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#65 Skill or luck: how many coin-flippers look skilled?
Past prices; no real orders were placed. Every figure is a share of the money, or a count.
Last checked: 18 October 2026.
Where the idea comes from
- Skill shows as persistence. Brad Barber, Yi-Tsung Lee, Yu-Jane Liu and Terrance Odean, "The cross-section of speculator skill: Evidence from day trading" (Journal of Financial Markets, 2014). They studied day traders in Taiwan, 1992 to 2006, ranking them by one year's returns. The top 500 earned 0.379% a day after fees the next year. Past winners kept winning, which luck can't do. But fewer than 1 day trader in 100 earned reliably.
- Most who persist still lose. Fernando Chague, Rodrigo De-Losso and Bruno Giovannetti, "Day trading for a living?" (working paper, 2019), followed Brazilians who began day trading index futures in 2013 to 2015. Of those who kept at it for more than 300 days, 97% lost money.
- The traders here are the 90,000 from our page "Coin-flip traders: can luck beat the fees?". They have no skill at all, by design. This page puts them through the usual tests of skill.
- Why the best of many looks good is on our theory page "Hard-to-beat markets, and why every test needs a random twin".
- Part of our series "Published edges against the coin".
The question
If 90,000 traders who pick their side with a coin are put through the usual tests of skill, how many pass? And does the persistence test, the one that found skill in Taiwan, tell them apart from real skill?
How we tested
- The traders: exactly those of the coin-flip page, with the same flips. Bitcoin, Ether and Solana; the Asian, London and New York sessions; two 4-hour trades a day, no leverage, one flip to trade and one for the side. 10,000 for each coin and session, from 15 October 2022 to 15 October 2026.
- Fees: none (pure luck), the resting-order fee (0.02%) and the market-order fee (0.055%), paid in and out.
- Test 1, one record: each trader's average trade over four years, divided by how uncertain that average is (the t). The usual test calls a t above 1.96 skilled. We also used a stricter line that allows for 90,000 tries at once.
- Test 2, persistence (Barber's): the four years cut at each 15 October. In each of the first three years, the top 1% and the top 10% of each coin and session, by that year's result at the market-order fee. Then how they did the next year, against everyone.
- Test 3, those who kept at it (Chague's): every coin-flipper traded all four years. How many lost money?
- Fixed before the run: about 2.5% would pass test 1 with no fee, none would pass the stricter line, and test 2 would find nothing.
The maths, step by step
1. The t. A trader made 700 trades averaging +0.1%, and single trades swing about 1.5%. The uncertainty of the average is 1.5% ÷ √700 = 0.057%. So t = 0.1 ÷ 0.057 = 1.76: not quite "skilled".
2. How often luck passes. For a fair coin the t lands on a bell curve. It is above 1.96 about 2.5% of the time: of 90,000, about 2,250.
3. The stricter line. To let luck pass only 1 time in 20 across all 90,000 together, each trader needs about 5% ÷ 90,000 by themselves: a t above 4.87.
4. The best of many. The luckiest of 90,000 pure-luck traders is expected around t = 4.2 to 4.4. It looks outstanding, and it is nothing.
5. Persistence. A skilled trader is skilled every year. A lucky one starts again from zero each year. So last year's winners should beat everyone next year only if they have skill.
What we found
1. The usual test called 2,263 coin-flippers skilled.
| fee | t above 1.96 | highest t | lost money |
|---|---|---|---|
| none | 2,263 (2.51%) | 4.34 | 61.0% |
| resting-order (0.02%) | 131 (0.15%) | 3.37 | 91.5% |
| market-order (0.055%) | 1 | 2.17 | 99.7% |
90,000 coin-flip traders, four years.
- With no fee, 2.51% passed, as luck predicts (2.5%).
- The best was t = 4.34, right where the best of 90,000 should be.
- None crossed the stricter line (4.87).
- The fee pulls everyone down, so fewer pass. At the market-order fee only one did.
The traders fall on the bell curve of pure luck; about 1 in 40 passes the usual test anyway.
2. Last year's winners did no better the next year.
- Top 1%: the next year they did +0.17% better than everyone. The 95% band is −0.91% to +1.26%, so this is zero. They came out ahead of everyone in 14 of the 27 coin, session and year cases.
- Top 10%: +0.02% (−0.32% to +0.37%), ahead in 14 of 27.
- Barber's top 500 in Taiwan earned 0.379% a day the next year. Our luckiest 1% earned nothing extra in a whole year. That is what this test is for: luck does not carry over, skill does.
Last year's best coin-flippers did no better than anyone the next year: luck does not persist.
3. Those who kept at it. Every coin-flipper traded for four years. 99.7% lost money at the market-order fee, 91.5% at the resting-order fee. Chague's real traders who kept at it lost money 97% of the time, between our two fees.
What it means
- A single good record proves little. With enough traders, about 1 in 40 looks skilled by the usual test, and the best looks outstanding.
- Persistence is the better test. Our coin-flippers failed it, as they should. Barber's top traders passed it, so a few real day traders do have skill. The 97% in Brazil were about as good as coins.
- For our own rules: a good backtest is one record. What counts is whether it keeps working on prices it hasn't seen. That is why each page in this series judges a rule on a second half it never saw.
Limits
- Coin-flippers by design have no skill, so test 2 can only show what luck looks like, not how much skill real traders have.
- Four years of three large coins, hourly prices, funding left out (two 4-hour trades a day pay it at most once, and on a coin-flip side it averages out).
- Barber's and Chague's traders traded stocks and index futures, not crypto.
Credits
- Brad M. Barber, Yi-Tsung Lee, Yu-Jane Liu and Terrance Odean, "The cross-section of speculator skill: Evidence from day trading", Journal of Financial Markets, 2014: ranking by one year, judging the next.
- Fernando Chague, Rodrigo De-Losso and Bruno Giovannetti, "Day trading for a living?", working paper, 2019: the 97% of persistent day traders who lost money.
- Carlo Emilio Bonferroni, Teoria statistica delle classi e calcolo delle probabilità, 1936; Olive Jean Dunn, "Multiple Comparisons Among Means", Journal of the American Statistical Association, 1961: the stricter line for many tests at once.
- Our own: the coin-flip traders (from our coin-flip page) and the three tests on them.
- Data: Bybit's public market data, 1-hour USDT perpetual prices; fees from Bybit's base fee schedule.
- PerpGremlin and Claude, Skill or luck: how many coin-flippers look skilled?, TerminalGremlin, 2026: the tests, the code and the words.
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Educational research from public market data; any trading discussed is paper, never real. Nothing here is advice. The full notice.