This study investigates the necessity and impact of a detailed rubric in automated essay scoring (AES) using large language models (LLMs). While using rubrics are standard in LLM-based AES, creating detailed rubrics requires substantial effort and increases token usage. We examined how different levels of rubric detail affect scoring accuracy across multiple LLMs using the TOEFL11 dataset. Our experiments compared three conditions: a full rubric, a simplified rubric, and no rubric, using four different LLMs (Claude 3.5 Haiku, Gemini 1.5 Flash, GPT-4o-mini, and Llama 3 70B Instruct). Results showed that three out of four models maintained similar scoring accuracy with the simplified rubric compared to the detailed one, while significantly reducing token usage. However, one model (Gemini 1.5 Flash) showed decreased performance with more detailed rubrics. The findings suggest that simplified rubrics may be sufficient for most LLM-based AES applications, offering a more efficient alternative without compromising scoring accuracy. However, model-specific evaluation remains crucial as performance patterns vary across different LLMs.