On cricket: This will be tricky because at any given moment each team can score in two very different ways. And the value of each particular “score” will change according to the match situation.
Batsmen are trying to score runs, bowlers (and the fielding team generally) are trying to take wickets. Generally speaking, any given ball is more likely to see a run scored than a wicket taken. Equally, while there are no restrictions in the laws about how many (or how few!) runs may be scored, you can only win a cricket match by taking 20 wickets. So any ball which takes a wicket is more exciting, and has a potentially bigger effect on the match, than any given ball which gets hit for runs (even if it’s a boundary).
So it might be tempting to argue that the relevant factor in cricket should be wickets - or, to allow for opportunities as well as scores - wickets and near-misses (e.g. dropped catches, near-run outs, appeals for LBW, or, most crucially, beating the bat). But there will be situations where this is misleading.
The most obvious is the run chase. Take the 1992/3 Australia vs W. Indies Test at Adelaide. Australia, in their second innings, have been set a target of 186 runs to win. They have 10 wickets in hand. If they score the runs, they win. If they don’t reach 186, but lose less than 10 wickets, it’s a draw. If they lose all 10 wickets, they lose the match. Despite losing 7 of those wickets for only 74 runs, they struggle on to 102/8 and then 144/9. With one wicket to go and 22 runs needed, each and every run is thrilling. A boundary unbelievably so. And the score mounts up, past 160, past 170, one or two runs at a time, occasionally four, all the way to 184. When finally, the bowler strikes and the match is won by one run. But of course, the nearer Australia got to their target, the more exciting each run became.
The second area where runs are thrilling is the general situation where bowlers are on top. In the recent South Africa vs India series, Dale Steyn took 5 for 75 - and in the same innings, Tendulkar scored a century (145, IIRC). When wickets are coming easily, it’s thrilling to see a batsman soak up the pressure, ride his luck, and start counter-attacking when the time comes.
Finally, of course, it’s possible for the batsmen to pile on so many runs (say, a 180-ish partnership) that taking a wicket won’t really make much difference to the game.
The upshot of this is that, for cricket, the metric would have to be weighted according to the game situation, to show the relative value of each “score”.