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## Break even ratios for development investment decisions

Developers are constantly being told that it is worth making the effort when writing code to make it maintainable (whatever that might be). Looking at this effort as an investment what kind of return has to be achieved to make it worthwhile?

Short answer: The percentage saving during maintenance has to be twice as great as the percentage investment during development to break even, higher ratio to do better.

The longer answer is below as another draft section from my book Empirical software engineering with R book. As always comments and pointers to more data welcome. R code and data here.

## Break even ratios for development investment decisions

Upfront investments are often made during software development with the aim of achieving benefits later (e.g., reduced cost or time). Examples of such investments include spending time planning, designing or commenting the code. The following analysis calculates the benefit that must be achieved by an investment for that investment to break even.

While the analysis uses years as the unit of time it is not unit specific and with suitable scaling months, weeks, hours, etc can be used. Also the unit of development is taken to be a complete software system, but could equally well be a subsystem or even a function written by one person.

Let be the original development cost and the yearly maintenance costs, we start by keeping things simple and assume is the same for every year of maintenance; the total cost of the system over years is:

If we make an investment of % in reducing future maintenance costs with the expectations of achieving a benefit of %, the total cost becomes:

and for the investment to break even the following inequality must hold:

expanding and simplifying we get:

or:

If the inequality is true the ratio is the primary contributor to the right-hand-side and must be greater than 1.

A significant problem with the above analysis is that it does not take into account a major cost factor; many systems are replaced after a surprisingly short period of time. What relationship does the ratio need to have when system survival rate is taken into account?

Let be the percentage of systems that survive each year, total system cost is now:

where

Summing the power series for the maximum of years that any system in a company’s software portfolio survives gives:

and the break even inequality becomes:

The development/maintenance ratio is now based on the yearly cost multiplied by a factor that depends on the system survival rate, not the total maintenance cost

If we take >= 5 and a survival rate of less than 60% the inequality simplifies to very close to:

telling us that if the yearly maintenance cost is equal to the development cost (a situation more akin to continuous development than maintenance and seen in 5% of systems in the IBM dataset below) then savings need to be at least twice as great as the investment for that investment to break even. Taking the mean of the IBM dataset and assuming maintenance costs spread equally over the 5 years, a break even investment requires savings to be six times greater than the investment (for a 60% survival rate).

The plot below gives the minimum required saving/investment ratio that must be achieved for various system survival rates (black 0.9, red 0.8, blue 0.7 and green 0.6) and development/yearly maintenance cost ratios; the line bundles are for system lifetimes of 5.5, 6, 6.5, 7 and 7.5 years (ordered top to bottom)

Figure 1. Break even saving/investment ratio for various system survival rates (black 0.9, red 0.8, blue 0.7 and green 0.6) and development/maintenance ratios; system lifetimes are 5.5, 6, 6.5, 7 and 7.5 years (ordered top to bottom)

Development and maintenance costs
Dunn’s PhD thesis <book Dunn_11> lists development and total maintenance costs (for the first five years) of 158 software systems from IBM. The systems varied in size from 34 to 44,070 man hours of development effort and from 21 to 78,121 man hours of maintenance.

The plot below shows the ratio of development to five year maintenance costs for the 158 software systems. The mean value is around one and if we assume equal spending during the maintenance period then .

Figure 2. Ratio of development to five year maintenance costs for 158 IBM software systems sorted in size order. Data from Dunn <book Dunn_11>.

The best fitting common distribution for the maintenance/development ratio is the <Beta distribution>, a distribution often encountered in project planning.

Is there a correlation between development man hours and the maintenance/development ratio (e.g., do smaller systems tend to have a lower/higher ratio)? A Spearman rank correlation test between the maintenance/development ratio and development man hours gives:

 ``` rho 0.2932334```

showing very little connection between the two values.

#### Is the data believable?

While a single company dataset might be thought to be internally consistent in its measurement process, IBM is a very large company and it is possible that the measurement processes used were different.

The maintenance data applies to software systems that have not yet reached the end of their lifespan and is not broken down by year. Any estimate of total or yearly maintenance can only be based on assumptions or lifespan data from other studies.

A study by Tamai and Torimitsu <book Tamai_92> obtained data on the lifespan of 95 software systems. The plot below shows the number of systems surviving for at least a given number of years and a fit of an <Exponential distribution> to the data.

Figure 3. Number of software systems surviving to a given number of years (red) and an exponential fit (black, data from Tamai <book Tamai_92>).

The `nls` function gives as the best fit, giving a half-life of 5.4 years (time for the number of systems to reduce by 50%), while rounding to gives a half-life of 6.6 years and reducing to a half life of 4.6 years.

It is worrying that such a small change to the estimated fit can have such a dramatic impact on estimated half-life, especially given the uncertainty in the applicability of the 20 year old data to today’s environment. However, the saving/investment ratio plot above shows that the final calculated value is not overly sensitive to number of years.

#### Is the data believable?

The data came from a questionnaire sent to the information systems division of corporations using mainframes in Japan during 1991.

It could be argued that things have stabilised over the last 20 years ago and complete software replacements are rare with most being updated over longer periods, or that growing customer demands is driving more frequent complete system replacement.

It could be argued that large companies have larger budgets than smaller companies and so have the ability to change more quickly, or that larger companies are intrinsically slower to change than smaller companies.

Given the age of the data and the application environment it came from a reasonably wide margin of uncertainty must be assigned to any usage patterns extracted.

## Summary

Based on the available data an investment during development must recoup a benefit during maintenance that is at least twice as great in percentage terms to break even:

• systems with a yearly survival rate of less than 90% must have a benefit/investment rate greater than two if they are to break even,
• systems with a development/yearly maintenance rate of greater than 20% must have a benefit/investment rate greater than two if they are to break even.

The availanble software system replacement data is not reliable enough to suggest any more than that the estimated half-life might be between 4 and 8 years.

This analysis only considers systems that have been delivered and started to be used. Projects are cancelled before reaching this stage and including these in the analysis would increase the benefit/investment break even ratio.

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## Brief history of syntax error recovery

Good recovery from syntax errors encountered during compilation is hard to achieve. The two most common strategies are to insert one or more tokens or to delete one or more tokens. Make the wrong decision and a second syntax error will occur, often leading to another and soon the developer is flooded by a nonsensical list of error messages. Compiler writers soon learn that their first priority is ensuring that syntax error recovery does not result in lots of cascading errors. In languages that use a delimiter to indicate end of statement/declaration, usually a semicolon, the error recovery strategy of deleting all tokens until this delimiter is next encountered is remarkably effective.

The era of very good syntax error recovery was the 1970s and early 1980s. Developers working on mainframes might only be able to achieve one or two compilations per day on a batch oriented mainframe and they were not happy if a misplaced comma or space resulted in a whole day being wasted. Most compilers were rented for lots of money and customer demand resulted in some very fancy error recovery strategies.

Borland’s Turbo Pascal had a very different approach to handling errors in code, it stopped processing the source as soon as one was detected. The combination of amazing compilation rates and an interactive environment (MS-DOS running on the machine in front of the developer) made this approach hugely attractive.

To a large extent syntax error recovery has been driven by the methods commonly used to write parsers. Many compilers use a table driven approach to syntax analysis with the tables being generated by parser generator tools such as Yacc. During the 1970s and 80s a lot of the research on parser generators was aimed at reducing the size of the generated tables. A table of 10k bytes was a significant percentage of available storage for machines that supported a maximum of 64k of memory. Some parser table compression techniques involve assuming the default behavior and then handling any special cases when these defaults are found not to apply, but one consequence is that context information needed for good error recovery is often not available when an error is detected. The last major release of Yacc from AT&T in the early 1990s managed another reduction in table size, just as typical storage sizes were getting into the ten of megabytes, but at the expense of increasing the difficulty of doing good error recovery.

While there are still some application areas where the amount of storage occupied by parser tables is still a big issue, e.g., the embedded market, developers of parser generators such as Bison ought to start addressing the needs of users wanting to do good error recovery and who are willing to accept larger tables.

I am pleased to see that the LLVM project is making an effort to provide good syntax error recovery. A frustrating barrier to providing better error recovery is lack of information on the kinds of syntax errors commonly made by developers; there are a few papers and reports containing small scale measurements of errors made by students. Perhaps the LLVM developers will provide a mechanism for automatically collecting compilation errors and providing users with the option to send the results to the LLVM project.

One of my favorite syntax error recovery techniques (implemented in a PL/1 mainframe compiler; I have never been able to justify implementing it on any project I worked on) is the following:

```// Use of an undeclared identifier is a syntax error in C and some other // languages, while in other languages it is a semantic error.   // no identifier with name result visible here   { int result; ... result=... ... } ... calc=result*2; // Error reported by most compilers is use of an undeclared variable```

The ‘real’ error is probably the misplaced closing bracket. Other possibilities include `result` being a misspelled version of another variable or the assignment to `calc` being in the wrong place.

There seems to be a trend over the last 20 years to create languages that require more and more semantic information during parsing. Deciphering a syntax error today can involve a lot more than figuring out which surrounding tokens have been omitted or misplaced, information on which types are in scope and visible (oh for the days when that meant the same thing) and where they might be found in the umpteen thousand lines of included source has to be distilled and presented to the developer in a helpful message.

For a long time compilers have primarily been benchmarked on the quality of their code. With every diminishing returns from improved optimization, the increasing complexity of languages and the increasing volume of header code pulled in during compilation perhaps the quality of syntax error recovery will grow in importance.

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