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The Economic Implications of Large Language Model Selection on Earnings and Return on Investment: A Decision Theoretic Model

Geraldo Xexéo, Filipe Braida, Marcus Parreiras, Paulo Xavier

TL;DR

The paper tackles the gap between LLM performance-focused analyses and the financial considerations essential for business decisions. It develops a decision-theoretic framework to evaluate LLM deployments in terms of earnings and RoI, incorporating gains, losses, per-token costs, task success probabilities, and scenario-specific parameters. Through single-transaction and binary-classification models, along with local and global sensitivity analyses (including Sobol), it shows how small token costs and accurate probability estimates can outweigh higher model accuracy in RoI, and it demonstrates when prompt strategies or model choice can shift financial outcomes. The practical contribution is a structured methodology for enterprises to optimize LLM selections and prompts to align technology investments with financial objectives, supported by analytic tools for assessing risk and sensitivity.

Abstract

Selecting language models in business contexts requires a careful analysis of the final financial benefits of the investment. However, the emphasis of academia and industry analysis of LLM is solely on performance. This work introduces a framework to evaluate LLMs, focusing on the earnings and return on investment aspects that should be taken into account in business decision making. We use a decision-theoretic approach to compare the financial impact of different LLMs, considering variables such as the cost per token, the probability of success in the specific task, and the gain and losses associated with LLMs use. The study reveals how the superior accuracy of more expensive models can, under certain conditions, justify a greater investment through more significant earnings but not necessarily a larger RoI. This article provides a framework for companies looking to optimize their technology choices, ensuring that investment in cutting-edge technology aligns with strategic financial objectives. In addition, we discuss how changes in operational variables influence the economics of using LLMs, offering practical insights for enterprise settings, finding that the predicted gain and loss and the different probabilities of success and failure are the variables that most impact the sensitivity of the models.

The Economic Implications of Large Language Model Selection on Earnings and Return on Investment: A Decision Theoretic Model

TL;DR

The paper tackles the gap between LLM performance-focused analyses and the financial considerations essential for business decisions. It develops a decision-theoretic framework to evaluate LLM deployments in terms of earnings and RoI, incorporating gains, losses, per-token costs, task success probabilities, and scenario-specific parameters. Through single-transaction and binary-classification models, along with local and global sensitivity analyses (including Sobol), it shows how small token costs and accurate probability estimates can outweigh higher model accuracy in RoI, and it demonstrates when prompt strategies or model choice can shift financial outcomes. The practical contribution is a structured methodology for enterprises to optimize LLM selections and prompts to align technology investments with financial objectives, supported by analytic tools for assessing risk and sensitivity.

Abstract

Selecting language models in business contexts requires a careful analysis of the final financial benefits of the investment. However, the emphasis of academia and industry analysis of LLM is solely on performance. This work introduces a framework to evaluate LLMs, focusing on the earnings and return on investment aspects that should be taken into account in business decision making. We use a decision-theoretic approach to compare the financial impact of different LLMs, considering variables such as the cost per token, the probability of success in the specific task, and the gain and losses associated with LLMs use. The study reveals how the superior accuracy of more expensive models can, under certain conditions, justify a greater investment through more significant earnings but not necessarily a larger RoI. This article provides a framework for companies looking to optimize their technology choices, ensuring that investment in cutting-edge technology aligns with strategic financial objectives. In addition, we discuss how changes in operational variables influence the economics of using LLMs, offering practical insights for enterprise settings, finding that the predicted gain and loss and the different probabilities of success and failure are the variables that most impact the sensitivity of the models.
Paper Structure (21 sections, 24 equations, 9 figures, 2 tables)

This paper contains 21 sections, 24 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Basic premises for our models
  3. How LLMs are charged
  4. An anedotal model from industry
  5. Choice of Costs in the Model
  6. Are there other costs?
  7. Why multiple scenarios
  8. A Decision Theoretic Model
  9. How to model success
  10. A Model for Commercial Operations Based on a Single Transaction
  11. Example of Using the Model
  12. Model Analysis
  13. Local Sensitivity Analysis
  14. Global Sensitivity analysis of earnings by Sobol technique
  15. Discussion of the RoI vs. Earning dillema
  16. ...and 6 more sections

Figures (9)

  • Figure 1: Transaction gain variation as a function of size for two models with different performance (95% and 80%) and cost (US$10 and US$1).
  • Figure 2: Global sensitivity analysis of earnings in a commercial operation.
  • Figure 3: Global sensitivity analysis using the second-order Sobol index of earnings in commercial operations.
  • Figure 4: Global sensitivity analysis of RoI for commercial operations.
  • Figure 5: Global sensitivity analysis of RoI using the second-order Sobol index for commercial operations
  • ...and 4 more figures