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Originally published January 11, 2007

At the heart of being able to quantify the value of any decision support system (DSS) is the notion that information has a different value based on the time of its first availability. The notion of the time value of information applies to both the macro level and the micro level. In order to see how it applies, two examples are in order.

At the micro level, an organization looks at the details of a customer. The bank manager looks at the credit worthiness of the customer. Suppose the bank manager ranks a customer on a scale of one to ten, where ten equals a good credit risk and one equals a bad credit risk. Of course the rating is important. But equally important is the timeliness of the rating. Suppose a prospective customer walks in and applies for a loan. Before making the loan, the bank officer wants to know the credit rating of the customer. Now suppose the bank officer can get that rating immediately. How much is the credit rating worth when it is available immediately? A lot. Now suppose the bank officer can get the credit rating a day later. How much is the credit rating worth? It is still valuable, but not quite as valuable as it was twenty-four hours ago. Now suppose the credit rating is available a week later. Is it still valuable? It may still have value, but it has far less value than it did a week ago. By now, the customer has probably gone on to other sources for this payday loans. And suppose the information was available a year later. How much is the information worth a year later? In truth, the information is practically worthless. The chances of the credit rating having value a year later are slim.

Information at the macro level also has a diminishing value over time. Suppose the president of the bank wants to know the profitability of the corporation for the quarter right now. The president of the bank is considering making an investment. How much is it worth to the corporation to know the position of profitability right now? It is worth a lot. Now how much is it worth to the president to know the position of profitability tomorrow? The answer is that it depends on the nature of the investment. In some cases, the opportunity for investment has faded. In other cases, the opportunity for investment will still be there. But in any case, there will be a somewhat diminished value the next day. And how much is the information worth a week later? It is worth less. And a year later, the information is practically worthless.

The diminishing value of information at either the micro or macro level over time equation can be depicted by the general graph shown in Figure 1.

**Figure 1**

Figure 1 shows that as time passes, the value of information diminishes to zero. Each unit of time causes the value to slip until, after enough time, the value of the information is effectively zero.

The drop-off of the value of information shown in Figure 1 is fairly uniform. With each passing moment, the usefulness of information diminishes at approximately the same rate. This may be the case with a decision such as that made by a loan officer to make a loan or not. There are no particular deadlines for this decision, but after enough time has passed, then there is no opportunity to make a loan at all.

The curve shown in Figure 1 is a classical Poisson distribution. There are several variations of this distribution. Figure 2 shows one of those variations.

In Figure 2, there is a very rapid drop-off over time of the time value of information. Unlike Figure 1 where there is a somewhat uniform drop-off of the value of information, in Fig 2 when a few units of time have passed, the information drops almost to zero. After those early moments have passed, then there is incrementally very little drop-off of the value of information because the value is almost at zero anyway.

**Figure 2**

The kind of drop in the time value of information shown in Figure 2 is representative of an opportunity that is a take-it-or-leave-it opportunity with a deadline. Once the deadline has passed (assuming that the deadline is real), the value of information about the decision relating to the deadline is worthless.

Figure 3 shows another variation of the Poisson distribution.

**Figure 3**

Figure 3 shows a perfectly linear devaluation of the value of information. With the passing of each unit of time, there is exactly the same rate of the diminishing of the value of information. At some point, the value of the information is zero.

The curve (or, rather, the line) shown in Figure 3 almost never occurs in nature (although, in theory, it can occur). The curve is much more of a curiosity than a depiction of reality.

Figure 4 shows another theoretical possibility.

**Figure 4**

Figure 4 shows that the value of information remains constant over time. There is no time value of information over time in Figure 4. The value of a unit of information is exactly the same, regardless of when the information becomes available.

Like the curve shown in Figure 3, the curve for Figure 4 is also mostly a theoretical possibility.

Curves are not normally discontinuous. Because curves normally represent functions which are not discontinuous, it becomes possible to ask a very important question. That question is: What is the value (or, more specifically, what would have been the value?) of information if it could have been determined earlier than right now? In other words, would there have been a different time value of information if the information could have been determined or developed earlier? The mathematical equivalent of this question is shown in Figure 5.

**Figure 5**

Figure 5 shows what the Poisson distribution would look like if it could be extended backward in time. Indeed, Figure 5 suggests that there would have been an even higher value to the information if the information could have been determined earlier.

What is not clear at all from Figure 5 is what the general shape of the function is extending backward from time 0. The only implication is that the curve is not discontinuous. Other than that, it is dangerous and wrong to draw further conclusions as to the shape of the curve heading into negative territory from time 0.

The classical Poisson distribution for the diminishing value of information over time certainly fits many paradigms; however, it does not fit all paradigms. Consider the curve in Figure 6.

**Figure 6**

Figure 6 shows that for at least a while, the value of information increases over time before it starts to diminish. In this case, the value of information is increased by waiting to access or calculate the information. An example of this might be the calculation of a value which at time 0 is less than full. For example, the number of seats sold at a concert may be calculated one day before the concert takes place. An even more accurate and even more up-to-date status of the seats sold can be taken a little later when the concert hall is just starting to fill. By waiting a small amount of time, the information can become even more valuable.

**Some Parameters**

The previous discussion has made it clear that the curve for the time value of information can be determined in its general shape and form. The shape of the curve is a Poisson distribution.

However, more than the general shape of the curve can be discerned. It is possible to actually lay out the rough outline of the general curve by identifying two very important points. Figure 7 shows those points.

**Figure 7**

The points that shape the Poisson distribution are the opportunity value at time zero and the point at which effective zero value is reached.

The value at time zero simply states that a value must be placed on the usefulness of the information at time zero. In the case of the opportunity to make a loan to John Smith, the value might be the interest and points that John Smith will pay during the life of the loan. Or perhaps the opportunity value is the money made on the loan minus the money required to service the loan.

In the case of the investment opportunity decision to be made by the executive, opportunity value may be calculated as the probable money to be made minus the probable money to be lost by the investment. Again, there are many ways to calculate the opportunity value of an investment at time 0. However the calculation is made, the value determines where the function touches the Y axis at time 0.

The effective value of zero is more difficult to calculate because many functions approach zero but never quite get there. Therefore, the analyst must decide what tolerances are applicable. Then, when the function reaches the limits of the tolerance, it is said that the effective value of zero has been reached (although, in actuality, zero has not been reached).

Once the two parameters have been established, the Poisson distribution for the time value of information has been established. Of course, the Poisson curve itself can be adjusted to fit the reality of the representation. If there is a deadline, the Poisson curve can exhibit a quick drop-off. If the time value of the data is a long amount of time, then the curve can be mapped across a lengthy amount of time, and so forth.

**Recent articles by Bill Inmon**

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