Bleg: Quantifying the value of bowling variety

A common critique of the current English ODI side is that they suffered from having a sameness to their bowling attack--a series of right-handed fast-medium swing bowlers. It's an interesting question. Obviously, diversity in bowling styles can only take you so far: there is a limit to how much aggregate quality a team would be prepared to sacrifice in order to increase diversity, but it is not clear that there is any value to diversity at all. The question was raised recently in the following tweets:

@CricketFanBob Variety is often said to be advantageous, but has this ever been tested with data? May not be true.
— ballsintherightareas (@ballsrightareas) March 3, 2015

There are some obvious ways in which diversity might improve a team's bowling as a unit. First, having the style of bowling change from over to over might make it harder for batsmen to settle into a rhythm. Second, if some bowling types are more effective wicket takers against right-handed batsmen and others against left-handed, then style diversity might help stop one batsman running away with a game. But these are big mights. The twitter thread above led to this request:

@ballsrightareas @CricketFanBob I wonder if we can interest @seamus_hogan to take on this challenge?
— Declaration Game (@chrisps01) March 3, 201

I'm up for the challenge, but I can't see obvious solutions to three conceptual problems:

1. As @CricketFanBob asks, how do you define variety?

If you look at the cricinfo player profiles, you will find that Bill O'Reilly and Clarrie Grimmett, who played in the same Australian test team, are both classified as "legbreak googly". This is true, but this simple classification does not tell you that O'Reilly was an unusually fast spinner who liked to bowl with the wind, while Grimmett was a more-classical flight-into-the-wind legbreak bowler. Similarly, player profiles will tell you that Joel Garner and Malcom Marshall were both "right fast", but the difference between quite fast delivered by a 6'8" bowler and extremely fast delivered by a 5'11" bowler is probably quite substantial. Maybe, however these examples are sufficiently rare that simple cricinfo categorisations are sufficient. But...

2. ...What is the best way of aggregating these bowling-type classifications into a measure of variety.

Is RFM, RFM, LF, RM, SLO more diverse than RFM, LF, RM, SLO, SLO? I think so, but how do you quantify that. And above all,

3.... How do you assess what performance a given set of individual bowler abilities would be expected to produce in order to assess whether variety (or its absence) can explain some of the difference?

In particular, how do you control for the endogeneity that, for example, a spin bowler in spin-friendly conditions will probably a) be in a team with other spin bowlers to take advantage of those conditions, and b) likely to do better than average because of those conditions, making it difficult to infer any value to diversity that might exist.

I have some ideas, but I suspect that the number of variables needed would exhaust the useful degrees of freedom. Any thoughts?