Applying to 15 reaches doesn't add up the way you think: the odds of at least one yes
Ten schools at 10% each is not a 65% shot at getting in somewhere. Build your list in the calculator and see why similar reaches rise and fall together.
The question we keep seeing
“If I apply to enough reach schools, won't I get into at least one by the law of averages?”
The short answer
- The coin-flip formula says ten schools at 10% each gives a 65% chance of at least one yes. That only holds if every decision is independent, and they aren't.
- The same application goes to every school. Similar schools tend to agree about it, so your real odds sit somewhere between your single best chance and the coin-flip figure.
- The way to raise the floor isn't more reaches. It's schools whose decisions don't move with the rest: true targets and likely admits.
There's a piece of math that circulates every application season. If each school is a separate lottery ticket, the chance that every one says no is the product of the individual no's, so the chance of at least one yes is 1 − (1 − p₁)(1 − p₂)… Ten schools at 10% each gives 1 − 0.9¹⁰, or about 65%.
The arithmetic is right. The assumption behind it isn't. Try it on a list of your own below, and move the last slider to see what happens when the schools stop being independent.
Your list, as odds
Example list below. Rename the schools and set each chance to your own estimate.
- 6%
- 9%
- 12%
- 35%
- 45%
- 80%
Chance of at least one yes: 87%
Somewhere between 80% (if every school decides the same way) and 95% (if every decision were a separate coin flip). Expected acceptances: 1.9.
The “how alike” slider blends the two limits in a straight line to show the range. It isn't a fitted model of any real applicant pool. Your own chance at each school is the input that matters most, and it's the hardest to know.
Why admissions decisions aren't coin flips
A lottery draws a fresh number for every ticket. An application doesn't. The grades, essays, activities and recommendations are the same file at every school. Selective schools read for broadly similar things. If a file isn't competitive at one highly selective school, the reasons it fell short are often there at the next one too.
Statisticians call this correlation. When outcomes are correlated, adding more of the same kind of bet adds much less than the independent formula suggests. At the extreme, ten schools that would all make the same call give you just one 10% chance, ten times over.
What actually raises your odds
- Add schools that decide differently. A school where your file sits comfortably above the typical admit isn't a gamble that moves with the rest. One genuine likely admit raises the floor more than five extra reaches.
- Estimate each chance honestly. The formula is only as good as its inputs. At schools admitting under 10%, the published rate already flatters most applicants, because many admits come from recruited and special-interest pools.
- Count expected acceptances, not just the chance of one. If the expected number is under 1, you're probably relying on luck, however long the list is.
- Use early rounds deliberately. Where a school's early round admits a higher share, applying early can change the chance itself. Check whether that's binding first (early decision and aid).
Try it in Katalyna
Chance-me and net price
Estimate your fit at each school from published admissions data, then balance the list.
Frequently asked
If the decisions were independent, it would be 1 minus the product of each school's rejection chance. But decisions are correlated, so the real figure is somewhere between your single best chance and that number.
Not necessarily. Independence would give about 64%, but similar highly selective schools tend to agree on the same file. Your real chance could be much closer to 5%. Adding schools where you're a strong admit raises the floor far more.
Only roughly. The published rate mixes recruited athletes, legacy and early pools with everyone else, and your file may be stronger or weaker than the typical applicant's. Treat it as a starting point.