DataSense8 Research
How Many Tournaments Does It Take to Estimate ROI?
With a standard deviation of 7 buy-ins per tournament, pinning ROI down to ±10 percentage points at 95% confidence takes about 18,824 tournaments. ±20 pp takes 4,706, ±5 pp takes 75,296. The answer barely depends on the ROI itself: it is driven by how widely single results swing.
Who it is for
Staking funds and backing teams that plan with ROI figures: their own, a segment’s, a whole portfolio’s. Every such figure is an estimate with an error, and the error is usually larger than it feels.
This is a method for measuring that error. We do not rate players and do not advise whom to stake.
The formula
- Standard error
- Let SD be the standard deviation of one tournament result in buy-ins, (prize − buy-in) / buy-in. The average of N such results, which is ROI, has a standard error of SD / √N.
- 95% interval
- ROI ± 1.96 · SD / √N. Example: an ROI of 8% measured over 2,000 tournaments with SD 7 has a half-width of 31 pp: the interval runs from −23% to +39%.
- Tournaments needed
- Solve for N at a target half-width E: N = (1.96 · SD / E)². Twice the precision costs four times the tournaments.
- Telling ROI from zero
- Set E equal to the ROI itself. For 8% and SD 7 that is 29,413 tournaments; at 500 a month, about 4.9 years of volume.
Tournaments needed for a 95% interval
| SD \ precision | ±5 pp | ±10 pp | ±20 pp |
|---|---|---|---|
| 4 | 24,587 | 6,147 | 1,537 |
| 6 | 55,320 | 13,830 | 3,458 |
| 8 | 98,345 | 24,587 | 6,147 |
| 10 | 153,664 | 38,416 | 9,604 |
For 90% confidence multiply by 0.70, for 99% by 1.73. Computed by the same code as the calculator below; a check script recomputes the table against this page.
Calculator
Why SD is so large in tournaments
Most of a tournament player’s profit comes from rare deep runs, while most entries lose one buy-in. That shape gives a large standard deviation, and it grows with field size.
The extreme case shows the scale. If a field of F players pays everything to the winner and there is no fee, the result in buy-ins is F − 1 with probability (1 + ROI) / F and −1 otherwise. Its SD is √(F·(1 + ROI) − (1 + ROI)²), roughly √F. At ROI 8%:
- field of 100: SD ≈ 10.3
- field of 1,000: SD ≈ 32.8
- field of 10,000: SD ≈ 103.9
Real events spread prizes over many places, which pulls SD far below this extreme; knockout formats and steeper payout tables push it up. The default of 7 buy-ins on this page and in our portfolio model is a working assumption for large-field online events, not a measured market figure. Use your own.
On small samples the interval is too narrow
The formula assumes the average is close to normal. With a skewed result it is not, until there are enough deep runs in the sample. We checked how often the “95%” interval, with ROI and SD estimated from the same sample as a fund would do, actually covers the true ROI. Setup: winner-take-all, field of 100, true ROI 8%, 4,000 simulated samples per size.
At 500–1,000 tournaments the interval misses the true ROI about twice as often as it claims, roughly one time in ten instead of one in twenty: the few deep runs in a short sample make SD look smaller than it is. Real payout structures are less skewed than this extreme case, so we expect a weaker effect in practice, in the same direction. On short samples treat the interval as a lower bound on the uncertainty.
How a fund estimates SD on its own data
- Take each tournament result in buy-ins of that tournament: (prize − buy-in) / buy-in. Do not mix dollars across buy-in levels.
- Compute the sample standard deviation with the n − 1 divisor, per segment with a similar format and field size.
- Use several thousand tournaments per estimate. One deep run moves a small-sample SD a lot.
- Pooling helps: a segment estimate across the portfolio rests on all players’ tournaments in it. If results are independent, N grows with the number of players and the interval narrows by √(players).
Using it with the portfolio model
Plug ROI into the staking fund portfolio model together with its uncertainty, not as a point.
The model’s “ROI spread between players” field partly is this uncertainty. If each player’s ROI estimate rests on 5,000 tournaments with SD 7, its error alone is 10 pp, more than the model’s default spread of 6 pp. The spread you enter should cover both the real differences and this error.
Limits
- ROI is not stationary. Fields, formats and players change; a sample collected over several years describes a game that partly no longer exists. More data buys precision at the cost of relevance.
- Different buy-in levels are different samples. ROI at one level says little about another; pooling them gives a number that fits neither.
- Survivorship. Samples that reach a fund are often the ones that looked good, partly by luck. An estimate taken right after a strong run is biased upward and tends to fall back.
- Structure. SD depends on field size, payout table and format. The formula assumes independent results from one distribution; a changing schedule breaks that.
- Normal approximation. On short samples the interval is too narrow; see the check above.
Not advice
This page explains a statistical method. It is not investment, financial or legal advice and it does not evaluate any player. Past results do not guarantee future results. The fund is responsible for its own decisions and for following the rules of the platforms where its players compete.
Want these intervals on your fund’s data?
The tournament selection audit estimates ROI by segment with confidence ranges, finds the segments the fund pays for at a loss, and forecasts makeup.