The Same Card, Sized Two Ways

Tuesday's card is posted as five plays for 7 units. It risks 9.27. Nobody is hiding anything: the card is quoted in units to win, which is a completely standard convention and the one most published records use. But quoting a card that way and sizing a card that way are two different decisions, and only one of them is bookkeeping.

Here is the argument in one line. Sizing to win means your stake goes up automatically as the price gets worse, and it goes down automatically when you find a plus number. That is a leverage rule, and it runs in the opposite direction from where the value usually sits.

The convention in use is the common one: every figure is units to win, except on a plus number, where the figure is what is risked. That exception is why the Petco under reads "risking 1 unit" and nothing else does.

Tyler Glasnow carries a 2.72 ERA, a 0.83 WHIP and a .149 opponent average into Truist Park. The Dodgers moneyline at -148 is the smallest return on the card and the second smallest risk. Photo: Reunion, Wikimedia Commons, CC BY 4.0

Take the identical five selections and size them the other way: risk the stated number instead of winning it. Nothing about the opinions changes, only the stake.

Six tenths of a percentage point. That is the entire difference in break even, and it is the reason most people conclude the choice does not matter much. On the aggregate number they are right.

The two most expensive tickets on the board, both at -148 and one at -140, absorb 70.6 percent of the risk under the to win convention and 64.3 percent under the other one. The only plus number on the card drops from 14.3 percent of the exposure down to 10.8 percent.

That is the mechanical consequence and it is worth staring at. To win sizing takes money away from the cheapest price on the card and hands it to the most expensive ones, purely because they are expensive. No opinion was expressed in that transfer. It happened as arithmetic.

There is a real defense and it is not a weak one. A published record is measured in units won and lost. If every ticket is sized to win the same amount, then every ticket contributes to the record in proportion to the conviction stated next to it, and a 2 unit play means the same thing whether the price is -110 or -180.

Size by risk instead and a 2 unit play at -180 contributes 1.11 units to a winning day while a 2 unit play at +150 contributes 3. The stated conviction and the recorded outcome stop lining up. For anybody publishing a record that other people read, that is a serious cost.

So the honest summary is that to win sizing buys interpretability of the record and pays for it with leverage that scales with price. Risk sizing buys constant exposure per opinion and pays for it with a record whose units stop meaning one thing.

The failure mode is not a card like this one. Spread across -115 to -148, the two conventions differ by 2.27 units of risk on a 9 unit day, and neither one is going to be the reason the day wins or loses.

It bites at the extremes. A 2 unit play at -300 costs 6 units to win 2. Under the other convention it costs 2 to win 0.67. Same opinion, three times the money, and the price that triggered the tripling is exactly the price at which most heavy favorites stop being worth backing. Anybody using a to win convention should have an explicit rule for what happens past about -200, because otherwise the convention is quietly sizing the worst prices on the board the largest.

Read it as 9.27 units at risk, not 7. Three of the five tickets need better than 58 percent on their own, and the whole card needs 56.8 percent to come out flat. The largest single exposure on the day is the Angels team total under 3.5 at 2.96 units, which is 31.9 percent of the card sitting on one lineup being held to three runs.

None of that is an argument against the selections. It is an argument for knowing which number you are actually quoting when you say a card is 7 units.