Williams Alligator: Smoothed Averages Pushed Into the Future

The Williams Alligator draws three lines over the price chart, coloured blue, red and green, and named after the jaw, the teeth and the lips of the animal.

Published accounts describe them as three moving averages of different lengths, and read the moment they separate as the start of a trend. Two things are missing from that description, and both are written into the formula itself.

Each line carries a third parameter that has nothing to do with its length: a shift into the future. And the shift is a different size on each of the three lines. The result is that the segment of each line sitting beside the newest price bar was computed from data that stopped 8, 5 or 3 bars earlier, so the three lines beside that bar are not three views of one moment.

This page states what the documentation defines, works out what the displacement does to anything read at the right edge of the chart, and identifies where the trend-frequency figure attached to this indicator actually comes from.

What the Three Lines Actually Contain

The platform documentation defines the three lines in one block, and each definition has the same shape: a smoothed moving average, a length, and a shift.

The Jaw is the blue line and is written SMMA(median price, 13, 8). The Teeth is the red line, SMMA(median price, 8, 5). The Lips is the green line, SMMA(median price, 5, 3). In that notation the first argument is the data being smoothed, the second is the smoothing period, and the third is the shift into the future, counted in bars.

The data argument is the same on all three lines: median price, which the documentation defines as the midpoint between the bar high and the bar low. The close never enters the calculation. A reader who has met that input before will have met it on the other Bill Williams indicator built on median price, which is where the properties of that input are set out in full; here it matters only as the shared starting point for all three lines.

What separates the lines is therefore two numbers each, and only one of the two is a length. Descriptions built on how a moving average is constructed account for the first number and quietly drop the second. The rest of this page is mostly about the second.

Each Line Is Drawn Ahead of the Data That Produced It

A shift into the future moves a line to the right along the time axis after it has been calculated. Nothing about the calculation changes. The value that would have been plotted at one bar is plotted at a later one instead.

For the Jaw the shift is 8 bars. The smoothed average is computed bar by bar in the ordinary way, and then the whole series is moved 8 bars to the right. The value now sitting above the newest price bar is the value the average reached 8 bars ago. The same holds for the Teeth at 5 bars and the Lips at 3.

Two visible consequences follow, and the first is easy to see once it is named. The three lines extend past the newest price bar into empty chart space, 8 bars for the Jaw, 5 for the Teeth and 3 for the Lips. Those extending segments are not forecasts. They are old values that have been carried forward, and they will not change no matter what price does next.

The second consequence is the one that affects reading. Whatever the lines appear to be doing beside the current bar, they are doing it with data that stopped several bars ago. A separation that looks like it began on the newest bar began, in the underlying averages, at least three bars earlier for the Lips and eight for the Jaw. The chart shows the arrangement late, and by a different amount on each line.

This is a property of the indicator as documented, not a setting to be corrected. The displacement is what the third argument does, and removing it produces a different indicator with three plain averages on median price.

At the Right Edge, the Three Lines Describe Three Different Moments

Because the three shifts are 8, 5 and 3, the misalignment is not uniform. At any bar on the chart, the Jaw reports the smoothed median price as it stood 8 bars before that point, the Teeth as it stood 5 bars before, and the Lips as it stood 3 bars before.

The three lines beside the newest bar therefore describe the market at three separate moments, five bars apart from end to end. Their vertical order at that bar is a comparison across time as much as a comparison across smoothing lengths.

The practical case is the crossing. When the green Lips line crosses the red Teeth line at the right edge of the chart, the two values being compared were produced 3 bars and 5 bars ago respectively. The crossing is a plotted event, and it is real, but the relationship it represents between the two underlying averages settled two bars apart and both before the newest bar closed.

On a chart with wide bars the gap matters more than on a chart with narrow ones, because eight bars of a daily chart cover eight sessions of price movement while eight bars of a one-minute chart cover eight minutes.

Smoothed Averages Do Not Drop Old Bars

The second word in the definition is the one most often lost. These are smoothed moving averages, and the platform documentation gives the smoothed formula separately from the simple one.

A simple moving average of length 13 adds the last 13 values and divides by 13. When a fourteenth bar arrives the oldest of the 13 leaves the calculation entirely and stops affecting the result.

The documented smoothed average works differently. Its first value is a simple average, and every value after that is built from the previous smoothed value plus the newest price, divided by the period. Because each result feeds the next, no bar is ever removed. Its influence shrinks with every step and never reaches zero.

Two things follow for a reader comparing indicators. A smoothed average of length 13 does not behave like a simple average of length 13; it responds more slowly, and it carries a longer memory than its period suggests.

The general formula in the documentation is also written on the closing price, while the Alligator substitutes median price through the data argument. Both the smoothing method and the input therefore differ from the plainest reading of the word average.

Anyone working through how the common indicator families are grouped will find that this pair of substitutions, rather than the animal metaphor, is what separates these three lines from three ordinary averages.

Reading the Three Phases Without the Missing Statistic

The documentation describes the indicator through three states of the animal. The lines closed or intertwined is described as sleeping. The lines opening is described as waking and feeding. The lines coming back together is described as the appetite fading.

Underneath the metaphor those states are geometric and can be stated plainly. Intertwined lines mean the smoothed median price over 13, 8 and 5 bars is at nearly the same level, allowing for the different displacement on each. Separated lines in a consistent vertical order mean those three averages stand apart. Converging lines mean the gap is closing.

What the documentation does not attach to any of these states is a frequency, a duration or an outcome. It does not say how long a sleeping phase lasts, how often a separation persists, or what proportion of separations continue. Published accounts frequently supply those missing quantities themselves, and the sources they cite for them are other published accounts.

Reading the phases as descriptions of what the three averages are doing is supported by the documentation. Reading them as predictions is not, and nothing cited on this page establishes a success rate for any of them. The same caution applies to instruments that describe where trading activity concentrated, such as a volume-weighted average price line: a description of what has happened is not a statement about what follows.

Settings People Change, and What Changing Them Costs

Both numbers on each line are editable in the platform, and the two have different effects.

Changing a smoothing period changes how quickly that line responds. Shortening the Jaw from 13 makes the slowest line faster and narrows the spread between the three under the same conditions, which produces more crossings. Lengthening it does the reverse.

Changing a shift changes something else entirely: how far the line is moved along the time axis after calculation. Setting all three shifts to zero removes the displacement and leaves three smoothed averages of median price plotted at the bars that produced them.

The crossings then sit where the underlying values actually met. That is a legitimate chart to read, but it is no longer the indicator the documentation defines, and no published description of Alligator behaviour applies to it.

The point worth holding on to is that these two parameters are frequently discussed as though they were one adjustment. They are not. A period change alters what is measured; a shift change alters only where the measurement is drawn. Comparing a chart with modified settings against any published account requires knowing which of the two was changed.

Where the Trend-Frequency Figure Comes From

One number travels with this indicator almost everywhere it appears: markets are trending between 15 and 30 per cent of the time. Published accounts state it flatly, and typically without a citation.

The figure does have a traceable origin. It appears in the platform documentation for this indicator, inside a passage written in the voice of the indicator author, alongside a description of the reasoning that led to building the tool. It is presented there as a statement by the author, not as the result of a study.

What is absent from it is everything needed to check it. No market is named, no instrument, no timeframe, no sample period and no definition of what counts as a trend. Two charts of the same instrument on different timeframes would produce different answers to that question, and without a definition the number cannot be tested against either. A trend-frequency statistic of this kind is not published by any exchange, standards body or regulator.

That is why the figure appears on this page as an attribution rather than as a fact. It is worth knowing that the number readers keep meeting comes from the author of the indicator rather than from an independent measurement, and it is worth not repeating it as though it described markets generally.

When the Alligator Adds Nothing to a Chart You Already Read

A chart that already carries two or three moving averages of different lengths is already showing the arrangement this indicator shows, without the displacement. Adding the Alligator to it supplies a metaphor and three more lines, not new information.

On very short timeframes the high and the low of a bar often sit a pip or two apart, and median price then stops being meaningfully different from the close. That removes one of the two properties separating these lines from ordinary averages, and leaves only the smoothing.

A reader whose question is where activity concentrated rather than how averages are arranged is asking something these lines cannot answer, and a volume profile addresses that question directly.

The case for keeping it on a chart is narrow and specific: a reader who wants three smoothing lengths compared in a fixed arrangement, who understands that the comparison is offset in time by a different amount on each line, and who treats the phases as descriptions rather than as signals. Anyone reading the right edge as a live event is reading data that is already several bars old.