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Babbitt-LA, On-line Tutorial
Before starting, it is important that you select the same data set that I have used to generate the tutorial. Otherwise, as you follow the subsequent sections, the results you obtain will not match those shown on this page.
Navigate to the Time Trends page.
Configure the Collation form to show the settings in the image below.
The Collation Form
Before we start analysing trends, it is important to know what the time-trends graph means and how to use it. The graph is intuitive to use once you understand the concepts of active and dormant periods.

A ball is in a dormant period if it has not appeared for 1 or more draws.
• if a ball makes an appearance in draw 24 and its next appearance is in draw 27, it has been through a dormant period of 2 draws
• if the same ball makes its next appearance in draw 42, it has been dormant for 14 draws
• dormant periods are contiguous - over time, each ball will continuously exit one dormant period and immediately enter another

A ball is in an active period if it has made consecutive appearances within a given tolerance level
• if a ball makes consecutive appearances in draws 1, 20, 24, 27, 42; it can be considered active between draws 20-27, inclusive
• active periods are distinct - over time, a ball may never enter an active period if it continuously enters long dormant periods

Analysis of time-trends in lottery data is analogous to analysis of form in sport.
A team or player will go through a run of good form (a 'purple patch'), winning several matches in quick succession - this is an active period.
The duration between wins is the dormant period. If the team or player goes without a win for several matches they have entered a bad run of form - their dormant period stretches beyond a tolerance level and the 'purple patch' is considered to have come to an end.

What time-trend analysis gives us, then, is the form of a given ball or combination of balls.


Let's take a look at a trend graph.
Enter number '4' into the time-trends form.
Ensure the 'Lapse active period' setting is set to 5.
The Time Trends form
Press the 'Display' button.
A new window will appear showing the time-trend graph for ball 4, with a active tolerance level of 5 draws.

Trend graph for Ball 4
The chart shows all dormant periods for the range of draws selected. These are shown as orange bars, which extend along the x-axis.
Due to the large range of draws we selected, not all the dormant periods are visible at any one time. Use the scrollbar to scroll left and right and view the whole of the graph.

The y-axis shows the length of each dormant period, in number of draws. So, the higher the orange bar, the longer the dormant period.

Very Important
The y-axis is scaled to maximise use of the graph area.
The longest dormant period for ball 4 is 54 draws, so Babbitt has scaled the y-axis: 0 - 54. If you bring up another graph for a different ball, the y-axis could (probably would) be scaled differently.
It is important to understand that you can only compare heights of bars on the same chart.


First dormant period for Ball 4 To view the details of a dormant period, simply click on the orange bar.
Click the first orange bar

The bar will highlight in a deeper colour.

The details of the dormant period will appear in the space below the time-trends graph. The information tells you how long the ball was dormant for and lists the details of those draws.

Below the x-axis you will notice pale-blue bars, which denote active periods.
Whenever a dormant period is shorter than the active tolerance (in this case, 5 draws), the ball is considered to be active. Active periods will in some cases stretch across several dormant periods. This is denoted by a single blue bar spanning several orange bars.

Fourth active period for Ball 4 To view the details of an active period, simply click on the pale-blue bar.
Click the fourth active period

The bar will highlight in a deeper colour.

The details of the active period will appear in the space below the time-trends graph. The information tells you how many appearances the ball has made over this active period and lists the details of the draws within the active period.

Now that you know how to operate the graph, let's look at ways to analyse the information we're given.
The time-trend tool graph insight into the characteristics of ball appearances over a range of draws.
The pattern of appearances is, of course, very complex and a ball (or combination of balls) may adopt several characteristics over time. For now, however, let's look to analyse some simple trends.
Enter number '44' into the time-trends form.
Ensure the 'Lapse active period' is set to 13.
Press the 'Display' button.
A new window will appear showing the time-trend graph for ball 44 (see below).

The first important thing to note whenever you open a new time-trend graph is the y-scale.
The scale on the y-axis ranges from 0 to 37. It is important to bare this in mind while you view the graph because the scale for each graph will vary and the relevance of the height of each bar in the chart is based on this scale.

Next, look at the flow of the graph; move the scrollbar along to pan across the whole chart.
As you do so, notice the pattern of the active periods (shown by the pale-blue bars below the x-axis).

Trend graph for Ball 44

What this graph shows is that ball 44 follows distinct active and then dormant phases.
Ball 44 appears in long active periods which are (with only one exception) punctuated with a single long dormant period. This is a 'consistent with peaks' characteristic - the length of each dormant period is consistent (small fluctuations) but is periodically interrupted with a long dormant period (sharp spikes).

This is an example of a 'Colorado' graph.


To contrast this style of graph, let's now look at the trend for another ball.
Enter number '33' into the time-trends form.
Ensure the 'Lapse active period' is set to 13.
Press the 'Display' button.
A new window will appear showing the time-trend graph for ball 33 (see below).

Again, first note the y-scale.
The scale on the y-axis ranges from 0 to 24. This is a wider range than the previous graph, so bars will appear to be longer on this graph than the previous one. (for example; a bar that reaches to the top of this graph represents 24 draws, but on the previous graph that bar would only reach two-thirds of the way up the y-axis)

Trend graph for Ball 33

As before scroll along to view the whole graph.

Although this graph is similar in some ways (long adjacent active periods) the dormant periods are far more erratic. The graph shows us that ball 33 follows distinct active periods, but does not follow any pattern in dormant periods.

This is an example of a 'Manhattan' graph.
The active period tolerance is a key parameter to the time-trends tool.

The higher the value, the more active periods will appear. Setting the value too high will cause patterns to appear that are not meaningful. Such superfluous trends can cause confusion and pull your focus away from the important patterns.
Getting the value right is not difficult, it just requires diligence to keep questioning the strength of any pattern found.

Let's take a prime example shown in the previous section.
Here we obtained a time-trends graph for ball 33. The chart showed long active periods, which implies stability. But casting an eye over the dormant periods within each active period, we saw large fluctuations in dormant durations. This indicates the trend is not as strong as first thought and suggests we should re-compile the graph with a tighter tolerance to check this.
Enter number '33' into the time-trends form.
Ensure the 'Lapse active period' is set to 5.
Press the 'Display' button.
Another trend graph for Ball 33 - using a different tolerance

This is the same chart as shown in the previous image, but with a reduced tolerance on active periods.
The affect this has is to remove weak active periods (where the combination appears relatively infrequently) and highlight only strong active periods (where the combination appears very frequently). You can see that in this graph there are fewer, shorter active periods than the previous graph we obtained. But the active periods that have been highlighted are more significant.

Typically you would not set the tolerance level above 12 when looking at trends for a single ball. Beyond this point, active periods become weak and less significant.
You may wish to increase the tolerance above 12 (even as high as 50) when analysing trends for combinations of 2 or more balls.

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