So today I was playing around with a little equation that may in fact explain nearly all of the principles of software design. I don’t know that it’s actually mathematically solvable in terms of numbers, but it does demonstrate the factors present in software development decisions and how they relate to each other. Before I go into the equation, though, I have to define the factors that are present when a designer is deciding whether or not to implement something, or how to implement it:

**Potential Value of Implementation**(V_{i}for short): How “valuable”*could*it be to implement this? For example, if we add something to the program that*could*directly prevent somebody from dying, that’s very valuable. If it simply*might*prevent a future typo in a single error message, that’s hardly valuable at all.The “value” can be for the end user or for other programmers. When we’re talking about design decisions that affect only code, and not the end user,

*flexibility*is one of the major values–how important*could*this flexibility be?The potential value is separate from how

*likely*it is that the situation will occur where you will need it. That’s the next issue.**Probability of Value**(P_{v}for short): What is the chance that this value will be, in fact, realized by an end user (for a feature or functional change) or by another developer (for some design decision)? If we’re adding in code flexibility to allow for potential contact with extraterrestrial apes, that’s not a very*probable*occurrence. If we’re adding in a feature that is immediately useful to every single user, that’s 100% probability. (The number of users that a feature will be useful to is also part of the Probability of Value.)**Effort of Implementation**(E_{i}for short): How hard will it be to implement this? This is a one-time cost–the immediate difficulty of performing the work required to create this thing the very first time. This would probably be measured in person-hours.**Effort of Maintenance**(E_{m}for short): How much effort will it require to maintain this in the future? (This includes any effort added to maintaining the entire program by implementing this.) Will this complicate maintenance for the whole system? This is an amount that increases over time. Similar to Effort of Implementation, this would be most likely measured in person-hours.

What we’re trying to determine is the **Desirability Of Implementation** (D for short). This answers the questions “Is this something we should do or not?” and “What should the priority of implementing this be?”

The simplest form of the equation is:

D = (P

_{v}* V_{i}) / (E_{i}+ E_{m})

Or, in English:

The Desirability of Implementation is directly proportional to the Probability of Value and the Potential Value of Implementation, and inversely proportional to the total effort, consisting of the Effort of Implementation plus the Effort of Maintenance.

However, there is a critical factor missing from the simple form of this equation: *time*. What we actually want to know is **the limit of this equation as time approaches infinity**, and that gives us the true Desirability of Implementation. So let’s look at this from a logical standpoint:

The Effort of Implementation is a one-time cost, and never changes, so is mostly unaffected by time.

The Value of Implementation may increase or decrease over time, depending on the feature. It’s not predictable, and so we can assume for the sake of this equation that it is a static value that does not change with time (though if that’s not the case in your situation, keep this factor in mind as well). One could even consider that the Effort of Maintenance is actually “the effort required to maintain this exact level of Value,” so that the Value would indeed remain totally fixed over time.

The Probability of Value, being a probability, approaches 1 (100%) as time goes to infinity.

The Effort of Maintenance, being based on time, approaches infinity as time goes to infinity.

At first glance, that might sound as though design is hopeless, because maintenance becomes infinite effort–an amount that no Potential Value could surpass–and it seems like *every* possibility must be accounted for, because given infinite time the probability seems to indicate that every possibility will occur. Those are not true statements, though, because you have to think about the *rate* at which both of those items increase. If the fundamental effort of maintenance is very small, then even as time goes on, it will remain small. You could say that there is a “coefficient of maintenance” on any design decision or feature, and that that determines how rapidly maintenance effort will accumulate over time. As far as the Probability of Value goes, if it is a very tiny number, it may remain tiny until thousands or millions of years have passed–so if the Effort of Maintenance increases at a great rate, then it will easily outstrip the Probability of Value and the Desirability of Implementation will approach zero as time approaches infinity.

What this equation *actually* tells us is that the most important factors to balance, in terms of time, are probability of value vs. effort of maintenance. If the probability of value is high and the effort of maintenance is low, the desirability is then dependent only upon the Potential Value of Implementation vs. the Effort of Implementation–a decision that a product manager can easily make. If the probability of value is low and the effort of maintenance is high, the only justification for implementation would be a near-infinite Potential Value of Implementation.

This interestingly indicates why small improvements in programming languages and development frameworks result in such enormous changes in the resulting products–because tiny reductions in the Effort of Maintenance can make tremendous changes in the Desirability of Implementation. Features that otherwise would be thrown away by a product manager as impossible become part of the basic design plan. Polishing the UI becomes more desirable, because it requires less effort for both implementation and maintenance.

And finally, I think that this communicates most exactly and truthfully why simplicity is so important–because *simplicity* is what determines the “coefficient of maintenance” that I talked about above. The effort involved in maintaining simple code increases very slowly over time–sometimes so slowly that you *never* will have to put any maintenance effort into it in your lifetime.

There’s a lot more that could be said about this equation. What are your thoughts on it? Anybody have any ideas of how Value of Implementation could be numerically calculated, or if it might break down into a set of other numerically-calculable factors? Anything you have to say about it, I’m interested.

-Max

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