← Expected value03 / 05
Activity 03 · Five prices, one night

EV on a
ladder

A goalscorer board looks like five bets sitting next to each other. It's one distribution sliced five ways — and the margin is not spread evenly across it. Find out which rung is quietly the worst price on the screen.

Snapshot · AFL match markets · 20 August 2026
Goalscorers
SGM
Player / Last 5
2+
3+
4+
5+
6+
34
Ben King
13222
1.47
2.45
5.00
12.00
34.00
31
Liam Ryan
22111
1.55
2.75
6.00
15.00
41.00
break-even %  =  100 ÷ decimal odds
Part one · Ten cells
RungOddsBreak-even %

Three to sit on before you check. Ben King can also kick nought, or exactly one — neither is on this board, and both happen. So: add his five answers together and you get 140. What does that number actually represent? Where do nought and one live in it? And if you divided every rung by 140 to strip the margin out, what would you have built?

Three things this board hides

You can't add a ladder up

King's five numbers total 140%. That is not a 40% margin. These outcomes are nested, not competing — kick four and you've also won the 2+ and the 3+. Adding a two-way market tells you the margin. Adding a ladder tells you nothing.

What you can do is subtract. Each rung minus the one above it gives exact goals:

Exactly 2  =  68.0 − 40.8  =  27.2%
Exactly 3  =  40.8 − 20.0  =  20.8%
Exactly 4  =  20.0 − 8.3  =  11.7%
Exactly 5  =  8.3 − 2.9  =  5.4%
6 or more  =  2.9%
0 or 1 goal  =  100 − 68.0  =  32.0% Total: 100%

Those add to 100. Now you're looking at a distribution instead of a price board, and you can ask whether it matches the night you think he's going to have.

Check the shape before you pick a method

This is the part that costs people money without them noticing. In Activity 04 you'll strip a margin out by dividing every price through by the board total. It works, and it's the standard method. It would produce garbage here.

Dividing through assumes the outcomes are mutually exclusive and exhaustive — exactly one of them happens, and one of them definitely does. A head-to-head qualifies: Detroit or Boston, no third option. A premiership market qualifies once every club is on screen.

A ladder qualifies for neither. The rungs overlap, so exactly one doesn't happen — a four-goal night wins three rungs at once. Total them and you get 140%, which looks like a margin and isn't. Divide through by 140 and you'd hand yourself five confident numbers that describe nothing.

Two-way market  →  competing outcomes  →  divide through
Full field  →  competing outcomes  →  divide through
Goalscorer ladder  →  nested outcomes  →  subtract adjacent rungs Same arithmetic, wrong shape, confident wrong answer

A confident wrong answer is worse than no answer, because you'll act on it. So the question before any de-vig is never what's the formula — it's what shape is this market? Get that wrong and everything downstream is fiction, no matter how clean the maths looks.

The biggest outcome has no price on it

Look at that list again. The single likeliest thing Ben King does on Saturday is kick nought or one — 32% of the time, comfortably bigger than any other slice. And there is no price for it anywhere on this board.

That's not an oversight. Ladders are built to sell the upside, so the board starts at 2+ and climbs. The downside is left implied, and because it's implied most people never look at it. When you say King's a good chance of a bag tonight, the board agrees with you at 68%. It also says he goes quiet nearly a third of the time and offers you nothing to think about it.

Two practical consequences. First, the 32% is where your EV actually lives — every rung on that ladder is a bet against it, so if your read on how quiet he goes differs from the market's, that disagreement flows into all five prices at once. Second, you can't split 0 from 1 using this board. There's no 1+ rung. If you want that split you need the anytime goalscorer market, which is usually the same screen a few markets up, and 100 ÷ that price gives you P(1+). Subtract it from 100 and you finally have P(nought) on its own.

Worth doing, because they're very different nights. A forward held goalless is usually a matchup or a tagging story. One goal is often the same good night with worse luck in front of goal. The board treats them as one lump, but your read on the game shouldn't.

Four from five is not 80%

King has kicked 2+ in four of his last five and the market says 68%. Free money? No. If his true rate were exactly 68%, hitting four from five happens about 43% of the time by chance alone. That sample tells you nothing the market doesn't already know. Five games is a headline, not evidence — and a headline plugged into the EV formula gives you a confident wrong answer.

The margin lives in the tail

Margin isn't spread evenly across a ladder. It's loaded into the big numbers, because that's where punters overpay. A board carrying 4.3% on a head-to-head might run 3% on the 2+ rung and 15% or more on the 6+. Same board, wildly different prices. The 34.00 and the 41.00 are almost always the worst value on screen — and they're the two that look the most generous.

What the market thinks about going again

Divide each rung by the one below it and you get the market's view of given he's got there, does he keep going:

ConditionalKingRyan
3+ given 2+60.0%56.4%
4+ given 3+49.0%45.8%
5+ given 4+41.7%40.0%
6+ given 5+35.3%36.6%

The decline is the model saying a big bag needs the game to keep cooperating. If you disagree with that shape — you think he's up against a side that'll bury it inside 50 all day — your disagreement lives on the top rungs, not the bottom one.

Part two · Build King's night

Enter your own percentage for each rung. EV recalculates live, the distribution rebuilds underneath, and anything that beats the price lights up.

Rung
Your %
Odds
Your EV

Your distribution

The top bar is the one with no price on it. Nothing on this board lets you back it or split nought from one — but it's the biggest number in your distribution, and every rung below is a bet against it. If it looks wrong to you, all five of your EV figures are downstream of that.

A negative slice means you've said a bigger bag is likelier than a smaller one. That can't be true — every four-goal night is also a three-goal night. If your rungs don't step down, your EV numbers are fiction.