The 2013 Harrison Goblins database for plays that we used had 306 runs and 281 passes. The probability distribution functions (PDFs) for the data are found in Figure 1. The PDFs provide the probability of the yards gained for a play within the Harrison offense last season.
|Figure 1. Probability Distribution Function for 2013 Harrison|
There are two other distribution functions (the cumulative distribution function [CDF] and the complementary cumulative distribution function [CCDF]) derived from the same data. Those functions are found in Figure 2 and Figure 3.
|Figure 2. Cumulative Distribution Function for 2013 Harrison|
|Figure 3. Complementary Cumulative Distribution Function for 2013 Harrison|
The most useful data to a coach in the 4th down decision making process are the CCDFs. Essentially, the CCDF will describe the probability that a team will gain AT LEAST a given number (X) yards. We have built an Excel tool to query the CCDF to give a coach the probability of gaining the yards needed for a 1st down with either a run or a pass play. Figure 4 shows a screen shot of the data query sheet of the Excel tool.
|Figure 4. Screen Shot from Excel Decision Tool|
The tool does not provide a coach with much help on a Friday night, but a table for inclusion on a play call sheet is easily created. A sample table created using the data and tool above is found in Figure 5.
|Figure 5. Sample Play Sheet Table Using 2013 Harrison Data|
The table above would fit in a corner of a play sheet allowing a coach to assess the degree of "gambling" with a given play call. However, the full degree of gambling is not known unless he includes the points the other team is likely to score if a conversion fails. We discuss this analysis technique (and a couple of others) in the book.
We are looking forward to a great 2014 high school football season in the Natural State. To learn more about decision making tools for high school coaches, pick up an eBook copy of Saturday Morning Wake-Up Call at your favorite bookseller for just $0.99.