Bootstrapping Our Way to Confidence and Probability
Over our 25 years of financial modeling for films and slates and funds, we have developed sophisticated methods for modeling a film or films in distribution. Because of our hard-won proprietary data and years of deep diving into markets arcana, leveraging our baleen whale tendencies toward information, we have modeled hundreds of films, from the quietly beautiful “Sweet Land,” to the challenging comedy of “Sleeping Dogs Lie” and the blockbuster-sized upcoming “The Meg.” All of these films were modeled using all of our skills, but we are continually seeking to enhance the quality of our work, and now we have again.
We here at FilmProfit have devoted significant time and effort into formulating a statistically meaningful approach to estimating Confidence and Probability (two different things in statistics) in our modeling for a single film (Illustrated below at different potential budget targets) and for slates of films. We have performed these analyses and refined the output tools to where we can now confidently share them with our clients.
Above is an illustration of a projections model we have developed for illustrating Confidence Levels when studying the potential performance of your film across a range of markets.
Our models take bootstrapped datasets and estimate these confidence levels based on target fee and costs structures. This can be done for a single film, for a slate of films, or for a fund strategy. We can divine market performances for a range of budgets determined by the data, so as to target maximum potential ROI and effective budget, or targeted to a single budget, based on bootstrapping thousands of iterations from our dataset.
The bootstrap method is a re-sampling technique used to estimate statistics on a population by sampling a data set with replacement.https://machinelearningmastery.com/a-gentle-introduction-to-the-bootstrap-method/
It can be used to estimate summary statistics such as the mean or standard deviation.
In our continual striving to provide clients with quality information and effective guidance, we have begun driving our Monte Carlo Bootstrap Analyses to higher standards of predictability.
In this pursuit we have developed algorithms which take key data through thousands of bootstrapped iterations that can be used to derive two levels of analysis.
In performing a Confidence Study, we are trying to ascertain within a high degree of confidence, the possibilities that a film will perform within a certain range of market parameters, for example, box office, foreign box office, various aftermarkets, and so on.
A study will typically consist of collecting a pool of Comparable Pictures Data, and then subjecting the market characteristics of that pool to a bootstrapping (Monte Carlo) that randomly generates thousands of iterations of each studied parameter. The resultant data will give us clear indications on each parameter as to the outside edges of Confidence, and at each Confidence Interval, what the different market parameters would be: for example, at 99% Confidence Interval, we might see that the highest box office could be $100 million, and the lowest box office could be $25 million in one study. In another, those same parameters at 99% Confidence could be $10 million and $2.5 million. The Confidence Intervals, say at 90% would give us a narrower range of possibilities, but could be sufficient for purposes of the target study. What it would also tell us is what performances have a very low Confidence of happening, those outside the 99% Confidence Fence as illustrated just below. These are not outside the realm of possibility, but they are very improbable. We calculate that improbability and give you a number for it.
Discrete Event Probability
If I was using typical statistician speak, you would begin to hate me and hate what I am saying, and with reason, because much of statistical talk becomes gibberish among those who are not statisticians. It does not reduce the value of their work, but it makes it not understandable to people who also need to understand it. A Discrete Event Probability is a higher level of Confidence that an event will transpire (domestic box office +plus foreign box office + domestic and foreign aftermarkets + cost to achieve those, both in production and marketing, could be called a discrete event in this parlance for us). Probability is typically a lower percentage, because it has an even higher potential for happening than confidence. It pulls the fences in, and in the illustration above, we have achieved a 99% Confidence Level, and with the same data achieved a 90% Probability (for a Discrete Event).
Discrete event simulation (DES) is a method of simulating the behaviour and performance of a real-life process, facility or system.https://www.ncbi.nlm.nih.gov/books/NBK293948/