# “Max” vs. “Min” vs. “MaxEx”—Which Recruitment Strategy for You?

*“There are two tragedies in life. One is to lose your heart’s desire. The other is to gain it.”—George Bernard Shaw, Act IV, “Man and Superman”*

In making your decisions about which candidate to push most aggressively, and even which employment sector to specialize in, about which client to engage, and, in general, how to utilize and allocate your resources of time, energy, money and contacts, you may want to think about three different and mutually exclusive decision-making strategies: “max”, “min” and what I will call “maxEx”—short for “maximize”, “minimize” and “maximize expected gain”, respectively.

One recruiting example should make the differences clear, and show 1. How using a “maxEx” decision-making strategy is not the same as the familiar approaches encapsulated by what I shall call “max” and “min”; 2. How “maxEx” can give a bigger and better picture of a candidate.

**Paint by Numbers**

Imagine that you have to place one and only one salesperson—to be chosen from a shortlist of three, primarily, the client says, on the basis of the candidate’s average weekly sales over a one-year period, given that, in the hypothetical instance below, they are in all other respects mostly indistinguishable. Using their 1-year weekly sales figure ranges as benchmarks, and assuming there were six months with the higher sales figure as an average and six months with the lower figure as the average, which one would or should you hire?

- Applicant A: $4 K-$8 K
- Applicant B: $0 K-$12 K
- Applicant C: $3 K-$10 K

**“Max” vs. “Min” **

If you were to follow the bold strategy of maximizing the potential gains—call that strategy “max”, you might considering hiring Applicant “B”, because of “B”’s demonstrated maximum “sales potential”, given (s)he had the maximum weekly sales—$12 K ($4 K/week more than Applicant “A” and $2 K/week more than Applicant “C”).

On the other hand, if you were to follow the equally clear, commonsense and tempting strategy of minimizing possible “losses”, you would choose Applicant “A”, since that choice virtually guarantees a minimum of $4 K/week, larger than the other two applicant’s weekly minimum sales. This choice reflects your focus on “dependability”.

Here, “loss” is interpreted as the difference between the highest minimum ($4k/week with Applicant “A”) and the given minimum (“C”’s $3 K/week and “B”’s $0 K/week)—a kind of opportunity cost. That means, choosing Applicant “B” entails a “loss” or opportunity cost of $4 K-$0 K=$4 K per week, while choosing “C” entails a loss of $1 K/week relative to choosing “A”. In using either “max” or “min”, Applicant “C” is eliminated from consideration, with “A” or “B” getting the placement when “min” and “max” are used, respectively.

It is very important to notice that you cannot follow both “max” and “min” strategies simultaneously with a single applicant, unless it’s the dream applicant, who scores highest for both minimum and maximum weekly sales. In the example given, if you follow “max” and maximize your potential gain, then it’s Applicant “B”; if you adopt “min” and maximize the minimum gain, i.e., “minimize the potential loss”, the choice is clearly Applicant “A”. Yet, as will be shown, there is some likelihood that a recruiter may mix these two strategies, and use “max” with one applicant and “min” with another—while trying to be “fair” to both.

Now, compare “maxEx”—“maximizing your expected gain”. To calculate the expected gain of any strategy or game, you simply multiply each of the payoffs (as gain or loss) x the probability of that payoff. For example, if you are tossing a fair coin and win $1 if the toss comes up “heads” and lose $1 if the toss comes up tails, your expected gain will be zero, i.e., (1/2 x $1) + (1/2 x -$1)= $0.50 – $0.50 = 0. So, if you play the coin-toss game very many times, that will be your average payoff, namely, nothing. If you have to pay to play the game, as you do in lotteries, the “admissions” cost has to be deducted from any positive expected gain and added to any negative expected gain, i.e., to any expected loss.

**“MaxEx” vs. Weighted Average**

You may have noticed how this approach gives the same numerical result as what is called the “weighted average” sales, with the weightings. here represented by the proportion of the year, which are to be multiplied by the average earnings. These proportions, interpreted as frequencies, are then interpreted as probabilities of each candidate’s future performance. The difference between the weighted average and expected gain approach is that the latter is a strategic concept in game theory and decision making, with a clear focus on goals and the net, long-term payoffs—viz., gains or losses.

Weighted averages are more generic, are not inherently strategic in their applications, and are not limited to probabilities for their weighting, e.g. the sum of the average number of days of sick leave x total number of employees per department, calculated for the whole company to determine overall sick-leave costs.

To the extent that you are trying to reach a decision about a candidate, the decision-making objective—to maximize expected gain—should remain salient in your thinking, which it might not be if you thought you were merely looking at weighted averages.

Your expected gain in hiring Applicant “A” would be the number of weeks as a percentage of 52 weeks (s)he earned the minimum figure x the minimum figure plus the percentage of the same calculation repeated with the maximum figure for the same applicant. To keep things simple, let’s, as stated above, assume all applicants earned exactly the minimum figures shown half of the time and the maximum figure shown the other half of the year, to make the odds the same as a coin toss, but with unequal payoffs for the maximum and minimum outcomes. This is also to assume, as suggested, that each applicant’s past performance gives a good estimate of future performance.

(Skip the next sentence, unless you are one of the two or three readers who like formulas, yet somehow don’t know this one: Ex=?(V)P(V), where “V” represents the “value” or “payoff”, e.g., sales in dollars, and “P(V)” designates the probability (e.g., as a frequency) of that specific outcome. The sigma, “?”, means add up all the results of those individual multiplications to get the (net) expected gain.)

**Betting on the Dark Horse**

Then, the expected gain from betting on and choosing Applicant “A” would be

(0.5 x $4 K) + (0.5 x$8 K) = $6 K/week

For Applicant “B”, it would be

(0.5 x $0) + (0.5 x $12 K) = $6 K/week

On this calculation, Applicant B is no longer the winner, as (s)he would be if you used a “max” approach of looking for the maximum weekly sales among the candidates. Instead, using maxEx, it becomes a tie between “A” and “B”—at $6 K/week, perhaps to be decided by a secondary consideration, e.g., the client’s risk aversion, with “A” being the less risky choice of the two.

But now, using “maxEx”, take a look at “C”, who would have been out of the running by both the “max” and “min” criteria:

(0.5 x $3 K) + (0.5 x $10) = $6.50 K/week!

Using the maxEx calculation, “C”, previously rejected by the “max” and the “min” rules, becomes the front-runner.

**The Smart Art of Being “Fair”**

Of course, in the final choice of a candidate, the “max” and “min” strategies, or the simple “maxEx” 2-dimensional calculations (probability x payoff) are never going to be the sole determinants of candidate suitability and superiority. But, consciously or unconsciously, you are very likely to have these rival rules dancing and prancing in some corner of your mind, competing for your attention and your decision.

It is extremely likely that in the course of reviewing applicants, you will shift from one rule to another. Dazzled by “X’s” high weekly sales, you immediately shortlist her for her “earnings potential”. Impressed by the dependable weekly minimums of “Y”, you immediately shortlist him. In effect, you are measuring applicants by different, incommensurable yardsticks, while trying to be “fair”.

In this waffling, you may imagine that you are using a fair approach and decision strategy: “Feel free to use the ‘max’ approach with one candidate and the ‘min’ approach with another, depending on which is the most eye-catching and impressive number—the maximum or the minimum average weekly sales.”

Fair enough. But then later you will have to make a final decision between the high-potential max “X” and the high-dependable min “Y”—perhaps on the basis of your client’s risk tolerance, going with the high-min “Y” if the risk tolerance is low and the mind set more conservative.

However, if you use the weighted average/”maxEx” criterion, you will forgo the bedazzlement by “potential” and “dependability” in exchange for a more objective estimate of the likely performance of each candidate—on the assumption that there were no weird factors accounting for the differences among them, e.g., a fire in the office that shut down operations, thereby lowering a given candidate’s sales numbers.

Probably the smartest thing to do is to note the sales figures’ range for each candidate, determine and compare the “maxEx” (weighted average) among the candidates, compile a separate shortlist based entirely on that calculation and then question the candidates about any (comparatively) extreme numbers—at least to exclude some skewing, one-time outlier events, such as a non-repeat huge order facilitated by the guy the candidate replaced or that office fire that inflated or deflated their sales numbers.

Even if you are not in a position to or of a mind to attempt such a calculation–even roughly, you can still be alert to the possibility that the applicant has done his or her math and is using his or her preferred strategy on you.

A candidate with a high max, but a low min may tray to sway you by stressing the max and hiding or burying the min. By showcasing the higher number in a resume or interview, by saying, “I achieved sales of as much as…”, the applicant may be able to trigger the max-mode in you, to get you drooling over his or her “potential”.

On the flip side, an applicant with a decent min but unimpressive max, may try to pull off the reverse, and highlight the “dependable” minimums scored, by saying something like, “I never averaged less than…..”. So, stay alert for such mathematical maneuvers.

In any case, you should add expected gain, and its associated goal of maxEx to your recruiter tool kit and keep it mind when reviewing candidates.

You have will have nothing to lose, and maybe something to expect to gain.

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