The average trendline will have a 45-degree slope as viewed on a typical price chart, but that slope can be steeper or flatter than 45 degrees. Because 45 degrees is the average slope of a trendline, one with a 75-degree slope, for example, will tend to revert back to the 45-degree slope over time. A slope that is greater than 45 degrees typically will not be sustainable for any significant amount of time. Conversely, a slope that is less than the average typically will accelerate (steepen) until it moves back in line with the equilibrium level of the slope.
The 45-degree angle was the most important to Gann and it is represented with a one-to-one movement of time relative to price. Whenever the price of an asset trades in an uptrend (downtrend) and it reaches a prominent top (bottom), the price typically will decline (rally) off of this high (low). W.D. Gann divided this price action into eighths, as well as thirds, and market action would be watched near these levels because of their historical significance.
According to Gann, the most important retracement levels are 50%, 37.5% and 62.5%, ranked in descending order of importance, with the rest of the levels believed to have diminishing importance the further they are from the 50% retracement (see “Retracement table,” right). Some of these retracement levels should be familiar because they are similar to those used in other schools of technical thought, such as Elliott Wave Theory. The 50% retracement is simply one of the most common retracement levels watched by chartists, and the 33% and 67% retracement levels are both used in Dow theory.
With respect to trend angle and the one-to-one relationship between time and price, it is important to think in terms of units of time, and units of price, to understand why the degree of the angle is important. Because the 45-degree angle is represented by a one-to-one relationship between price and time (that is, when time moves forward by one unit, price moves forward by one unit as well), a one-by-two relationship will be equal to 63.75 degrees and, inversely, a two-by-one relationship will be equal to 26.25 degrees, where each inverse relationship is equal to 90 degrees. The one-by-two angle means that as time moves forward by one unit, price moves forward by two units. The two-by-one angle has an inverse relationship (time moves forward by two units as price moves forward by one unit).