Market Impact explained for betting

In one sentence

Market impact is the price you pay for size: the bigger your bet relative to the money waiting, the further down the ladder you go and the worse your average odds.

How it works

When you back at the best available price you are taking money that layers left waiting in the blue column. If your stake is bigger than what sits at that price, the rest is matched at the next price down, and so on. This is called walking the ladder.

There are two kinds of impact. Temporary impact is the slippage on your own fill. Permanent impact is when other traders see the price move and the whole market resets, which also matters if you plan to add more later.

Professional markets often use a rule of thumb called the square-root law: impact grows roughly with the square root of your size relative to typical volume. Doubling your stake does not double the cost, but it does not come free either.

The maths

\bar{o} = \frac{\sum_{i} s_{i} \, o_{i}}{\sum_{i} s_{i}}

\Delta \approx Y \, \sigma \sqrt{\frac{Q}{V}}

ō: your average matched odds.
si: the stake matched at price level i.
oi: the odds at that level.
Δ: the expected price impact of your order.
Y: a constant fitted from data, usually of order 1.
σ: the market's typical volatility over the period.
Q: your order size; V: the typical volume traded over the same period.

In plain English: your average odds are a stake-weighted mix of every level you hit, and the damage grows with the square root of how big you are relative to the market.

Worked betting example

Pre-match, you want to back the home team in a Match Odds market for £1,500. The blue "available to back" column shows:

4.0: £600
3.95: £500
3.90: £800

(Between 3 and 4 Betfair ticks are 0.05 apart.)

Your fill:

£600 at 4.0 returns £2,400.
£500 at 3.95 returns £1,975.
£400 at 3.90 returns £1,560.

Total return if it wins = £5,935. Average odds = 5,935 ÷ 1,500 ≈ 3.957.

Profit if it wins = £4,435. Had all £1,500 been matched at 4.0, profit would be £4,500. The impact cost is £65 of winnings.

In probability terms you paid 25.27% instead of 25.00%. If your model rates the home win at 26% (illustrative), expected profit after 2% commission falls from about 2.4p to 1.3p per £1 staked, so impact takes almost half the edge before kick-off.

Where it's good

Deciding the largest stake a market can take before your edge disappears.
Splitting a large order into smaller pieces or using unmatched bets instead of taking prices.
Choosing between markets: the same bet in match odds versus Asian handicap can have very different impact.
Sizing Kelly stakes realistically, since Kelly assumes you get the quoted odds on every pound.

Limitations and pitfalls

The visible ladder is not the true depth: money appears and disappears as you trade, and some is placed by bots reacting to you.
The square-root law is an empirical rule from financial markets; its constant must be fitted for Betfair and each market separately.
Permanent impact is hard to measure because the market moves for many reasons at once.
Backtests that assume you got the displayed best price overstate profits, sometimes massively.

How to build it

Store full ladder snapshots from the Betfair Stream API via betfairlightweight, then simulate walking the ladder for different stake sizes.
Fit the square-root rule with numpy or statsmodels on your own past fills against recent volume and volatility.
Tip: always include simulated impact in backtests, using the ladder as it stood at the time of the bet.

Order book imbalance shows how thin each side is before you trade.
Queue position is the alternative: wait in line rather than pay impact.
Tick size maths sets how far each level down the ladder costs you.
Kelly criterion sizes stakes, and impact limits how far you can follow it.