easiest to understand graphically:
The lines cross at x=36, as we expected. We indeed find out that the no-pass option (represented by the blue line) is cheaper than the monthly pass up to 36 rides in a month, they are equally effective at x=36, and the monthly pass is more effective for any number greater than 36.
This math is probably pretty straightforward for a lot of people who are comfortable with algebra, and agrees with the brief mental math I did to select my monthly pass. I know there are at least 4 weeks in every month, and with daily classes, this meant a minimum of 20 days of class, and each day I needed to ride route 271 to and from class, so I was guaranteed 40 rides in a month even if I walked everywhere else. Spoiler: I don’t, as I often take the 44 or 65 to or from the IMA, or the 44 to or from anywhere close to campus. There are also, on average, slightly more than 20 weekdays per month — this calendar from UCLA suggests an average of 21.75.
My initial belief was that the < $2.75 options were perhaps cheaper somehow for some number of rides, or maybe even just a scam to see if anyone would somehow pay more than necessary. It should be very obvious that any monthly pass greater than the value of a fare can’t be the best option, as it deducts no more from the fare while costing an initial $9 (or more) extra. Therefore, the $2.75 monthly pass should be compared to other monthly pass options between $0.50 and $2.50, inclusive.
Note: remember that the general form equation for money spent is not [monthly pass price + (monthly pass value x rides)] — a $1.00 pass does not mean you pay 36 + 1.00x. The pass value is deducted from the price of your ride, and for this calculation, we assume the rider is taking only buses with fare of $2.75. Thus, the general form equation should be:
f(x,V) = 36V + (2.75–V)x,
where V is the value of the monthly pass and x is the number of rides taken.
To start, I added to my graph the equations for monthly pass values of $1 and $2:
f(x, 1) = 36 + 1.75x
f(x, 2) = 72+ 0.75x
The resulting graph looks like this:
Remember, the goal at any point is to minimize the price paid, so in visual terms, the function with the lowest y-value (price) at any given x-value (# of rides) is the best option. If you remember from the first graph, the BLUE line is the no pass option and the RED line is the monthly pass $2.75 option. The two new options, the GREEN line representing monthly pass $1.00 and the PURPLE line representing monthly pass $2.00 are not the lowest function at ANY POINT.
Conclusion
The conclusions from the first graph hold true — the no pass option is the cheapest for the first 35 rides, all options are equal at 36 rides, and the monthly pass of equivalent fare value is the best option if you’ll take 37 or more rides per month. (And never choose an option with value higher than any bus you’ll ever take.)
This is the point where I believe I could mathematically prove that this is true for all bus fares, not just the $2.75 fare, if I had the right tools. Instead, I will construct a similar graph for the cost of riding a $1.50 bus, using monthly passes of $1.50, $1.00, and $0.50 as well as the no pass option.
Again, this graph shows the same conclusions as the previous one. I ensured that the four colors represented the same options as before to make the two graphs easy to compare: BLUE for no pass, GREEN for the lower-valued monthly pass ($0.50, previously $1.00), PURPLE for the middle-valued monthly pass ($1.00, previously $2.00), and RED for the monthly pass equivalent to the fare. At this point, it seems safe to assert that the above Conclusion holds true for any fare value, so long as it remains consistent throughout all bus rides in a month. The math is different if a rider takes buses of different fares in any given month — the outcome depends entirely on the frequencies x and values V, which need to be handled on a case-by-case basis, so I will not address it here.
What ORCA should do to improve user experience
As we discovered in the research portion of this article, every monthly pass option correlates with at least one fare value on some vehicle somewhere within the systems ORCA cards work for. This means that ORCA isn’t presenting too many options unnecessarily, since they are all uniquely correct options somewhere, as proved by the math portion of this article. To answer my titular question, then, Too many choices? — the answer is no, so I’ll save discussion of the drawbacks of presenting users with too many choices for another day. Instead of reducing choices, the way ORCA could improve is by providing more informative descriptions of their monthly pass options somewhere on their website to help users make a decision. Providing an exhaustive list of fare prices across different transit systems is unnecessary. I think that the inclusion of one sentence everywhere the monthly pass is explained is the key. I would recommend something like “Frequent users of transit services should buy the monthly pass equal to the fare they most commonly pay. Refer to your regional transit provider’s fares for more details.” The Sound Transit ORCA card page actually does a great job of this, but the ORCA card page and the Sound Transit ORCA card PDF do not (my guess for the PDF is that if they added one or two more lines, it wouldn’t cleanly fit on a page, so they might have even had this inclusion once upon a time and then removed it for space).
Having clear communication between the many organizations that have information about ORCA cards — ORCA card itself plus the nine affiliated transit providers — is difficult, but making sure they all provide information to help users make purchasing decisions for their services would greatly enhance the experience of ORCA card users as a whole.
