La Bourse / Volume II / Nº II.02 / Workbook — the Gainshare employee

A woman in linen standing at a tall window, looking out, morning light laid across the wall beside her. — Plate II.02 · Workbook — the Gainshare employeeThe Slate, Before Opening.No equilibrium was computed here. A price was made by somebody who knew things, and it will be made again at eleven, and again if the weather turns.

WORKBOOK — THE LUMINOUS GAINSHARE EMPLOYEE

Chapter II.02 · Markets as Living Systems

For the person working inside a gainshare arrangement — where a defined share of verified improvement returns to the people who created it. This chapter is about distributions, and a gainshare is a distribution problem wearing a payroll disguise. Read it once and you will never look at a scheme average the same way again.

WHY THIS CHAPTER IS YOURS

Every gainshare has four parts: a baseline, a measure, a share, and a period with a verifier. Three of the four are statistics computed on a series — and this chapter is about what happens when a series is heavy-tailed and somebody computes an average on it anyway.

Here is the consequence, stated plainly, because it is money:

If the improvement your scheme measures is heavy-tailed, then the average improvement is not a stable number, the baseline drawn from it is not a stable baseline, and a scheme designed around the mean will pay less than it appears to promise in most periods and far more in rare ones.

That is not a complaint about your employer. It is a property of the distribution, it can be measured, and once it is measured it can be designed around. This workbook is how you measure it and what to ask for once you have.

PART ONE — DISCOVERY

Days 1–30: find the shape of your own gain

Exercise 1.1 — Get the series (one week)

You need the history of whatever your scheme measures — units, savings, defect rates, throughput, cycle time, margin — at the finest period available, for as long as it exists.

Ask for it in exactly these words, because they are the words that get it:

"I would like the underlying series our scheme's measure is computed from, at the period it is recorded at, for as far back as it goes. I want to understand the variability, not to query a payment."

The last clause matters. It is also true.

If the answer is that nobody has the underlying series and only the aggregates survive, that is the finding, and it is the most valuable thing you will produce this quarter. A measure whose inputs are not retained cannot be audited by anyone, in either direction.

Exercise 1.2 — Plot it before you compute anything (2 hours)

Two plots, both cheap:

The series over time.
The values sorted descending, on log-log axes, against rank.

If the second plot is straight at the top, your gain is heavy-tailed. Most operational improvement series are, because improvement arrives in occasional large discoveries rather than in even monthly increments.

Exercise 1.3 — The team's own appreciative sweep (45 minutes)

Run this with your team, in these words:

"Think of a time here when an improvement was much bigger than usual. Not the typical month — the one that surprised us. What were the conditions? What did we do that we do not normally do?"

Take notes on conditions, not outcomes. You are looking for the causes of the tail, because in a heavy-tailed series the tail is where most of the total sits — and a scheme that only rewards the median is paying for the part of the distribution that matters least.

PART TWO — THE ARITHMETIC

Days 31–50: compute what the shape is worth

Exercise 2.1 — Mean, median, and the gap (1 hour)

Compute both on your series, and the ratio.

  mean / median  ≈ 1.0      roughly symmetric; an average is a fair summary
  mean / median  > 1.5      skewed; the average is being carried by a few periods
  mean / median  > 3        heavy-tailed; the average is not a planning quantity

In the third case the scheme's "typical improvement" is a number that most periods will fall below. If your baseline was set from a mean drawn from a heavy-tailed history, you are being measured against a level that most honest periods cannot reach, and the fix is a different summary statistic, not harder work.

Exercise 2.2 — Estimate the tail exponent, two ways (half a day)

Rank-frequency. Sort descending, plot log(rank) against log(value), take the slope of the straight part. The exponent α is the negative of that slope.
Hill. On the top 5 percent: α̂ = k / Σ ln(x_i / x_{k+1}).

Report both and the gap. Then:

α < 2 — the variance does not exist. Any standard deviation quoted about this series is an artefact of the sample length.
α < 1 — the mean does not exist either. Rare, but it happens in savings series driven by occasional structural changes.

The chapter's benchmark: US firm sizes sit at α = 1.059 (Axtell, 2001), and financial returns at about 3 (Gabaix et al., 2003). If your series lands between 1 and 2, you are in the region where averages are least trustworthy and where this argument is worth the most money.

Exercise 2.3 — What the shape does to your share (2 hours)

Simulate your own scheme. You do not need software beyond a spreadsheet.

Resample your historical series 1,000 times (draw periods at random, with replacement, in blocks the length of your scheme period).
For each resample, compute what the scheme would have paid.
Report the median payout, the 10th percentile, the 90th, and the fraction of resamples in which the payout was zero.

That last number is the one to carry into the conversation. If the scheme pays nothing in a large fraction of plausible histories, it is not a share of gain — it is a lottery ticket with a job attached, and it can be redesigned in an afternoon.

Exercise 2.4 — The honest negative on your own case (1 hour)

Write the strongest argument against your own finding. Candidates: your series is too short for a tail estimate; the apparent tail is one merger or one contract; the scheme's period already smooths what you are measuring; the firm carries the downside of the tail as well as the upside and is entitled to price that.

Bring this paragraph to the meeting yourself. The single fastest way to be taken seriously by a finance function is to arrive having already made their best objection, in their own vocabulary, and answered it.

PART THREE — DESIGN

Days 51–75: what to ask for, and in what order

Exercise 3.1 — The four asks, ranked by how hard they are to refuse

Ask	What it does	Cost to the firm
1. Publish the underlying series	Makes the measure auditable by anyone	Near zero
2. Set the baseline on the median, not the mean	Removes the phantom level nobody can reach	Near zero; often lowers volatility of the payout
3. Smooth the share across periods — a rolling three-period average, or a reserve that carries forward	Converts a lottery into an income	Zero in expectation; it is the same money, differently timed
4. A tail clause — an explicit share of improvements above a stated multiple of the median	Pays for the discoveries that produce most of the total	Real, and worth negotiating for

Ask in that order. Each one makes the next easier, and the first two are almost never refused because they cost nothing and make the scheme more defensible.

The third ask is the one that changes a life and is most often not asked for. A heavy-tailed payout stream with the same expected value as a smooth one is worth materially less to a household, because a household cannot borrow against the tail. Smoothing costs the firm nothing in expectation and transfers real value to you. Say exactly that.

Exercise 3.2 — The ratchet check (30 minutes)

One question, and it decides whether the scheme is worth being in:

What happens to the baseline when a gain is realised?

If it resets to the improved level each period, you are on a treadmill — every gain raises the bar you are measured against. A well-designed scheme holds the baseline for a stated term, three to five years, or ratchets on a published, gradual, visible schedule.

Now combine it with this chapter: a baseline that ratchets on a heavy-tailed series ratchets on the tail. One exceptional period permanently resets the level everyone is judged against, and nobody can repeat it on demand. That is the single most damaging interaction in gainshare design and it is almost never noticed, because it requires someone to look at the distribution rather than the average.

You are now the person who looked.

Exercise 3.3 — Make an uncounted gain countable (the quarter)

The highest-leverage thing available inside any gainshare is to make a real gain visible that the measure does not currently see.

Use the chapter's frame. Concentration is a real risk and reducing it is a real gain: a second qualified operator on a critical process, a second supplier with genuinely different coupling, a second route into a customer. None of these usually appear in a scheme measure, and all of them raise the robustness of the system the scheme depends on.

Propose one, with a number: what the outage or the failure would cost, and what the second path costs. A gain that is not counted is not shared, and making it countable is work only someone on the floor can do.

PART FOUR — DESTINY AND DELIGHT

Days 76–90: make it hold

Exercise 4.1 — Get one distributional line into the scheme report

Not the mean alone. The median, the 10th percentile, and the fraction of periods that paid nothing. Three numbers, one line, every period. Once they are in the report they are in the conversation permanently.

Exercise 4.2 — Find the second reader

One colleague who can reproduce your exponent estimate independently. Not to check up on you — because a number that two people computed separately is a different object in a meeting from a number one person brought.

Exercise 4.3 — Write the conditions down

From Exercise 1.3 you have a list of the conditions under which the exceptional periods happened. Write them up as one page and give it to whoever schedules the work. In a heavy-tailed improvement series, arranging the conditions for the tail is worth more than optimising the median, and it is the part of the job nobody has asked you for.

Exercise 4.4 — Delight

The specific pleasure here is watching your own team's data come out straight on log-log axes, and realising that the "lucky months" were never luck. They were the tail of a distribution with a shape, and shapes can be worked with.

Do it together, with the plot on a screen, with something good to drink. That picture is the argument, and a team that has seen it once will not go back to quoting the average.

KNOW YOUR SCHEME — A CHECKLIST

Answer all ten in writing. Gaps are findings.

What exactly is the baseline, and on what date was it set?
Was it set from a mean or a median, and over what window?
What is the measure, as a formula?
Is the improvement gross, or net of the cost of achieving it?
What is the share percentage, and of what?
What is the allocation basis — headcount, hours, salary-weighted?
Who verifies, on what method, and how often?
What happens to the baseline when a gain is realised?
In what fraction of the last twenty periods did the scheme pay nothing?
Where is the underlying series kept, and for how long?

Questions 8, 9 and 10 are the three that almost never have an answer on file. Getting them answered, in writing, is a real contribution to the scheme and to everyone in it.

THE CONVERSATION, SCRIPTED

Ten minutes, with your manager or the scheme owner. Bring one page.

Open with what is working.

"The scheme has paid out in fourteen of the last twenty periods and the verification has never been disputed. That is a working mechanism and it is worth protecting."

The finding, as a measurement.

"I pulled the underlying series and fitted the tail two ways. The exponent comes out at about [x], which means the variance of this series doesn't exist — so the standard deviation in the scheme documentation is a function of how long a window we happened to use."

The consequence, in their terms.

"Practically: the baseline was set from a mean that a majority of honest periods can't reach, and the payout is lumpy in a way that costs us more than it saves the company, because the expected value is identical either way."

The ask, smallest first.

"Three things, and the first two cost nothing. Publish the underlying series. Set the baseline on the median. And smooth the share over a rolling three periods — same money, same expectation, much better for the people receiving it."

Close with the one you are giving them.

"And separately: here are the conditions under which our four biggest periods happened. That's worth more to the company than anything in the paragraph above, and it's yours whatever happens with the rest."

APPRECIATIVE QUESTIONS FOR YOUR TEAM

When have our biggest improvements happened, and what were the conditions? What would it take to arrange those conditions on purpose?
What are we doing that clearly makes this place more robust and that the scheme does not currently count? How would we count it?
Which of us could reproduce the scheme's numbers independently, and what would it take for two of us to be able to?
If our scheme report carried three numbers instead of one, which three would tell us the most about how we are actually doing?
What has this scheme already got right that we would defend if someone tried to replace it?