LECTURE 4#
SHOULD YOU#
WAIT?#
SLOP3746 · Week 10
Today’s question#
When does it make sense to wait for a better price?
By the end of this lecture: when the expected saving is bigger than the costs of waiting, using a rule you set before you know the outcome.
Waiting is a bet#
Buying now locks in a known price. Waiting trades that certainty for a chance at a better one. That’s a bet, in the exact sense a bet always is: a range of outcomes, none of them guaranteed, some of them worse than just paying today.
Treating it as anything other than a bet — a guarantee, a trick, a certainty — is where this reasoning goes wrong.
Why future price is uncertain#
Week 5 showed price moving over time. Week 6 showed it responding to context. Put together: next month’s price for this item is not a fixed fact waiting to be discovered. It depends on demand, stock, season, and decisions nobody’s made yet.
This course does not claim to predict it. It claims something simpler and more useful: you can make a reasonable estimate.
You cannot know the future price. You can only estimate it. Those are different claims.
Expected value, in plain language#
You don’t get “the discount, if it happens.” You get the discount, discounted again by how likely it is to happen at all.
A guaranteed small saving and an unlikely large one can be worth exactly the same amount — or wildly different amounts — and you can’t tell which without doing the multiplication.
The formula#
expected saving = probability(better deal) × size of that deal
- a 10% chance of a $100 saving → expected saving $10
- a 50% chance of a $30 saving → expected saving $15
The second bet sounds far less exciting and is worth more.
Stock-out risk#
Waiting risks the item disappearing entirely — this exact model discontinued, sold out, or replaced by a new version at a higher price before any sale appears.
A saving you never get to collect is worth exactly nothing, no matter how large the discount would have been.
Urgency cost#
If the item is needed by a fixed date — a gift, a trip, a broken pair that needs replacing now — the window to wait may be shorter than the window a “maybe” discount needs to arrive in.
Urgency doesn’t change the probability of a sale. It changes how much of that probability you’re actually allowed to use.
The value of having it now#
A want satisfied today is not interchangeable with the same want satisfied in six weeks, independent of price. Two headphones at the same price, delivered on different days, are not the same purchase to someone who wants to use them tomorrow.
This isn’t sentiment. It’s a real input the expected-value formula above doesn’t include on its own.
What waiting costs in attention#
Waiting isn’t passive. Watching for a sale — checking prices, tracking a listing, comparing near-identical deals — takes attention, and attention spent watching is attention not spent elsewhere.
Week 11 turns this into a number. For now: waiting has a cost even when no money visibly changes hands during it.
Worked example: the headphones at $249#
The running scenario, restated: the headphones are $249 today, with no sale currently active. That’s the certain option — buy now, done, $249.
Everything on the next few slides is about what it would take to make waiting the better bet instead.
A hypothetical possible sale to $199#
Hypothetically: this model has, in past years, been discounted to around $199 during a known annual sale event roughly six weeks away.
This is not a promise, and it is not evidence about any real retailer’s future pricing — it’s the kind of estimate a buyer can reasonably form and should explicitly label as a guess, not a fact.
Probability of the sale#
Suppose, hypothetically, the buyer estimates a 40% chance the sale includes this exact model at that price this year — based on it happening in two of the last five comparable events they remember.
That’s a rough, self-reported estimate, not a statistic. It’s still better than pretending no probability exists at all.
Expected saving, calculated#
- possible saving: $249 − $199 = $50
- probability of getting it: 40%
- expected saving: 0.4 × $50 = $20
Twenty dollars, not fifty. The $50 headline number is what you’d get if the sale happens — the $20 is what waiting is actually worth, on average, across every version of how this could go.
When expected saving is not enough#
$20 of expected saving has to be weighed against six weeks of stock-out risk, urgency, the value of having the item now, and the attention cost of watching for the sale.
If any of those costs, honestly estimated, exceed $20, waiting is the worse bet — even though the $50-if-it-happens number is real and the 40% estimate is reasonable.
Risk tolerance#
Two buyers can face the identical $20 expected saving and reasonably disagree about waiting: one is comfortable with a 60% chance of getting nothing extra, the other isn’t. Expected value tells you the average outcome across many repeated bets — it doesn’t tell you how much one buyer should mind the spread of possible outcomes.
Risk tolerance is a stated assumption, not something the formula supplies.
Comparison with Week 11’s time cost#
Week 11 adds a second bet-cost on top of this one: the time actually spent watching for the sale, priced at whatever the buyer’s hour is worth. Add the two together — expected saving from waiting, minus urgency and stock-out risk, minus time cost — and you get a single number instead of two separate vibes.
How this feeds Assessment 3#
Build a Buying Engine takes exactly these inputs — current price, possible discount, probability, urgency, time cost — and asks for a system that reaches BUY NOW, WAIT, or another recommendation and can explain why, rather than outputting a number with no reasoning attached.
Decision threshold: buy now vs wait#
A simple clear rule: wait only if
expected saving > stock-out risk + urgency cost + attention cost
all measured in the same units, and all honestly estimated by the buyer. Change any one input and the recommendation can flip — which is the point of writing it as a clear rule rather than a feeling.
In-class challenge#
Hypothetically: a different item is $120 today. A buyer estimates a 25% chance of a $40 sale in three weeks, no meaningful stock-out risk, no urgency, and about $6 of attention cost from watching for it.
Question: does the threshold above say buy now, or wait?
Solution walkthrough#
- possible saving: $40, probability 25% → expected saving = $10
- stock-out risk: ~$0 (stated as negligible)
- urgency cost: $0 (stated as none)
- attention cost: $6
$10 expected saving clears $0 + $0 + $6 = $6 of stated costs → the threshold says wait, but only because urgency and stock-out risk were both genuinely negligible for this item — change either one and the answer changes with it.
Summary: waiting only works under stated assumptions#
- waiting is a bet with an expected value you can calculate, not a guarantee
- expected saving = probability × discount size, always
- stock-out risk, urgency, and attention cost all belong on the other side of the ledger
- this course never claims to predict a real future price — only to reason honestly about an estimate of one
One more distortion, previewed#
Everything today assumed you’re deciding cleanly between buy-now and wait, with nothing already spent pulling on the answer. That assumption breaks the moment money is already down — which is exactly next week’s topic.
The sunk cost effect#
Arkes and Blumer named and measured a bias with a simple shape: people are more likely to continue an endeavour once money, effort or time has already gone into it — even when that spending cannot be recovered and has no bearing on what happens next.
Arkes, H. R., & Blumer, C. (1985). The Psychology of Sunk Cost. Organizational Behavior and Human Decision Processes, 35(1), 124–140.
Applied to waiting: money already spent researching, tracking, or nearly buying this item is real, but it is sunk — it changes nothing about whether waiting further is still the better bet from here.
Their field evidence#
Arkes and Blumer ran a real field study at Ohio University’s theatre season: patrons who happened to buy season tickets at a discount attended fewer plays over the season than patrons who paid full price for the identical tickets — despite owning an identical product. A companion questionnaire study found people who imagined already paying for a nonrefundable ski trip were more likely to say they’d go anyway through unpleasant conditions, citing “not wanting to waste the money” already spent.
Neither group’s future enjoyment changed. Only the sunk amount did.
Thaler’s wine, reframed#
Richard Thaler and Eldar Shafir studied a related twist: shoppers who buy a case of wine as an “investment,” then drink a bottle years later once its market value has risen, often describe the drinking as free — or even as saving money — rather than as spending the bottle’s current value.
Shafir, E., & Thaler, R. H. (2006). Invest now, drink later, spend never: On the mental accounting of delayed consumption. Journal of Economic Psychology, 27(5), 694–712.
The same $249 already spent researching a “maybe wait” decision can get the same free-feeling treatment — it’s gone either way, but it doesn’t feel gone the same way to the person who spent it.
Why this belongs on today’s ledger#
Today’s decision threshold —
expected saving > stock-out risk + urgency cost + attention cost
— has no room for “but I already spent time on this.” That’s deliberate: a sunk cost is not a real cost of waiting or of buying, so a rule that lets it onto either side of the ledger is a rule already bent by the money that’s gone. Next week asks how much that bend actually costs.