Budgeting for executive assessment consultants necessitates a strategic approach, much like a chess game where each move is carefully planned, and the potential outcomes weighed. It is not merely about allocating funds, but also understanding the value and return on investment these services can provide. This is especially true when we consider that the effectiveness of your executive team can profoundly impact the trajectory of your organization.

Executive assessment consultants specialize in identifying, assessing, and selecting top-tier executives for your organization. They possess an in-depth understanding of the unique blend of skills, experience, and temperament required for effective leadership in various industries. Their services are an invaluable asset in securing the right individuals to drive your organization's growth, innovation, and competitiveness.

Strategically budgeting for executive assessment consultants requires an understanding of the different types of consulting fees. These typically include retainer fees, project-based fees, and hourly rates. Retainer fees offer a set amount for a specified period, project-based fees are for a single, defined task, and hourly rates charge per hour of consultation. Deciding on the best payment structure depends on your organization's specific needs and long-term plans.

Consider the intricacies of your organization, the industry in which you operate, and the specific executive roles you need to fill. For example, if you're operating in a highly specialized or rapidly evolving sector such as technology or pharmaceuticals, the value and thus the budget allocation for these services may be higher.

Additionally, it is essential to consider the potential risks and rewards associated with executive selection. A well-chosen executive can propel your organization to new heights, garner increased market share, and foster an inspiring culture. On the other hand, a poor choice can result in significant financial loss and reputational damage. Therefore, investing in executive assessment consultants is a form of risk mitigation, and the budget should reflect this.

Moreover, the utilization of advanced statistical tools and techniques, such as psychometric testing, can provide a more comprehensive understanding of an executive's suitability for a role. These tools can assess cognitive abilities, personality traits, leadership styles, and other relevant competencies. The use of such tools, although adding to the cost, enhances the accuracy and effectiveness of the selection process.

Incorporating Game Theory into your budgeting strategy can also prove beneficial. This mathematical model of strategic interaction could provide useful insights into the potential outcomes of different budget allocations. By considering the 'games' played between your organization, potential executives, and competing firms, you can make more informed decisions about the value of executive assessment services.

The timing of the hiring process also plays a vital role in budgeting. A rushed process may result in increased costs due to hasty decisions and inadequate assessments. On the other hand, a prolonged process can lead to lost opportunities. Therefore, it's important to budget for a process that is thorough yet efficient.

Lastly, remember that your organization is not merely purchasing a service, but investing in its future. Allocating resources to executive assessment consultants is investing in the quality of your leadership, which ultimately shapes your organization's culture, performance, and sustainability.

In conclusion, budgeting for executive assessment consultants is a complex, strategic process that requires consideration of a variety of factors. Remember to consider the industry, the risks and rewards, the statistical tools and techniques employed, the timing, and the long-term impact on your organization. By doing so, you can ensure that your budget is not only cost-effective but also value-adding.