Published · · Last reviewed · · 6 min read
English · 한국어
After a record prize, an ordinary one: regression to the mean
"Why does the amount drop so much the week after a record prize?" Rounds where each first-prize winner received about KRW 3.8 billion or more make up the top 10% (116 rounds) of 1,153 pairs of consecutive rounds. In 92.2% of them (107 rounds) the next round paid less per winner, and the median next amount was 37% of the previous one. In the other direction, the round after the bottom 10% (KRW 1.23 billion or less) was higher 92.2% of the time, with a median of 1.9 times. Luck did not run out and nothing lost its energy. This is a statistical effect called regression to the mean, and this page also shows how it clouds judgement outside the lottery.
How the per-winner prize is set
The prize per first-prize winner is the first-prize pool of the round divided by the number of winners. The pool is nearly proportional to sales and does not leap from week to week, but the number of winners varies a lot by chance. Among rounds from 88 on with a first-prize winner, the median number of winners is 8 and the median pool is about KRW 15.4 billion (aggregates also used in the winner-count analysis). Fix the pool at KRW 15.4 billion and change only the number of winners:
| First-prize winners | Per winner (before tax) |
|---|---|
| 1 | KRW 15.4 billion |
| 3 | KRW 5.1 billion |
| 8 (median) | KRW 1.9 billion |
| 14 | KRW 1.1 billion |
| 30 | KRW 0.51 billion |
With about 3 winners the per-winner amount is in the KRW 5 billion range; with 14 it is a little over KRW 1 billion. The 116 rounds in the top decile of per-winner prizes had a median of 3 winners, and the 116 in the bottom decile had 14. The large amounts did not come from "good luck that week" but from "few winners that week by chance". The next round's winner count is drawn afresh, so a return to about 8 is the normal outcome.
In the real record
I looked at the change in the per-winner prize over 1,153 pairs of consecutive rounds from round 88 on in which both rounds had a first-prize winner. The median of these amounts is KRW 2.03 billion.
| Previous round's per-winner prize | Rounds | Median winners | Next round lower / higher | Next ÷ previous (median) |
|---|---|---|---|---|
| Top 10% (KRW 3.80 billion or more) | 116 | 3 | 92.2% lower | 0.37× |
| Bottom 10% (KRW 1.23 billion or less) | 116 | 14 | 92.2% higher | 1.90× |
| All | 1,153 | 8 | next lower in 50.0% | - |
How well one round's amount predicts the next (correlation of the logs) is 0.023, effectively zero. Whether the previous round was high or low carries no information about the next; extreme values are simply likely to come back near the middle. Overall the next round is lower in exactly half of the pairs (50.0%).
Splitting into five groups
Looking only at the extremes can exaggerate a selection effect, so I also sorted the 1,153 pairs by the previous round's per-winner prize into five groups of about 230 pairs and looked at the next round. The previous amount differs by more than a factor of three across the groups, yet the median of the next round is almost the same.
| Previous-round group | Previous amount range | Previous median | Median winners | Next-round median | Share where next is lower |
|---|---|---|---|---|---|
| Lowest 20% | KRW 0.41–1.46 billion | KRW 1.23 billion | 12 | KRW 1.93 billion | 12.2% |
| 20–40% | KRW 1.47–1.84 billion | KRW 1.65 billion | 9 | KRW 2.00 billion | 32.9% |
| 40–60% | KRW 1.84–2.26 billion | KRW 2.03 billion | 9 | KRW 2.01 billion | 49.1% |
| 60–80% | KRW 2.27–3.04 billion | KRW 2.58 billion | 7 | KRW 2.21 billion | 67.5% |
| Highest 20% | KRW 3.05–14.22 billion | KRW 3.80 billion | 4 | KRW 2.00 billion | 88.3% |
Whichever group the previous round was in, the next round's median sits between KRW 1.9 and 2.2 billion. A previous KRW 1.2 billion or KRW 3.8 billion gives no clue about the next round, and the share of "next is lower" approaching 100% or 0% for more extreme previous rounds is the same effect. Only in the middle group (40–60%) is the share where the next is lower about half (49.1%).
The key is that an extreme was selected
Every measurement contains a stable part and a part due to chance. In the per-winner prize the pool is the stable part and the number of winners is the part due to chance. Pick out the rounds with unusually high values and you mostly pick rounds in which chance happened to push high. In the next round chance is drawn again, so the part that was pushed high drops away. The round did not "cool down"; it was high from the start with the help of chance. Pick low rounds and the next one is usually higher.
How far values come back depends on the share of chance
The size of the return can be judged from the correlation. Only the correlation times the deviation of the previous value from the average can be expected to persist into the next round. At correlation 1 values simply persist; at 0 the previous value says nothing about the next. The per-winner prize has a correlation of 0.023, so nearly everything comes back. Whether the previous round was KRW 1.2 billion or KRW 3.8 billion, the next round starts afresh around the usual KRW 2 billion.
The opposite extreme is adult height. Measure the same person a year apart and the two values are nearly equal (correlation close to 1); pick the tallest person and measure again and they are still among the tallest. Chance plays a small part in height, so there is almost no regression. The larger the share of chance (winner counts in a lottery, the score of one game, one week's sales), the larger the return after an extreme. When comparing any number, first ask how much chance drives it.
Where it misleads in daily life
Without knowing about regression to the mean, people read cause into places where there is none. Consider the imagined situations below (invented stories, not data from any shop or school).
Acting after the worst week. After the lowest-sales week of the year a shop changes its advertising and sales rise the next week. Was it the advertising? In the lottery data above, with no action at all, 92% of the bottom-10% rounds were followed by a higher one. The worst week was probably unlucky, and the next will simply be nearer the average. To know the effect of the advertising you need to compare with similar weeks without the change.
The top scorer on a mock exam. When the top student of a mock exam ranks lower on the next, it is easy to say "got complacent". Ability may be unchanged: the first score included some chance in the student's favour, which was absent the second time.
The opposite direction to the gambler's fallacy
This effect is easily confused with the gambler's fallacy, the belief that after a run on one side the other side is due, but it is different. The gambler's fallacy is the belief that independent events have memory. Regression to the mean arises because they have none. The next round is independent of the previous one, so after an extreme value the next value is a fresh draw from the usual distribution, which tends to be nearer the middle. To say of the next round "it is its turn to be lower" would be a fallacy again. The chance of being lower comes from the fact that the high value was an extreme, not from any force acting on the next round (The gambler's fallacy).
Questions that come up
"Then should I buy in a week with a low prize?" The per-winner prize is a share after winning; a ticket's chance of winning is 1 in 8,145,060 in every round. This page does not recommend when to buy.
"How was the top 10% defined?" It is the pairs whose previous amount is at or above the 90th percentile of the 1,153 pairs. I did not check whether 80% or 95% give the same direction.
Simplifications in the per-winner prize
The per-winner amount is simplified to the first-prize pool divided by the number of winners. Tax and round-to-round differences in the pool (which follow sales) are ignored in the fixed-pool table above, while the data analysis uses each round's actual amount. Rounds with no first-prize winner have no amount and were dropped from the pairs. The data are the results for rounds 88 to 1,247 published by Donghaeng Lottery; only aggregates are published.
LottoFlick is independent and not an official lottery operator. Numbers are random and cannot be predicted.
Sources and verification
- Donghaeng Lottery: Lotto 6/45 round results, rounds 1–1247 (collected by hand 2026-10-24) — verified
- LottoFlick aggregate output: median first-prize pool per round — computed by LottoFlick
- LottoFlick calculation: next-round change after extreme per-winner prizes, autocorrelation — computed by LottoFlick