What a red card does to a live price
A sending off is worth far more in the eightieth minute than in the tenth, and the market's instant reaction is often the wrong size in a predictable direction.
A red card in the tenth minute and a red card in the eightieth are the same event on the scoresheet and completely different events in the market. Eighty minutes of playing a man down is a different game. Ten minutes of it is an inconvenience.
The two variables
Time remaining is the obvious one, and it is close to linear: the value of the extra player is roughly proportional to the minutes it will be enjoyed.
Score state is the one that gets handled badly. A side sent down to ten while leading behaves differently from a side sent down to ten while trailing. The leader drops deep, concedes territory, and gives up a large number of low quality chances. The trailing side must still attack, which means the extra man produces high quality chances against an exposed defence.
So the same numerical disadvantage produces very different goal distributions depending on which way the score is running, and a live model that adjusts a single expected-goals figure for "ten men" cannot express that.
Where the reaction goes wrong
The direction is instant and correct at every book. The size is set by an automated adjustment that is a function of time and, at the better books, score. What it usually does not capture is the specific pattern above, which means the largest errors are in the totals and both-teams-to-score markets rather than in the result.
That is the familiar shape: the headline market is priced properly and the derivatives underneath it are approximated.
What it means for the pre-match number
Very little, which is worth saying. Red cards are rare enough that pricing them into a pre-match assessment adds more noise than information, except for referees with strongly atypical records, and even there the effect is small.
What this does not tell you
How this specific referee will behave, or whether the card was correct. A model that adjusts for expected cards is estimating a number with very wide error bars from a small number of matches per official.
Common questions
How much does a red card change a football match price?
It depends heavily on when it happens and what the score is. Early in a level match the effect is large; late in a settled match it can be almost nothing.
Do teams down to ten men always concede more?
On average yes, but the effect is concentrated. A side leading with ten men often drops deep and concedes chances of lower quality than the raw shot count suggests.
Is the live market slow to react to a sending off?
The direction is instant. The size is what varies, because it depends on game state in ways an automated adjustment handles crudely.