How ordinary does a Mega Millions draw look?

Sort a draw from smallest to largest. Chance does not centre those numbers on the middle of the pool, it centres them on five evenly spaced positions: the smallest number is centred near the bottom, the largest near the top, and the rest spread between them. At a pool of 70 those positions are 11.83, 23.67, 35.50, 47.33 and 59.17. The measure on this page is the total distance from them, added up over all five numbers, and it is one figure that reacts to everything that makes a draw look strange at a glance: numbers bunched together, numbers crowded into one end of the pool, a gap wide enough to swallow a decade.

This game has drawn from one pool of 70 numbers throughout, so a single prediction of 45.67 per draw stands behind the whole record. Each figure here is still worked out at its own draw's pool, because that stays right if the pool ever changes, and a wider pool would raise the prediction rather than leave it alone. The spread of the measure is exact rather than estimated: counting up the pool one number at a time gives the share of draws at every possible distance, with no sampling and no normal curve standing in for one.

Each row is a slice of how far a draw sat from its own draw's prediction, measured in standard errors of that prediction rather than in distance, so draws from different pool sizes can sit in the same table without the eras being ranked against each other. The predictions add up to 160 exactly, which is the number of draws read, so the table compares the shape of the record against the shape chance predicts rather than its size. Some two rows carry no range: their predictions are under five draws, too thin for a standard error to mean anything, so no reading and no red mark is given for them. The bands measure single draws against their own prediction. The red marks measure the row counts against theirs, which is a different question asked of the same table.

At the ends of the record, here are the draws that came closest to the evenly spaced positions.

And here are the draws that sat furthest from them.

Nothing in those two lists is printed in red, and that is deliberate rather than an omission. These draws were picked out for being the extremes, so marking them as extreme would only repeat how they were chosen. The honest reading is a pair of counts. One draw came within 13.83 of the positions, where chance predicts 1.87 across the whole record, and chance gives about 85 chances in a hundred that a record this long holds at least one. At the other end one draw reached 110.50, where chance predicts 1.41 and gives about 76 chances in a hundred of at least one. Draws are independent of one another, so both of those readings are exact.

That is a short enough stretch to move about on its own. The opening stretch of the record measured 41.04 per draw against a predicted 45.67, and the recent one measures 42.73 against 45.67. The recent figure sits 2.94 below its prediction, or 1.41 standard errors. The two draws named beside it are the extremes of that stretch, picked out for being extreme, so neither carries a red mark either.

Oldest block on the left, newest on the right. The band is what chance predicts for those same draws, worked out from each draw's own pool, so a block that straddles a change of pool size is not read as a trend. A point outside the band is marked. One point sits outside the band. Across eight blocks, chance alone puts 0.36 of them outside.