Sorry if this is known, but why are we assuming lower volatility is better for an offense? Wouldn’t it be better to have a team that scores 4 runs in half of its games and 0 in the other half than a team that scores 2 runs in every game (assuming an average pitching staff)?
That is indeed the big question. Trying to reason it out would be fruitless. I need to see what, if any, correlation there is to winning before I could care about it.
A very rough eyeball comparison to winning and volatility in the team chart above doesn’t encourage me to think this is worthwhile.
On a team level, the answer would obviously be 1/3 every day. Obviously 1/3 is high, but even if we took 1/4. Basically the team is losing 3 out of 4, and then winning a blowout. 1/4 from everyone every day, and some days the other pitcher might dodge that and only give up 0-2 runs, but that is a better result than the 0-fers.
On an individual level, it just comes down to situation. One probably isn’t that much “better” than the other, as long as the hits come when they are beneficial.
Maybe this is an oversimplification but I think you can look at it like this. Two basic aspects to the game. Pitching and hitting. Both can be considered poor, average or good. Both can be considered inconsistent, somewhat consistent or very consistent.
All told you have 18 different “terms” (ex. consistent average hitting). I think you then have to see how they matchup with each other to see what is best option for one aspect of the game, given the other. For example, if you have consistent poor pitching and an average offence, than you want that offence to be volatile to have any hope of winning more than you lose.
I find this very interesting and have always wondered whether there is a way to take a measurement like this and use it better construct a lineup using the basic concept of diversification from portfolio theory. The thought stems from the idea that it seems that teams, rather than just players, are often inherently streaky and volatile. A ideal team therefore would want to minimize its volatility with the highest expected run output not have a bunch of low volatility players but have all highly volatile players, whose performance is lowly or negatively correlated to the other players (likely through other factors such as time of season, home/away etc)
I’m very much a newbie at this stuff so I’m sure this concept has been well thought-out. I guess a very basic example of this occurs with right/left hand platoon splits but I’ve never seen any analysis that attempts to identify other factors that create volatility and could be used on a team-wide basis.