There is a column on the Prediction Alpha markets table labelled Kelly%, sitting between Misp% and Whales. It is the most dangerous number on that screen, and not because it is wrong. It is dangerous because it looks like a measurement when it is an output, and the input it depends on most is the one you supplied.
Kelly sizing on a binary is a short piece of arithmetic with one term you cannot observe. Everything else is on the row in front of you. That single unobservable term is what the rest of this is about, and it is why the number that comes out the other end needs a haircut before it becomes a ticket.
The arithmetic, and the one term you are guessing
A binary contract costs you some price and pays one dollar if the event happens. Call the price q and your belief about the true probability p. The fraction of bankroll that gives the fastest long run growth is (p minus q) divided by (1 minus q).
Work it at a price of 30 cents. If you think the true probability is 45 percent, that is 0.15 divided by 0.70, which is 21.4 percent of bankroll. On a five thousand dollar account that is a 1,070 dollar ticket on one question. Most people seeing that for the first time assume they have made an arithmetic error.
They have not. The formula is right. What is wrong is the confidence implied by feeding it a single point value for p. The price is a fact: it is on the screen, and if you cross the spread you know exactly what you paid. Your probability is an opinion, and it got carried into the calculation to two decimal places because the calculation demanded two decimal places, not because you had them.
Notice what the screenshot shows. The exchange half of each row is complete: prices, 24 hour volume, total volume, liquidity, end date. The derived half, including Kelly%, is empty on all four rows, with an Analyze button at the end. Whatever fills that column has to be asked for, and only ten of the thousand markets displayed had been. When it does hold a number, that number inherited somebody's probability estimate, and inherited all the uncertainty in it without carrying any of it forward.
A seven point error nearly doubles the bet
Keep the price at 30 cents and move the probability estimate around, since that is the term that moves.
| Your probability | Kelly fraction | Ratio to the 45 percent case |
|---|---|---|
| 45 percent | 21.4 percent | 1.0 |
| 42 percent | 17.1 percent | 0.80 |
| 38 percent | 11.4 percent | 0.53 |
| 35 percent | 7.1 percent | 0.33 |
| 32 percent | 2.9 percent | 0.13 |
| 30 percent | zero | zero |
Read the third column backwards. If you sized on 45 percent and the truth was 38 percent, you did not bet 7 percent too much. You bet 1.9 times the correct amount. A seven point error is not an unusual error on a question you spent an evening reading about. It is a normal one.
The mechanism is in the denominator. Every point of error in your probability moves the Kelly fraction by one divided by (1 minus q). At a 30 cent price that multiplier is 1.43. At an 80 cent price it is 5, so on expensive contracts a single point of probability error moves your position size by five points of bankroll. The more likely the event, the more violently the sizing reacts to being slightly wrong about it.
There is a cleaner way to ask the same question, and it takes ten seconds. The trade is exactly break even when p equals q. So your entire edge is the gap between your estimate and the price, which here is 15 points. Now ask yourself honestly whether your probability estimate is accurate to within 15 points. If the answer is no, or is anything other than a confident yes, the full Kelly number is not describing your situation.
Overbetting and underbetting do not cost the same
This is the part that makes the haircut cheap. Growth rate as a function of position size is roughly a hill: it rises to a peak at full Kelly and falls away on both sides. Near the peak it is well approximated by two times your fraction of Kelly, minus the square of that fraction, times the peak growth.
Put half Kelly through it. Two times 0.5 is 1.0, minus 0.25, is 0.75. You keep three quarters of the growth for half the position size and roughly a quarter of the variance. Now put double Kelly through it. Two times 2 is 4, minus 4, is zero. Betting twice the correct fraction gives up the entire growth advantage. At two and a half times, the expression is negative, which means you are shrinking the account on average while being right about the direction.
So the two errors are not symmetric. Betting half as much as you should costs you a quarter of your growth. Betting twice as much costs you all of it. Then look back at the table: a seven point probability error already put you at 1.9 times. The asymmetry and the estimate error point in the same direction, and that direction is down.
The price in the formula is not the price on the screen
One retail specific correction before you use any of this. The q in the arithmetic is what the contract actually costs you, all in. That is your fill, not the quote, plus whatever the venue charges, plus the fact that you will pay again to get out if you do not hold to resolution.
Push the effective price from 30 to 32 cents and the edge falls from 15 points to 13, and Kelly falls from 21.4 percent to 19.1 percent. That looks minor. It is minor at 30 cents. Run the same two cent adjustment on a contract quoted near a penny and the edge can disappear entirely, which is exactly the situation on the second row of the screenshot: a market quoted at 0.9 percent Yes with 686 dollars of resting liquidity behind it. There is no sizing formula that survives that book.
The other input people get wrong is the bankroll. Kelly is a fraction of the capital the strategy is allowed to lose, not the balance sitting on one venue. If your prediction market account holds 5,000 dollars but that is money you would not replace after a loss, the bankroll for this purpose is 5,000 dollars, not your net worth. If it is one sleeve of a larger book you would top up, the bankroll is bigger and the dollar ticket goes up accordingly. Decide which before you multiply by anything.
The rule to write down this week
Take whatever Kelly percent you compute or the screen shows you, halve it, and treat that as the ceiling rather than the target. Then apply two hard limits underneath it that have nothing to do with the formula.
The first is a book share limit. Compare your intended ticket to the Liquidity column on the row. On the screenshot those figures were 497.3K, 686 dollars, 648.8K and 282.0K on four of the highest turnover markets in the whole feed. A 250 dollar order is a rounding error against 282.0K and it is 36 percent of 686 dollars. Kelly does not know that and will happily size you into a book that cannot fill you.
The second is a per question cap regardless of edge. Set it as a percentage of the account, write it on paper, and let it override the arithmetic whenever the arithmetic argues for more. The situations where Kelly demands 21 percent of your account are exactly the situations where you are most excited and least calibrated, and a cap written on a calm day is the only thing in this process that is not downstream of your own estimate.
If halving feels like leaving money on the table, run the growth expression once more with your own numbers. Three quarters of the growth, a quarter of the variance, and a large amount of protection against being seven points wrong is not a compromise. It is the trade the arithmetic actually recommends once you admit that p was never a fact.