American Odds Ladder: Implied Probability by Price Step

The American odds ladder is the ordered set of prices a sportsbook can quote, such as -105, -110, -115 and -120 for favorites and +100, +105, +110 for underdogs. Each rung of the ladder corresponds to one implied probability, and moving a single rung changes that probability by a small, predictable amount. Near even money, one 5-point step shifts implied probability by roughly one percentage point: 52.38% at -110 becomes 53.49% at -115. The ladder also has a hole in the middle, because no price is quoted between -100 and +100. This article walks the ladder rung by rung, computes the probability change at each step with the standard formulas, explains why the steps shrink in probability terms as prices lengthen, and describes why books quote in increments and skip the middle of the number line. It does not teach the basics of reading a price, which are covered in how to read American odds. All prices here are hypothetical illustrations, not current sportsbook lines.

What the American Odds Ladder Is

A ladder is a useful picture because American odds are not a continuous scale a bettor can slide along. A sportsbook picks from a menu of discrete prices, and every price on the menu is a distinct implied probability. Favorite prices climb as -100, -105, -110, -115, and so on, while underdog prices climb as +100, +105, +110, +115, and so on. Moving up either side makes the quoted team look less like an even-money proposition and more like a clear favorite or a long shot.

The two sides meet at even money. A price of -100 and a price of +100 describe the same bet, risking $100 to win $100, and both carry a 50.00% implied probability. A bettor who wants the full story on that price point can read about even money betting. From there, the ladder runs outward in two directions but the number line itself has a jump in it, because nothing sits between +100 and -100. The jump is a quirk of how the two formats are written, not a gap in probability, a point examined from a different angle in the guide to plus and minus odds.

Understanding the ladder helps with a practical question: when a price changes by one rung, how much has the market really said? A one-rung move is a small statement near even money and an even smaller one far from it. The next section puts numbers on that.

American Odds to Implied Probability, Step by Step

Converting a price to a probability uses two formulas, one for each sign. For a favorite with negative odds, implied probability equals the absolute value of the odds divided by the absolute value plus 100. For an underdog with positive odds, it equals 100 divided by the odds plus 100. The result is the break-even win rate for that price: the share of equal-priced bets that must win before the price stops costing money, before considering any other variable. The wider concept is explained in the article on implied probability in sports betting.

The American odds to implied probability formula, applied to a ladder

Take -110. The calculation is 110 divided by 210, which is 52.38%. Take -115: 115 divided by 215 is 53.49%. The step between them is 1.11 percentage points. On the underdog side, +110 is 100 divided by 210, or 47.62%, and +115 is 100 divided by 215, or 46.51%. Each rung on either side moves the probability by about one point, as the table below shows for the first six steps from even money.

Read the table across a row to see that a favorite price and its numerically matching underdog price sit on opposite sides of 50.00%. The final column shows that the step size shrinks as you move away from even money: the first step changes probability by 1.22 points on the favorite side, while the sixth changes it by 0.97 points. The pattern is gentle here because the table covers only a short stretch of the ladder. The next sections show how much faster it shrinks at longer prices.

Worked Example: What One Step Costs

Suppose, hypothetically, a bettor compares three prices on a two-way market that would be a coin flip if the true chance were exactly 50%: -105, -110 and -120. The break-even rates are 51.22%, 52.38% and 54.55%. Each 5-point step adds roughly one point to the bar a bettor must clear, so -120 asks for 3.33 more percentage points of winning than -105 does.

Now look at the cost in dollars. Assume the true win chance is exactly 50% and the bet is sized to win $100. At -105 the bettor risks $105, so the expected result is 0.50 x $100 minus 0.50 x $105, which is -$2.50. At -110 it is -$5.00, at -115 it is -$7.50, and at -120 it is -$10.00. Every 5-point step costs another $2.50 on a bet to win $100, a straight-line increase in dollars even though the change in probability is a curve.

These are averages, not predictions. A single bet at -105 can lose and a single bet at -120 can win, and a short run of results says almost nothing about which price was cheaper. The point of the example is that the ladder prices a bet’s cost: a rung closer to even money lowers the toll, and a rung farther away raises it. The same logic is applied to full markets in the discussion of reduced juice. Lower cost does not turn a bet into a good one, and no price removes variance.

Implied Probability Chart: Same Step, Different Size

A natural assumption is that a 5-point step is always worth the same. It is not. The probability change per step falls sharply as prices lengthen, because both formulas have the odds in the denominator. The table below applies a single 5-point step at several points on the ladder, using the same formulas as before.

Near even money a step moves probability by 1.22 points. At -500 the same step moves it by 0.14 points, and at +1000 by only 0.04. A step near even money carries about 9 times the information of a step at -500, since 1.22 divided by 0.14 is roughly 8.9. The favorite and underdog sides mirror each other near the middle, and both flatten toward the extremes.

This has a direct consequence for reading price movement. If a line shifts from -110 to -120, implied probability rises 2.16 points. A move from -500 to -510 changes it by only 0.27 points. The same numeric move can be large or trivial depending on where it happens, which is why bettors who track line movement usually convert prices to probabilities before judging a move.

Why Prices Move in Steps and Skip the Dead Zone

Books quote in steps for practical reasons rather than any single rule. A discrete menu of prices is easy to display, easy to compare, and easy to adjust quickly when the money is lopsided. Near even money, a 5-point increment moves probability by about one point, which is enough to be meaningful and small enough not to overreact. Conventions vary by book and by market, and some sportsbooks list finer steps, such as -112 or -118, in certain markets, so the 5-point ladder shown here is a common pattern rather than a universal law.

Longer prices commonly use wider increments. Because a 5-point step is nearly invisible at +1000, books tend to move in bigger jumps there. A move from +1000 to +1100 changes implied probability by 0.76 points, and a move from +500 to +550 changes it by 1.28 points. Wider steps at long prices restore a step size close to the one-point steps seen near even money, so the ladder stays roughly even in probability terms across its length.

The dead zone has a similar explanation. There is no -50 or +50 because a price of -100 already means risking $100 to win $100, and a price of +100 means the same thing. Anything between would not describe a different bet. Crossing the gap is a real step, though. A move from -105 to +105 changes implied probability from 51.22% to 48.78%, a change of 2.44 points, exactly two ordinary steps even though the numbers appear 210 apart. The relationship of these cents to market margin is covered in the explanation of the dime line and 20-cent line.

Common Mistakes When Reading Price Steps

The most common error is treating the numeric distance between two prices as the distance in probability. A 5-point step is not a fixed amount: it is 1.22 points near even money and 0.14 points at -500. Comparing two moves by their raw difference in odds numbers will mislead.

A second mistake is reading the jump across the dead zone as huge. Going from -105 to +105 looks like a 210-point change on the screen, but it equals 2.44 percentage points of probability. The screen exaggerates the move because the number line skips from minus to plus without any intermediate values.

A third is assuming that a price one step cheaper is automatically good value. Moving from -110 to -105 lowers the break-even rate from 52.38% to 51.22%, but a bettor still needs a true win chance above that bar, and any estimate of the true chance is uncertain. A fourth is believing that small steps do not matter. Over many bets, a one-point difference in break-even rate compounds, which is why the steps are worth understanding, yet no step makes losing runs disappear. Wagering should only ever involve money a person can afford to lose.

Where the Ladder Shows Up at the Sportsbook

On a real odds board, the ladder shows up as the prices on each side of a market. A typical two-way line lists a favorite and an underdog, and the two prices are usually a few rungs apart rather than exact opposites. The distance between the rungs on the two sides is the sportsbook’s margin, a topic treated in the guide to the cents between two prices.

When a bettor sees a price change on the board, the useful habit is to convert both the old and new price into probability, subtract, and ask whether the move was large for that part of the ladder. A shift of one rung near -110 is a one-point statement, while the same shift at -500 is a fraction of a point. Converting before comparing avoids reading noise as news.

The bet slip confirms the exact price at the moment of wagering, so the ladder position that matters is the one shown there, not one remembered from earlier. Prices shown in this article are hypothetical and meant only to illustrate the arithmetic.

What to Learn Next

If the ladder made the step sizes clear, the natural next topic is what a single price implies. The article on implied probability explains why that number is a break-even bar and not a forecast. To see how margin is measured across both sides of a market, read about the dime line versus 20-cent line, and to compare how much a rung costs on a single bet, see reduced juice at -105 versus -110.

For the starting point of the ladder itself, the article on even money betting covers the +100 and -100 convention in detail. Knowing how prices step is a small skill, but it makes every later topic in this category easier to read.