Revisiting Aoristic Analysis

by Joseph Ryan Glover

Attention users of I have retired the web tool and replaced it with a downloadable Excel spreadsheet. Discussion and reasoning below.

Back in 2012 I wrote a post about Aoristic Analysis where I introduced a web-based tool for conducting aoristic analysis. The reason I built the tool as a web page was that the code allowed me to split events down to the second so that they could be properly apportioned across time units. The drawback of making a web based tool is that law enforcement analysts, typically a suspicious bunch, never liked the idea of submitting their data (which is only dates, by the way, it is completely context-less) to a web server. Fair enough, we’re a paranoid bunch.

I recently had an email discussion with someone who was using my tool but wished they could have some software to do the work locally. I resolved to create an Excel version of the tool that would work in seconds like the web site. I have completed that work and the result is now available for download here: Aoristic_v3.xlsm.

The spreadsheet is a macro-enabled XLSM and that’s because I use VBA to perform the aoristic analysis. There are three custom functions –  AoristicHourOfDay, AoristicDayOfWeek and AoristicMonthOfYear  – and all the code in the spreadsheet can be seen in the following GitHub GIST:

Understanding the Code

If you open the XSLM file you will notice that there are worksheets with example usage of each of the functions. Since all three functions follow a similar approach I will discuss the logic behind AoristicHourOfDay used on the ‘Hour of Day’ sheet.


The ‘Hour of Day’ sheet has in column B the start time for an event and in column C the end time for the event. Following that there are 24 columns, one for each hour of the day, where the AoristicHourOfDay function is called. Looking at the embedded code above you can see on line 23 the function declaration for AorisiticHourOfDay and that it accepts a start and end time as well as the particular hour of interest for calculation.

I will now go through the function line by line to explain the reasoning behind it:

Line 24, 25: The function begins by first determining how many hours and how many seconds have elapsed between the start and end time.

Line 27-30: A check to make sure that the end time is not before the start time. If it is, an error is raised and the function exits.

Line 32-35: Next, the amount of one ‘unit’ is determined by dividing 1 by the number of seconds. Because this code is interested in apportioning an event down to the second, it is necessary to be able to assign units down to the second. For example, say an event was 2 hours long (7200 seconds) then every second is worth 1/7200 of the total event.

Line 37: A variable captures the starting hour based on the event start time.

Line 39-41: The code checks to see if the total number of hours for the event is 1 and the hour passed into the function is the start hour. If both of these conditions are met then the hour should be assigned the entire event (i.e. a value of 1) and the function can safely exit. This is the trivial case.

Line 43-68: If these conditions are not met then the more elaborate assignment method is used. The aoristic variable for this hour is initialized to 0 and a variable for the current hour is initialized to the starting hour for the event. Next, a for loop is initiated that loops from 1 to the total number of hours calculated for the event.

There is a lot going in this for loop so I will break it down, section by section.

Line 45: Within the loop the code first checks to see if the current hour equals the hour passed into the function. If the hours match it means that we need to assign some portion of the event to the hour.

Line 47-51: Next, the code checks to see if the current hour is equal to the start hour and if it matches the code determines the remaining seconds in the hour and assigns that to the share variable. The reason this is done is because, for the start hour, we only want the balance of the hour assigned and to determine the balance of the hour we need to subtract the current number of minutes and seconds from 3600, the number of seconds in an hour.

Line 53-55: Next the code checks to see if the loop counter is greater than 1 and less than the total number of hours. If this is the case the hour is given 3600 seconds. The reasoning here is that if the hour matches and the event started at an earlier hour and ends at a later hour then the event existed across this particular hour and should therefore be assigned a full 3600 seconds.

Line 57-61: The final if statement checks to see if the loop counter is equal to the total number of hours. This is the same as asking if it matches the last hour and if it does we include only those seconds in the part of the hour before the event ended. This is kind of like the reverse of the reasoning for the first if statement.

Line 62: After each of the if statements are complete the variable for tracking the aoristic total for the hour is incremented by adding to it the value of the share multiplied by the unit calculated above.

Line 64-67: Outside the if statement the current hour variable is incremented and reset to 0 if it passes the 24 hour mark.

One thing people may be curious about is why I did this in loop instead of just checking with the if statements and that has to do with the fact that an event can span days and therefore the same hour could be hit again and again. The loop allows for this calculation in a way that the if statements on their own could not.

Wrapping Up

The sample spreadsheet has a lot of example scenarios that illustrate different edge cases for the code. The key check on each of them is that the sum total of the values for all 24 hours should sum to 1. Excel also makes it easy to calculate percentages by hand and compare them to what the code has spit out. Having said that, while I have tested it to my satisfaction there is always the possibility for error. If you come across any odd behaviour or incorrect results please let me know and I will fix it and put a new version up.

I think this Excel method is superior to the web based tool as it allows the same level of detail as the web page plus it allows analysts to look directly under the hood and see how the work is being done. Best of all, you can download the spreadsheet and run everything locally and not have to worry about submitting sensitive data over the web.

One final tip: if instead of the share of event you want to instead know total time spent in each hour, create a new column that contains the event duration in seconds and multiply that by each of the portions in each of the hours. This new table will then show how much time was spent in each hour for each event.