Speculative Decoding is a widely used technique to speed up inference for Large Language Models (LLMs) without modifying its outcome. When performing inference on an LLM, speculative decoding uses a smaller draft model which generates speculative tokens and then uses the target LLM to verify those draft tokens. The speedup provided by speculative decoding heavily depends on the choice of the draft model. It has been widely suggested to select a draft model that provides a high probability of the generated token being accepted by the LLM to achieve the highest throughput. However, our experiments indicate the contrary with throughput diminishing as the probability of generated tokens to be accepted by the target model increases. To understand this phenomenon, we perform extensive experiments to characterize the different factors that affect speculative decoding and how those factors interact and affect the speedups. Based on our experiments we describe an analytical model which can be used to decide the right draft model for a given workload. Further, using our insights we design a new draft model for LLAMA-65B which can provide 30% higher throughput than existing draft models.