Posts Tagged ‘Doing the Math’

April 17, 2016

Not that Bad

I’ve been told I share a lot on social media. Every time someone makes a comment about how photographed my kids are a little voice inside my head shouts “I’m not that bad!” but truth be told, I’m hard pressed to think of people in my social circle who post more. So when I was rocking a sick child this afternoon and came across a marketwatch article which cited the actual average amount of sharing I was immediately curious how I compared.

The average parent will post almost 1,000 [specifically 973] photos of their child online before he/she turns five

The study is not exactly scientific, so I had to create my own methodology. The original study stated on average children were “feature” in 973 photos posted by their parents on social media before the age of five. Not knowing how they defined “featured” I decided to count every photo each child was in, including just fingers and toes. I also decided to count frames, individual shutter actions, not images. That means counting each photo in a collage individually. Near duplicates were included since they’re technically different photos. Exact duplicates, such as reposting the same image, or different post processings of the same photo, were not. I’m counting photos, not shares, after all. Almost no one posts photos of the girls besides myself, so for simplicity, I’m not counting those.

Unique Photos Shared on Each Platform (Nicole /Alexis):
Facebook: (337 / 77)
Instagram: (128 / 29)
Blog: (360 / 77) – And, man, this post did not help my count!

(Normally I double check my numbers, but this time I opted not to. I like math, but counting is rather boring.)

Removing the duplicates cross platform and I’ve only shared 364 of Nicole, and 141 of Alexis. We would expect the average person (according to the above study) to have posted 729.75 by the time the child was 45 months old (like Nicole) and 259.5 by the time the child was 16 months old (like Alexis). My posting rate is roughly half of the average. See – I’m not that bad!

Of course, you can’t really draw too much of a conclusion from the study, one way or the other. The methodology is unclear, it relies on self reporting which is notoriously unreliable, and it has a sampling issue. Besides, if you’re measuring how exposed our children are, number of photographs is a bit of a flawed metric. Is 1000 photographs taken at a single event really more exposed than 500 photographs taken on 500 different days? If I’m being honest, I think that’s why my number is lower than someone who knows me might expect.

In my effort to only showcase my best photographic work, I limit myself to no more than three photos per post, and only a few posts with photos a month. On facebook I have just two to four photo albums a year, including a yearly highlights album where I again limit myself to an average of two or three photos per month. I may not share a lot of photos in any one instance, but there’s a nearly constant stream of photos in my feed. Because I post fewer photos per iteration, but more iterations, it probably appears like I’m sharing more than I actually am.

On a side note, I still maintain some of this fear over social media sharing is blown way out of proportion. There are legitimate cases of detrimental over sharing, obviously. Re-punishing a child to capture a photo of ensuing tantrum is cruel (and hopefully just a one time lapse in judgement from that parent in the article). I also think the concern over the number of over-sharers may also be overly done. If one over-sharer has hundreds of friends, then hundreds of people know at least one over-sharer. The fact that those hundreds of people know an over-sharer doesn’t necessarily imply there are hundreds of over-sharers.

My willingness to spend money has increased the past couple of years. I hemmed and hawed about purchasing the the wine bottle wall art that decorated our dinning room walls with when Domingo and I first moved in together. Domingo had to convince me that it really wasn’t that expensive to buy both the white and red pieces. A few years later I lamented not having purchased a backup set. Sadly, they broke in our move not two years after that, thank you movers who put them in a box without wrapping them first.

The ‘I should get a back up set’ (or ‘should have gotten’ in this case) is the good I-wish-I-spent-more feeling. Lately I’ve had a few of the not so good I-wish-I-spent-more feeling. The reading chair we purchased for the office came cheap from Amazon. Sadly it both looks and feels as cheap as it was. I wish I had purchased a different chair, a nicer one. The deck furniture was similarly disappointing. It’s already has some rust after just one season of use. I can’t really bemoan the purchase of the Ikea couch. We got it at a basement bargain price for the apartment. We weren’t sure where we were likely to move, and I didn’t want to spend a penny more than I had to on something that might not work in the new place. It was the cheapest couch I could find, and meant to only be temporary.

Then there were the good purchases. The Mainstays table for the kitchen was a steal. The initial table I bought that arrived broken, only had two chairs and cost more. Our dinning room table was another great purchase, though the shipping and handling surcharge eat into the discount a bit. And, of course, I ended up liking our Christmas trees that were a bit of a gamble. I’m glad I didn’t spend one penny more on those items because it’s hard to imagine a different table or tree that I would have appreciated measurably more.

Reflecting on past purchases has me thinking about price points, and whether mine is at the right point. The lower the price point, the greater the chance of being disappointed with the product. (In general at least, price and value may be interlinked but they’re not interchangeable). The higher the price point the less likely to be dissapointed, but the greater the chance that another product may have been equally good for less. The greater the risk of over paying. There’s a trade off between paying as little as possible, and being happy with one’s purchases.

dissapointed missingout
Probability of being disappointed as a function of price point, and probability of missing out on a deal as a function of price point.

Putting the two charts together to get an idea of overall happiness.
Minimizing the probability of being disappointed means maximizing the probability of over spending and vise versa. The trick is finding the sweet spot where the both probabilities are in the acceptable range for your sensibilities.

I could lower my price point, but it means more back and forth. More returning items I’m really not happy with. More accepting items I’m marginally happy with. I initially assumed my batting average wasn’t that great. I’m starting to think my price point might be just about right after all. I certainly wouldn’t go lower. I don’t have as much patience as I once did, or time, to handle more returns and more calls to customer service. But I’m happy I’m not spending more too. A penny saved, and all.

This weekend we purchased a new set of patio chairs. I spent a bit more than I typically do. Here’s hoping I don’t regret it.


I don’t regret it!

February 16, 2016

The Deep Freeze

Domingo and I finally went ahead and bought a second freezer for the garage. We were primarily thinking of it as a time savor, so we could reduce our trips to the grocery store. The more we think about it, the more a second freezer appears to be a money saver as well.

Unlike Mommy, who could subsist a month off of PB&J, the kids will get bored with and stop eating even their favorite meals if we make them too often. This necessitates having a wide variety of meats and vegetables at the ready. We prefer not to repeat a dish twice in a week if we can help it. As for the leftovers that don’t freeze well, they become Mommy lunches.

Our current refrigerator/freezer combo is better than anything we’ve had so far, but we still can’t stock up from Costco (or any other store) the way we’d like to. Inevitably, we sometimes realize we’re approaching 5 o’clock and don’t have a dinner option. That means a quick run to the closest, but sadly not cheapest grocery store. It’s marginally more expensive for vegetables, and much more expensive for meats. Fish runs us nearly double. Meats are not only cheaper at Costco, but they come individually wrapped so it’s easier to just make the amount you want and save the rest. It’ll also save us some eating out dollars (and calories). Just last week I was going to make salmon for our dinner once the kids were asleep when I discovered we were completely out. I could muster the energy to cook, or go out, but not both.

After looking around I settled on the 10.6 Cubic foot GE Chest Freezer. It’s on sale ($359, down from $399) just about everywhere, which pushed the price below the “free shipping” threshold at a few different places. Of course the shipping cost was nearly double the sale discount. Of course. I ended up contacting BestBuy, and Home Depot to see if I could get the non sale and thus free shipping price before realizing Lowes had both the sale price and free shipping.

Initial Cost: $389.52 after taxes.
Ongoing Yearly Costs: $39.68 (218 kWh at 18.2 cents per kWh)

Assuming a super conservative estimate of $10 a week savings on food (equivalent of saving on just 1 dinner a week), we’d save ($10 – $39.68/52), or $9.24 a week. After 43 weeks the freezer will have paid for itself. A more optimistic guestimate savings of $20 a week on food means the freezer will have paid for itself in just 4 & 1/2 months.

January 28, 2016

Debt: The Good, Bad and Ugly

Back when I first moved to California, I was a bit overwhelmed with the start up costs of creating a new life on a new coast. I was sure I was going to exhaust my savings and need to carry a balance on my credit card. Naive in the ways of finance, I believed that credit card balance was to be avoided at all cost. I had learned credit card debt is bad debt.

It wasn’t until a few years ago that I finally understood debt is not as clear cut as that. An acquaintance posed the question: is it better to drain the emergency savings account and pay of a credit card debt now, or keep the savings in tact and pay off the credit card debt over the course of a few months. The group consensus was to spend down the savings account. That didn’t sit right with me. Even with the large interest rate, the credit card would have only accumulated $30 of interest over those few months. Rather than thinking of the interest as wasted money, one could think it as the price of having that emergency fun. A pseudo insurance policy, if you will. Would it have been a good decision? Possibly. Being without an emergency fund carries it’s own risks.

It’s tempting to reduce complex concepts to simple sound bytes: Credit card debt bad, Mortgage debt good. But when we do, we tend to lose some of the nuances.

Good debt is debt on assets that appreciate, that add value above the cost of the debt. Bad debt is debt that doesn’t. Historically, mortgages have been considered good debt because homes tend to increase in value while student loans were considered good debts because education made you more employable, which lead to a higher salary. Recent history has shown us that neither is always the case. Revolving debt like credit card debt is usually considered bad because it tends to be spent on items that depreciate in value such as electronics or fashion. Even when credit cards are used to finance assets that appreciate, that appreciation is usually eaten up by the high interest rates.

It’s counter intuitive but a large interest rate on a small balance paid quickly still only generates little interest. My mistake when I first moved out to California was to not do the math, and see that for myself. I would have saved myself some unnecessary stress.

Each individual debt has a fixed cost. As a frugal penny pitcher, it’s tempting to avoid that cost at all costs. I need to train myself to compare costs, including opportunity costs. Sometimes, extra money is best spent elsewhere, like a high yielding savings account. The best way to make good decisions is to be informed. With that in mind I spent a little time the past couple of weeks working on some financial web apps. I can already see a little clearer.

This afternoon I decided to take advantage of the rare June rain to break out my macro lens to practice photographing some water kissed flowers from our garden.

I like to think I have a pretty good handle on my most used lenses – the 30mm and 50mm primes. I know what shutter speeds about I need to freeze fast moving toddlers (1/320s-ish), and what aperture I need to bring their whole faces into focus (f2.8 – f3.2 usually does the trick). I use my 60mm f/2.8G Micro for macro photography. With a focal length so close to my 50mm prime, I expected it to handle about the same. One thing that immediately struck me was how large an f-stop I needed to get the whole flower in focus.

Even at f/8 little of the flower was in focus, and flowers are not that big!

Here’s another example, at f/18

So why the incredibly shallow depth of field? Distance to subject seems an obvious culprate. A quick search lead me to the mathematical formula for calculating the nearest in focus point, and farthest in focus point using depth of field from distance, focal length, aperture and something called circle of confusion.


NearestInFocusPoint = s x f2 / (f2 + N x c x (s – f))
FarthestInFocusPoint = s x f2 / (f2 – N x c x (s – f))


s is distance to the subject being focused on
f is Focal Length
N is the f-Number and
c is the Circle of Confusion

Then the total depth of field can be calculated as the nearest in focus point subtracted from furthest in focus point and simplifying. For simplicity, let Dn be the denominator of NearestInFocusPoint, and Df be the denominator of FarthestInFocusPoint:

DoF = FarthestInFocusPoint – NearestInFocusPoint
DoF = [s x f2 / Df] – [s x f2 / Dn]
DoF = [s x f2 x Dn / (Df x Dn)] – [s x f2 x Df / (Df x Dn)]
DoF = [s x f2 x (Dn – Df)] / [Df x Dn]
DoF = s x [f2 x (Dn – Df)] / [Df x Dn]

Df x Dn = (f2 – N x c x (s – f)) x (f2 + N x c x (s – f))

From the above equation my hypothesis appears to be correct; as distance approaches zero, the numerator approaches zero and the denominator approaches (f2 + N x c x f) x (f2 – N x c x f) or (f4 – (N x c x f)^2). For my camera, c = 0.02mm with a maximum aperture of Æ’/32, far less than the 60mm focal length. Thus (N x c x f)^2 is far, far, smaller than f4. Thus the denonimator, Df x Dn, is positive and non zero. Thus as distance approaches zero, DoF approaches zero.

Of course there are practical limitations and focusing distance to subject cannot be zero. My 60mm lens has a minimal focusing distance of about 7.5 inches, or 190mm. Using my camera’s specs, if the flowers were only 10 inches from my lens, at f/3.2 the dept of field is just .1 inches. At f/8 the depth of field is just 0.17 inches. I’d have to back up another foot to have a depth of field at least 1 inch wide.

Values of 0.02 – 0.03mm seemed to be pretty typical circle of confusion values, at least according to the sites I visited while researching this blog post. Even with a very wide angled lens, capable of a very narrow aperture, I suspect my hypothesis would still generally be true. Nikon has a 6mm fisheye lens, and even for that lens the math holds.

When my first job was going through a series of layoffs, I couldn’t help but notice most of the people being laid off where new in their careers, like me. During our usual one-on-one I asked my boss if I should be worried. He replied “correlation does not imply causation.”

“Correlation does not imply causation” is one of my statistical pet peeves because it’s so often misunderstood and misused. It’s a typical response when the speaker wants to dismiss an observation or study he or she doesn’t agree with, without addressing the merits of the observation or study itself. If my boss had said “the square of the hypothesis is equal to the sum of the square of the sides” he would have been just as accurate, and just as irrelevant.

What is Correlation and Causation?

Correlation means two events tend to occur together more frequently, or infrequently, than could be explained by random chance.

Causation means one event causes another event.

If two events have a causal relationship, by definition there is also a correlation between the two. Events that are correlated is a superset of events that are causal. There exists some events that are correlated and not causal.


Ice cream sales and crime rates (or sometimes shark attacks) tend to be a favorite example of a correlated relationship that’s not causal. All three increase in the summer when the temperature rises and people tend to be out more. Since the rate of each event rises in warm weather, and falls in cold whether, the events are correlated. If you know crime rates have increased recently, there’s a good chance it’s summer and ice cream sales have also increased. Criminals aren’t turning to a life of crime to support their ice cream habit, and ice cream isn’t altering a persons’ brain chemistry making them more susceptible to their impulses. The relationship is not causal.

What can be deduced if a relationship is Causal vs Correlated?

If the relationship between two events is causal, then altering the causal event will effect the other.

If the relationship between two events is correlated you cannot assume you can control one event by manipulating another, however it is perfectly reasonable to make predictions about one event by observing another.

If I witnessed an increase in ice cream sales, I might expect to see more reports of shark attacks in the news. I can’t grantee a band on ice cream sales to change the crime rate and vice versa. I can hypothesize that the band may effect the crime rate, but I cannot guarantee it. I would first need to conduct an experiment to see if manipulating one event causes the other to change, ie that the relationship was causal and not just correlated. The observation that two events are correlated is usually the precursor to such an experiment.

If I noticed the layoffs seem to disproportionately include younger employees like myself, it’s statistically valid to be concerned. This conversation happened right around the time I decided to go to grad school, so while it may have been a statistically valid concern, it wasn’t a very practical one.

This mathematical post brought to you by the number Pi. Happy Pi day!

I always joke with friends that I’m going to make my fortune by winning the lottery someday. I’ve yet to actually purchase a ticket because I can’t get the meme that only people bad at math play the lottery. It’s rather unfortunate meme because I don’t actually think anyone is bad at math, just lacking in practice, confidence and/or good teaching. Besides, as much as us number crunchers like to put down the lottery, there is a sound economical case for playing with it.

Let’s get one thing off the bat. Clearly using the lottery as an investment strategy is a terrible idea. No one should ever play the lottery with money they can’t afford to lose. But there are other reasons to play the lottery other than to get rich quick – namely to have fun!

In economic terms, a lottery ticket is a consumption good, meaning it is used (consumed) once, as opposed to durable goods such as cars which are usable over a long period of time. A lottery ticket lets you play one lottery. A movie ticket would be a similar consumable good because it lets you into the theater exactly once. So in economic terms, a lottery ticket is a better buy than a movie ticket if it provides more utility per price.

Let’s assume we can quantize fun. It’s not a completely unreasonable assumption. A trip to the beach is certainty more fun than a root canal.

Let’s say that going to the Movies cost $10 (we don’t get out much now that we’re parents, can you tell?) and gives you 10 units of total fun. We consider total units of fun, those aquired before the event, during and after. Maybe 8 of those units are from watching the movie itself, one comes from the joy of looking forward to the movies, and another from repeating favorite lines with friends in the following days. In contrast, a lottery ticket may only cost $2. The fun units come before the lottery drawing, while you imagine you’re self a millionaire, and during the drawing when you eagerly scan your ticket for those winning numbers. There likely won’t be any additional fun units after the drawing. If you get more than 2 units of fun from a lottery ticket, the per fun unit price is lower than then movie ticket. Even if the movie ticket gives you more total fun units, the lottery ticket may be the better value.

There’s a diminishing rate of return on fun units, however. You probably don’t get twice the enjoyment out of two lottery tickets for the same drawing than you would with one. Similarly, you may enjoy the same movie as much seeing it the second time. Which is the better deal for you will depend on what you enjoy doing more.

February 2, 2015

Capturing Sisterly Love

I’ve gotten so much better with my camera, and photographing Nicole, that I didn’t really give much thought to how much more difficult it would be to photograph the girls together. I thought I’d be able to hammer out a few good photos in time for our Christmas card. In retrospect, the difficulty should have been obvious.

When I’m photographic Nicole I can easily take ten frames to get that one good frame. That’s why I always shot on burst mode – better odds that I’ll hit that perfect hundredth of second moment. Some frames her eyes may be closed, the framing is off, the exposure is wrong, etc. And she’s mostly a cooperator! If we treat the photographing the two girls as independent events (a not unreasonable assumption when they’re both in a good mood, terribly inaccurate if one of them is upset for whatever reason), then it’d be 1 in 100 frames to get a good shot of both of them simultaneously. Mathematically the probability of getting a good shot of one kid (1/10) times the probability of getting a good shot of the other (1/10).

We can extrapolate out for n kids getting the function: probability_of_good_shots = photographer_hit_ratenumber_of_kids. Thus the number of frames needed when photographic n kids to get one good frame as a function of n can be plotted as follows:

number of frames needed
f(n) = 10n

In other words, it gets exponentially harder with each additional kid.

Hmm. Alexis looks mighty concerned.

My hit rate is less than 1%, so I might be underestimating the difficulty. Or overestimating my skill.

going in for a kiss
My best one so far. I just wish I had panned a little more to the right and the lighting was a little better on Alexis’ face.

Here’s what I’ve learned:

  • Swaddle the Baby. It helps keep the baby calm and, as an added bonus, helps the baby appear more newborn like. That’s very handy when it may take you multiple tries to get those 10^n frames! Alas, Alexis is now a champion swaddle buster.
  • Have an Assistant. Not only are you going to want a safety spotter (depending on the age and activity level of your toddler, a total must!) but getting the girls ready in unison helped maximize our in-front-of-the-camera-time. Daddy swaddles while mommy assembles the camera.
  • Bribes. Yeah, I know what you’re thinking, but hear me out! I’ve found that my energetic, rambunctious toddler exhibits a little more self control when a piece of candy or new toy is on the line. When photographic near a baby, that’s a trade off I’m willing to make.
  • Patience, Patience, Patience. I feel like a amateur photographer again, which can be frustrating. Nicole is pretty perceptive. If I let my frustrations get the best of me she’ll pick up on it and will instantly be done with photo time. It’s better to keep it fun, and hope I get lucky.
  • and Learn to Love the Outtakes. Hi, my name is Sarah, and I’m a recovering perfectionist…

Use Turbotax? If you do, and you are due a federal refund, you can put some of that refund towards Amazon gift cards and get a 5-10% bonus. Which begs the question, how much of our return should we put into gift cards?

While I’m usually not one to say no to free money, and we do use amazon frequently, I don’t want to tie up too much money into Amazon. Money spent on Amazon gift cards can not be used for useful things, like 529 plans. I want to find the sweet spot of maximizing the bonus, without overspending. It was once again time to take another peek at how much we’re spending on Amazon.

The amount (actual and project) I’ve spent on Amazon since 2009


The 2012 bump was anticipated. With a newborn baby I knew there would be many supplies we needed, and that we’d have limited time to go to the store. I figured between prime & camelcamelcamel most of my purchases would shift from brick and mortar type stores, like target, to amazon. I knew initially necessity would win out over frugality, and I’d find myself with many purchases that couldn’t wait. But I figured most of those purchases (crib, car seat, etc) would be single time purchases. As I became more experienced with this Mom thing, I was sure I’d be able to be better at predicting what we’d need and when so I could be more frugal about my purchases. So then what the heck happened in 2013?!

2013 Amazon Spending Breakdown.

By in large the bump in 2013 comes in part from additional subscribe & save discounts beyond just diapers. We started subscribing to all manor of paper towels, toilet paper, tissue paper, detergent, etc since it was both slightly cheaper and much more convenient. I was surprised how much all that added up! We spent 20 times more in 2013 than we did in 2012 on subscribe and save items. I was expecting the increase in incidental spending (toilet paper, toothpaste, etc) in 2013 to be offset by the reduction in baby gear spending, but that’s hard to do when you spend so much on incidentals! Yet another example where I paid attention to the individual prices and not the totals.

The next two categories are home related. “Basic household” are every day things we need but don’t regularly replace (fans, carbon monoxide testers, etc). I added up everything house related in this category. Alas, moving is expensive in more ways that one. There are some setup costs. New lights and new linens are sometimes necessary to fit new places. Some dishes and other odds and ends broke in the move. I did my best to maximize what we did have so we wouldn’t have to buy much. Our linens are very miss-matchy, but who cares? I didn’t want to buy a whole new set for the apartment, and then again when we move in a year or two. Admittedly not all the new purchases were necessities. I do love my new vacuum.

The Nicole category includes everything other than diapers – toys, books, Christmas presents, etc. Infants require tons of gear. We spent 6% less in this category in 2013 than in 2012. I expect we’ll continue to buy less in gear going forward, but make up the difference with toys and books.

If we ignore the Subscribe and Save purchases (since that wasn’t an apples to apples comparison), and the new home setup costs (how often am I going to buy a new vacuum cleaner anyway?!), I spent 31% less in 2013 than 2012 rather than 38% more. Phew. Now that’s a more palatable number!

Better, we don’t expect to see another rise in spending on Amazon in 2014. I did a crude estimate for our spending for 2014 based on our 2013 and current 2014 spending. It’s no surprise I spend more around Black Friday. Last year I spent 31% more on average in November and December than any other month. To come up with my projected total I use January & February’s expenditure and assumed a similar 31% rise for the end of the year. The result? We expect to spend about 3% less. Double Phew.

With my Amazon Prime membership account up for renewal next month it’s time for me to go back over my receipts and ask the age old question: “was it worth it?” Which means I am going to face the reality of just how much I spend on Amazon. gulp.

Momappriciation Events:
Being a paid member of Prime and also an “Amazon Mom” I was able to participate in Momappriciation Events. During these events many of the baby and toddler merchandise is 20% off with coupon code. There were three events last year that I know of and I participated in two for a savings of $101.04. Most of that savings can be attributed to the convertible car seat and stroller. Good timing on my part, but unlikely to be repeat purchases any time soon.

I spent $361.56 on diapers averaging 19.4 cents per diaper. Don’t think that’s just because I’m on top of things with the Subscribe and Save discount. The additional 15% subscribe and save discount through Amazon Prime translated to $67.80 in savings. I missed the cutoff on for subscribe and save three times and had to pay full price. Had that not been the case I would have saved an extra $21.19. Amazon has some of the best prices for diapers.

This has me thinking that every disposable diaper cost analysis I’ve ever seen is crazy off. They all seem to think it will cost an average 30 cents per diaper for a $800 total price tag to diaper a baby in disposables. I’d be shocked if it cost more than $500 to diaper Nicki in brand name, non-generic diapers. (Huggies for the curious, they fit around her umbilical cord stump best as a newborn and we’ve never had the need to switch.) Not included in this total is gifted diapers (a friend’s baby outgrew his size 2s, so we got half a box plus some overnights for free – maybe $30 worth?) or in store purchases. We purchased 3 packs of various brands of newborn diapers to try out prior to giving birth (3 packs costing roughly $10 a piece, some of which were given away). My parents also bought a small pack of regular and overnight diapers when we flew East so we wouldn’t have to travel with them, and we ended up needing another small box while there (Maybe $50 total?). That would put the total cost of diapers at $470, well below $800.

Shipping Savings:
Out of the 42 purchases I made last year, 11 were under the $25 threshold needed for free Super Saver Shipping. Guestimating an average shipping cost of $4.99, that translates to about $54.89 shipping charges I would have faced without Prime. Now, that’s assuming I act rationally. I hate paying shipping costs, and am just as likely to look for additional items to add to my cart to qualify for free shipping. In order to qualify for free shipping, however, I would have had to add at least $173.32 worth of merchandise spread out over those eleven orders. Of course, I probably wouldn’t have spent quite that much. Some of those small purchases were not time sensitive and could have been combined into a single purchase that would have qualified for free shipping. Some, not all.

The true savings is probably somewhere between $54.89 and $173.32, so we’ll go with the lower number of $54.89 to make our savings estimate a conservative one.

Impulse Buys:
It’s been speculated that Amazon Prime is so profitable for Amazon because it encourages impulse buys and extraneous purchases. Since it’s so quick and easy to purchase from Amazon, people purchase more than they initially intended to.

To figure out the additional cost of impulse buys, I first considered what items I purchased are a part of the long tail. The long tail refers to items that only a few customers would want (e.g. table bumpers in less popular colors) as opposed to mass marketable items that appeal to a large group of customers (e.g. table bumpers in common colors). Big box stores do not stock long tail items because they’re likely to sit on the shelf for a while since they appeal to very few customers. An example of a long tail purchase I made is an unusual shaped cake pan. It’s not popular enough for box stores to keep it in stock, so my choice was to buy it online or don’t buy it. I’m only considering these long tail impulse buys because if the item was also available in box stores it might be just as likely to be impulse buy at some later point in time.

Of all the long tail purchases I made, $29.98 were on impulse buys. That is, $29.98 were on items I would not have felt compelled to shop for it outside of Amazon.

The Verdict:
Total Savings: $101.04 (mom appreciation events) + $67.80 (savings on diapers) + $54.89 (savings on shipping) = $223.73
Total Cost: $29.98 (the cost of impulse buys) + $39 (the cost of Prime with student discount) = $68.98
Net Result: A savings of $154.75

Definitely worth it this year, but I’m predicting the savings I enjoy will go down over time. Next year I’m less likely to benefit from the mom appreciation event since we won’t need new items like car seats and strollers, and when we’re out of diapers we’ll save even less. But for now, I’m a very happy prime customer.

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