My first actual attempt at a weight function was actually just a log function, which reproduces something fairly similar to what Cribb has there (hence the weird IF code, to avoid explosions due to log[0]), but that just felt wrong to me.
I can see how this works but it certainly doesn't fit my general intuition -- I take point about stopping collapses is a good one, but on the other hand, how many bowling teams have been let back into what seemed an increasingly one-sided match because a set batsmen on 60 or 70 threw it away? What good is seeing off the wicket-taking spell if you don't cash in a la Cook a few weeks back and make it count? What's the gain to be had in seeing off a top-class Boultee burst and then chipping one to mid-on off the spinner? I've been a believer for a long time now that big scores have a disproportionately large value to the team because they define an innings, and allow other batsmen to make those smaller scores and build partnerships (which are the core currency). It'd be interesting to "control" for this somehow, and see what proportion of these "useful" lower scores come with a big score being compiled at the other end, but off-hand I'm not sure how you'd do that. Alternatively, what if the graph there is just a function of the simple fact that smaller scores are simply more likely for obvious reasons, and with the number of batsmen who bat in a Test, you're going to have some small scores in any winning total somewhere along the line?
This is all part of a broader conversation that I want to have btw, and this is partially aimed at starting - to what extent is batting non-linear, and why do we assume it is when we measure averages, strike rates, etc etc etc?
