# The A-Shaped Model

### What is the “A” shaped Model?

The A-Shaped model is an attribution model that assigns weights to eligible touches based on each touch’s proximity to the date an opportunity was created. The closer the proximity to the create date, the greater the weight. When the values of touches are graphed, the graph resembles two curved mirrored lines that meet at a peak.

#### Why use an A-Shaped Model?

The A-Shaped model is most appropriate used when an analyst believes:

- Touches closest to the opportunity being created are the most important touches
- Touches that happened well before or after the opportunity was created are significantly less important
- Have a defined process for when someone creates an opportunity in their CRM

If you have a very long sales cycle, you may want to choose a model that weights touches more evenly throughout the sales process. Touches that keep the momentum going in a sale may be considered equally important as the “Last Touch” before opening the opportunity by the rest of the business. In the A-Shaped model, touches that happen closer to opportunity closure receive less value.

#### How does the A-Shaped model work?

CaliberMind’s A-Shaped model anchors its weighting calculations to the date an opportunity was created. From this date the A-Shaped model uses an exponential decay equation to calculate weights for touches based on how far from the opportunity create date each touch is. Once the weights are calculated, the opportunity amount is divided across the touches according to the weight each touch has received.

The standard A-Shaped model weights pre-opportunity touches equally to post-opportunity touches. This means that a touch that happened 10 days prior to an opportunity being created will receive the exact same weight as a touch that happened 10 days after an opportunity was created. As with all other CaliberMind attribution models, the model has a look back window of 365 days from the date the opportunity was created by default and does not consider touches that happen after the opportunity is closed.

#### Extra Credit Reading: The A-Shaped Decay Formula

The decay formula used by CaliberMind’s A-Shaped model is:

- W(t) = the weight of a touch
- |T| = the absolute value of the days between the touch date and the opportunity created date
- This function when written in Microsoft Excel would look like this:
- =(2^(-ABS(T)/28)) + 0.5

##### Why this formula?

There are 2 constants in the formula that affect the shape of the curve, 28 & 0.5

**28**: represents the Half Life or decay period. An over simplified explanation is that every 28 days, the potential value of a weight is reduced by half.**0.5**: 0.5 represents a weight floor, by the nature of an exponential curve, it will converge on an asymptote of 0. However, even when using a longer half life (such as 28 days), by day 180, the calculated weights get so small that they are indistinguishable from 0 and when normalized and converted to touch values, they are rounded down to zero. This means without a floor, as long as there is one touch within 180 days of the opportunity creation, all touches beyond 180 days are calculated as being worth $0. The model is meant to have a look-back period of 365 days. Putting in a floor ensures that every eligible touch will receive some weight as designed.

##### Linear Decay vs. Exponential Decay

At CaliberMind we call this model the A-shaped model because the curve of weights vs time resembles a capital “A”. A chart graphing the weights would look something like this:

While a linear decay would much more closely resemble the letter “A” than an exponential decay, the exponential decay model is better suited to this situation because it will skew weights to create a greater importance on touches closest to the opportunity create date rather than a more gradual slope.

##### Example Calculations

Let’s assume that there an an opportunity worth $10,000 has 5 eligible touches occurring at the following times:

Touch # | Days Before/After Opp Create |

1 | -100 |

2 | -30 |

3 | -5 |

4 | 10 |

5 | 60 |

The weights and touch values would get calculated like this:

Touch | Weight Calculation | Weight | Normalized Weight calculation | Normalized Weight | Touch Value |

1 | (2^(-100/28)) + 0.5 | 0.58411 | 0.58411 / 4.95 | 11.80% | $1,179.87 |

2 | (2^(-30/28)) + 0.5 | 0.97584 | 0.97584 / 4.95 | 19.71% | $1,971.14 |

3 | (2^(-5/28)) + 0.5 | 1.38357 | 1.38357 / 4.95 | 27.95% | $2,794.72 |

4 | (2^(-10/28)) + 0.5 | 1.28070 | 1.28070 / 4.95 | 25.87% | $2,586.93 |

5 | (2^(-60/28)) + 0.5 | 0.72643 | 0.72643 / 4.95 | 14.67% | $1,467.33 |