Since I know that all of you at home have been dying to make your very own Weibull curves, I'm releasing another fun tool today. It's a Weibull Worksheet that allows you to generate Weibull run distributions and associated charts with only a few pieces of information:
- The average number of runs allowed (or scored) for a team.
- The run environment, which is the average total number of runs scored in a game by both teams. You can "grain" this any way you like - I prefer coarse grain run environments which take into account league and era, but I suppose you could use fine grain run environments which take into account league, era, teams, and park. All standard sample size caveats apply, blah blah blah.
Once you've opened the worksheet, you'll see three sheets: Engine, Freq Char, and Cum Freq Chart. In the Engine sheet, you'll see an Input and an Output section. In the input section, there are three cells with are highlighted in green: RE, <RA>, and <RS>. In the RE cell, enter the run environment; in the <RA> cell, enter the average number of runs allowed by a team; and in the <RS> cell, enter the number of runs scored by a team.
Technical note: the parameter α is computed such that the actual <RA> or <RS> matches the model <RA> or <RS>. I do realize that a better way to do this would be to minimize the least squares error, but I was too lazy to do it. The parameter generated here is close enough for almost any application. The parameter γ is calculated using the Smyth-Patriot model.
That is enough information to generate two Weibull curves: one for runs allowed and one for runs scored.
In the output section, you'll find the frequency with which a particular number of runs are scored as a function of runs for both runs allowed and runs scored. These data are used to generate the Frequency Chart on the Freq Chart tab. You'll also find in the output section the cumulative frequency with which a particular number of runs are scored (e.g., the frequency with which 4 or fewer runs are scored) as a function of runs for both runs allowed and runs scored. These data are used to generate the Cumulative Frequency Chart on the Freq Chart tab.
I hope you find this enjoyable and useful. More run distribution resources: