The Case Of Russia: How To Choose The Most Profitable Contract Using The Tools Of Probability Theory

Director of business development, advertising and marketing agencies Task &Solution Marketing Grigory, Bolotov wrote a column about how using probability theory to determine which lead will be more important and more profitable. Every lead company on the potential profit. Sometimes that leads more than resources to perform them. But if the company sells finished goods and services, the situation with the choice of leads even more complicated.

Sales managers and commercial Director should choose Lida to get the most out of the money and minimize the risks that the tender is won and the project will not take place. We at Task &Solution Marketing sometimes use a method that allows with sufficient accuracy to identify contracts that will require special attention and those that can be given to management trainees to practice skills. The method also allows to determine how much time (and therefore money) will have to spend on the draft. It is based on mathematical probability theory, but it is used without fanaticism, therefore, to apply the method of can anyone who knows how to use a calculator. Note for mathematicians.

The text contains many simplifications, the article is intended as a practical manual, not a theoretical treatise. Our company sells complex services. Strategic marketing and branding. We have regular customers from time to time we participate in competitions, tenders. In any such presale for us there is a nonzero probability to win it (positive scenario) or lose (negative scenario).

If you know how to calculate the percentage probability of winning the presale, you can understand whether or not to get involved in this story. It would seem, what here to calculate. Win or lose, Yes or no — the probability is 50: 50. But the payout presale — not the coin-toss. In a complex project, the result can influence several variables, so the probability of winning will be different from zero or one.

For example, the variable “hospital key employee” (responsible for project work). If the team of one 3D Modeler and preparation of the project is to create 3D models, so this variable is important for calculation — it is necessary to take into account. In the project “to prepare a text for a landing page” the Modeler is not needed, one of the variables will be “sick copywriter”. Now lets figure out how to calculate the probability of the positive scenario variable. 100% result for presale is a contract with terms that suit us.

This result always consists of a sequence of certain events. Each event is a variable, which we talked about above. The probability of any event is one of three options:1 (unit, 100% of the event will definitely occur), 0 (zero, 0%, the event definitely will not occur), or something between 0 and 1. Work on the project is a chain of dependent events (we call them steps), so the probability of the result is calculated as the product of the probabilities at each step. The product, not the sum.

Why. So is written in the textbook. Let me explain. For example, the occurrence of three steps in our project. 10% + 99% + 50% = 159%.

If you add up the probability that the result will exceed 100% (or unit). This is contrary to common sense. Now we calculate the final probability by multiplying the steps. 10% * 99% * 50% = 4,95% (0,1 * 0,99 * 0,5 = 0,0495). An important consequence.

The probability of each event affects the probability of occurrence of the event. The smaller the probability of at least one event, the less likely that we will get the desired result, namely, contract. Lets take our example and increase the probability of the first step in six times from 10% to 60%. The final possibility, too, will grow six times and will be equal to almost 30% (0,6 * 0,99 * 0,5 = 0,297). Conclusion.

When calculating the total probability must consider the probability of each event in the presale. The more events in this scenario, the more variables the harder it is to manage probabilities. Let us now determine the probability of occurrence of a step. There are two possible approaches. The first approach is used when pre-accumulated information on the steps.

Calculate the probability that the employee at the time of preparation of documents for the tender will take sick leave. Suppose the employee works in the company for three years (even take 600 days to 200 each year), was on sick leave in each year of the 10, 7 and 9 days, in total 26 days of 600 workers. Approximately 4% of the time. The probability that is indispensable to the tender officer will be in place and not get sick of 96%. Can already hear the mathematicians require to take into account the setting of the time of year, which determines when employees are sick more often.

I have simplified the situation for example, and not in favor of the winning outcome. Another example. Courier service from 156 cases of delivery twice delivered the documents after the deadline. The probability of delivery of documents in time will be 98.7% of the (probability of delay = 2/156 = 1.3 percent; the probability of delivery in time = 100% – 1,3% = 98,7%). To calculate the probability of each step when you have accumulated the information about these steps is quite simple, isnt it?.

But if we have no information on specific steps, and do not understand what can happen. Here to help second campaign. Count up the number of all possible outcomes and how likely each of them. All the outcomes which we are satisfied, in sum, will give the probability of a positive outcome. If the event ten different outcomes, each has a probability of 10%.

For example, if three outcomes suit us, then the likelihood of a favorable outcome will be 30% and the probability of a negative — 70%. In order for the second approach to work correctly, you need to consider significant events with nonzero probability. The probability of a meteorite on the office or start the third world war, though nonzero, but very small, these events are not taken into account. Now we know how to calculate the probability of individual events and the whole chain of events. Suppose we have obtained a probability equal to 15%.

Only 15. Its small, so it is not necessary to prepare for the tender. Not in a hurry. It is obvious that in any project the important value. And it can be expressed using the mathematical expectation.

The mathematical expectation (here I am again oversimplifying) is the product of the probability of the event outcome on its “weight”, that is, the amount of the contract. This is the “cost” of your project, which takes into account the expected profit and the probability of the conclusion of the contract. For example, there are two presales. One with a probability of 87% and the amount of the contract 567 400, the second with a probability of 32% and a contract amount of 1 235 400 rubles. The expectation for first contract.

0.87 x 567 400 = 493 638 rubles. The expectation for the second contract. 0,32 * 1 235 400 = 395 328 rubles. Suppose that in the second case, the probability is greater than 32%, for example, 45%. Then the sum would be 555 930 rubles.

The second contract wins in the first, where, with greater probability below the amount of the contract. If you have a few of prasalov, and resources for training is not enough, choose presely, the most interesting from the point of view of mathematical expectation. You can balance your “portfolio of prasalov” risky projects with low probability, but large amount of the contract, and projects where the value can be much lower, but the high probability of a favorable outcome. This will also help expectation. In addition, the mathematical expectation will allow you to determine a very important parameter — the maximum amount of work in preparation for the presale.

The expectation presale is the maximum amount of any costs presales. PAYROLL, subcontractors and so on. Time employees of the company is worth some money. Salaries, taxes, rent. Of them is the amount of labor that can be spent by the company on presales.

If the mathematical expectation is less than this amount, the company will work in the negative — the average for all projects over a long time. Probability theory and mathematical statistics allow you to build forecasts and make management decisions. For this you need the source data. A sufficient number of prasalov and projects. It is important.

One project or presale activity — not an indicator. The more projects and prasalov on your account over the long term, the more accurate you can predict the result for each of the following. How many will need such prasalov to predict. This is a topic for another conversation about “statistical significance” and “statistical power”. Send a private cases, in which you managed to improve (or, conversely, worsen) the performance of the project, [email protected]

Interesting experiments are sure to get heading Growth Hacks.

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