Corporate life · Expected value
Why the Sales Forecast Is Almost Never Right
The short version: an expected value is an average over many repeats, not what will happen this quarter. With 20 deals at 25% each, the forecast of 5 is right only about 20% of the time; the result is 4 to 6 in 56% of quarters, 3 or fewer in 22% and 7 or more in 21%. If the deals share a risk, such as a good or bad economy, the spread widens: 4 to 6 happens only 35% of the time. Over a year of four independent quarters, at least one quarter comes in at 3 or fewer 64% of the time. A useful forecast gives a range.
Quarterly sales review. The pipeline has 20 deals. Each, according to the sales system, has a 25% chance of closing. Forecast: 5 deals. The sales director has promised 5 to the board.
The quarter ends with 3. The director has been asked for an explanation and an action plan. The quarter before ended with 7, and nobody asked for an explanation of that.
What 5 means
Twenty deals at 25% each gives an expected value of 5: if you could run the same quarter thousands of times, the average would be 5 deals. But you only get to run this quarter once. How far from 5 can one run be, with every probability exactly right?
When each deal is an independent yes-or-no with the same chance, the number of wins follows a binomial distribution, and we can work out every outcome:
| Deals closed | Chance (deals independent) | Chance (deals share a risk) |
|---|---|---|
| Exactly 5 | 20% | 12% |
| 4 to 6 | 56% | 35% |
| 3 or fewer | 22% | 35% |
| 7 or more | 21% | 30% |
Even with perfect probabilities, the exact forecast comes true one quarter in five, and a "disaster" of 3 or fewer happens about as often as a "triumph" of 7 or more.
When the deals move together
Deals aren't usually independent. In a good economy, many customers say yes; in a bad one, many say no. In the third column, the chance per deal is 35% in half of the quarters and 15% in the other half, still 25% on average. The forecast is still 5, but outcomes spread out: the comfortable 4 to 6 drops to about a third of quarters.
Deals closed out of a forecast of 5 (20 deals at 25% each)
A year of quarters
Over four independent quarters, all four land in the 4-to-6 band only 10% of the time, and at least one comes in at 3 or fewer 64% of the time. So a sales director with perfect probabilities will have at least one "explain yourself" quarter in most years, and an "outstanding" quarter in most years too. Neither says much about the director.
Statistics for noobs: an average isn't a forecast
An expected value tells you where results centre over many tries. For a single try, you also need the spread: what range covers most outcomes. "5 deals, probably between 3 and 7" is a better forecast than "5 deals", because it's honest about what one quarter can do.
To judge a forecaster, look at many quarters: are their probabilities right on average, and do the results land inside their ranges as often as they should?
Where it costs you money
A strategy with a positive expected value can still lose for months. Twenty bets at 25% will often produce 3 winners, or fewer. Before judging a method on one quarter, work out what spread of results it would produce if it worked exactly as claimed.
The moral
Kevin suggested reporting the forecast as "5, most likely between 3 and 7". The board found that vague. The sales director now forecasts 4, because 4 or more happens 77% of the time, and is praised most quarters for beating the forecast. The pipeline hasn't changed.
What this model can't tell you
- The probabilities are assumed right. Real pipeline probabilities are often optimistic, which adds a bias on top of the spread.
- Equal deals. Real deals differ in size; one big deal can dominate the quarter and widen the spread further.
- A simple shared risk. The good-or-bad economy is one example; real dependence between deals can be stronger or weaker.
The sales review and the director are an illustration. The figures come from the binomial distribution for 20 independent deals at 25%, and from our own simulation of one million quarters for the shared-risk case. Educational content, not business or financial advice.