What REALLY Happens When You Ladder a Prop

Chaos is a ladder. Chaos isn't a pit. Chaos is a ladder. That works for dragon-based political intrigue, and it works for sports betting. Prop ladder plays try to turn a single opinion into massive profits. But, what's really going on inside these bets, and why do they actually cost you money? If you don't know what these bets are, a ladder is when you make several bets at increasing milestones on a single prop type. A receiver to have over 74 and 1/2 yards, as well as 80 plus, 85 plus, and 90 plus yards. That sort of thing. Ladders seem like you're baking in a bigger reward for being more right.

But, that's not quite what's happening here. Today, I'm going to show you what really happens under the hood when you build a ladder. We'll look at how laddering sort of looks like the stock market, where it goes wrong, and what you can do instead to truly maximize your ROI on your prop opinions. And, we'll get into the three times that ladder bets do actually make sense. Don't get me wrong. I get that a big part of the appeal of these bets is that they're fun. Once you hit the first rung, it's like you're in the bonus round.

Here's one you could have done with Shohei Ohtani strikeouts. Starting with over 6 and 1/2 at minus 146, and going all the way up to over 10 and 1/2 at 9 to 1. That's five rungs to climb, but if you bet $20 on each rung, you'd need him to hit nine strikeouts before you'd win a nickel, and you're piling on more vig on your plate as you go. That's the biggest problem with building ladders.

But, first, let's talk about the upside, and how it works a lot like options trading.

Ladders Going Up

If your guy goes off for a day, your payouts skyrocket. That's why these things are so popular. You're hoping to ride a convex payout structure. Your risk is the same as it is in a basic prop. You bet $100 on over 6 and 1/2, or spread out that $100 betting up the ladder. Either way, your downside is capped at $100. But, the ladder offers a lot more upside if you reach the highest rungs. It's the same way stock options work in the market. You're buying different strike prices. For instance, if Nvidia is trading at 198, and you think it's about to take off, you can buy options at 200, 205, 210, and 215.

If Nvidia is at 205 by your target date, you can sell some of your options and turn a tidy profit. If it balloons to 225, you make a pile. Ladder bets have the same basic structure. In the Ohtani game, the main prop line of 6 and 1/2 made sense, but you expect much more on this night because the one detail I didn't mention, he was facing the Mets. And if there's one thing we know, it's that the Mets always go full Mets. So, Ohtani's alternate prop markets let you find strike prices in strikeouts. If he throws 11 strikeouts, your ladder could profit over $370.

That's $370 in upside for just $100 risked, as opposed to settling for his main line prop, where that same $100 would only net you about $68. I'm not begging, but I'm not begging, either. Anyway, part of the reason that you're able to get that kind of payout on the high end is because the distribution here isn't actually a nice normal bell curve. Instead, there's a big spike on the left side that represents cases where a guy gets hurt, or he uses the ball to club someone on the other team in a brawl like he's in the street fight scene in Anchorman.

After that, you have a more normal distribution of outcomes, but the entire thing ends up being right skewed, which means there's more opportunity to cash in on those rare times that a player blows past his number. The upside sounds nice. So, what's the problem, exactly? Well, for starters, it preys on the same instinct that drives parlays.

Ladders Going Down

You bet a little to win a lot, and you make correlation work for you. But, here, the correlation has already been priced in. The books are well aware of how it works. You're not compounding a stake. Instead, you're making a series of independent bets on each rung. And, that's why ladders really treat your bankroll like a Margaritaville mermaid. You see, it's a it's a giant blender. It's a gimmick for Jimmy Buffett fans. Just ask your dad about it. It's because you're paying vig on each bet. And, as those bets go higher up the ladder, the more each rung carries more vig, especially after you move past two-way props. At least then, you can see exactly how much juice you're paying.

When you get to the higher rungs, they become one-way markets, where the books can hide all the vig they want. It's hard to figure out just how bad it is, but we can approximate it. So, let's look at those Ohtani rungs again. The price on the main line at DraftKings was minus 146 to the over, and plus 114 to the under. That bet had a theoretical hold of a little under 6%. It also implies the book uses a mean projection between 6.8 and 6.9.

Now, we can use that projection number to work out the fair prices on each of the other rungs, and compare that to the book prices that were being offered. And the discrepancy between the book and the fair lets us ballpark the vig on each rung of the ladder. So, if you got a fair price of over 6 and 1/2, you'd win $78.70. At minus 146, you win 68.50. Betting one line means you're short about $10.

But, now look what happens if you go rung by rung, paying vig on multiple bets. Betting $20 rungs, you're short about two bucks on the main line. Fine. But, when it gets to 9 and 1/2, you get paid 96 when the fair price is $123. Overall, you're giving up about $100 compared to the fair prices. The whole reason you built the ladder were for the tail payouts. The 9 and 1/2 and 10 and 1/2 strikeout rungs, where Ohtani goes nuclear and turns $100 into $370 for you.

But, look where the biggest gap between book and fair is. It's on those exact rungs. The ones you built the ladder for are the ones that also hurt you the most. You're compounding something with these bets, but it's not your edge. So, maybe you think, "Okay, fine. I'll just weigh the base heavier, more money on the main line, and less on the higher rungs." So, let's say you take graduated steps, where you bet $40 at 6 and 1/2, 25 at 7 and 1/2, 15 at 8 and 1/2, and $10 each at 9 and 1/2 and 10 and 1/2. You do lower the amount you're surrendering, but only to about $57.

The good news is that you do better on nights where a player only hits a couple of rungs. $20 bets on each rung didn't show a profit until you hit nine strikeouts. When you weigh your ladder heavier at the base, you're profitable at eight strikeouts. You don't need quite as big a night out of Ohtani to make money. You limit the amount you give up in vig, and you make it easier to turn a profit, but you also cap your upside on the tails, which is where you make the real money for being more correct.

In other words, you made a regular bet with a couple of lottery tickets stapled to it, and you didn't even really maximize the lottery's potential. You're like the guy in the 7-Eleven playing the sad pick four tickets. If you're going to buy the ticket, make the ride worth it, right? The vig takes bigger bites the higher you go. You have to do contortions to get a bet to a reasonable break-even point, and there's a lot of uncertainty around the tails. Laddering isn't really about being rewarded for being more right, it's about being more right under the right circumstances. And, there are a few of those circumstances.

Three Times to Use Ladders

First, fundamental pricing issues create the most obvious one. If a book just absolutely collapses in its pricing, laddering will let you scoop up multiple rungs, so you can maximize your exposure to a bad price in the short window before it gets corrected. Another reason would be if your projections are just that much sharper, and your model distribution has fatter tails than the market is pricing. You need that variance around a performance to be fundamentally different than the way the books would price the normal part of the distribution, though. Or, a ladder makes sense if you can just identify a correlation mechanism that the books aren't pricing in.

Say it's the last game of the season, and an ace is pitching to get his team into the playoffs. His normal strikeout prop line is 7 and 1/2, minus 115 to the over. He's a righty starter facing a team that's usually lefty heavy, but there was a late scratch of a big left-handed bat, and instead, the opponent has to send in a righty with a worse than average platoon split. The book still shows 7 and 1/2 minus 115. It's pricing this like it's a normal game, but it's not. You have a pitcher who's likely to go deeper into the game if he's pitching well, and a circumstance that enables him to do it as well.

So, it's a positive feedback loop. The deeper he goes, the more batters he faces and the lineup is already weaker than normal. It's a recipe for more batters faced and a higher K rate per batter. Therefore, the whole distribution shifts to the right and spreads out. But, unless you have one of those circumstances, what's the best thing that you can do? Well, let's pick the best, most mispriced rung of all of them and attack it. What you give up in convexity, you make up for in raw expected value. And over time, that's going to put more money in your pocket than those occasional times where a pitcher goes off for 10 plus strikeout.

The concepts in laddering are similar to the issues with another kind of popular bet. Same lottery mentality, same distortion of EV, and the same long-term hole if you bet too many same game parlays.