I think the idea that there is any kind of "maths" in that there's some kind of formula you should follow when it comes to a declaration is the main fallacy here.
It should be done on intuition on feel, because the captain will be best placed to make a judgement on the match situation, the pitch, the opposition and the conditions, and let's face it, the captain will know faaaaaaar more about those than us armchair captains here.
It's not about a strict runs vs. time remaining formula. It's clear to me that Clarke felt that, given that time might be lost, his best chance of winning the match would come by making inroads into the SL middle order before stumps and put them under pressure going into Day 3. It's more about gut feel than about maths.
And I say that as a mathematician.
The scorecard tells you how quickly a team is likely to score, how many they're likely to score and so on.
Clarke's intuition is clearly a load of horse**** in this instance. You can use some cricketing intelligence to factor in that maybe you're a bowler down, or they're a batsman down and that sort of thing. But really you're getting most of the intuition from seeing the game play out and the scores on the board.
Ultimately whether the pitch is doing a lot, will break up and so on doesn't really have a impact in most declarations. The conditions don't tend to change much - which takes away most of the strategy and intuition.
The numbers dictate roughly when you should declare. You cannot get away from that.
All of the responses about Clarke pulling off a masterstroke because the team took a couple of early wickets after a declaration, these people need to GTFO of the thread (not talking about you, but one or two members posting in this thread).
It's like when Australia used to have a good cricket team and whether they batted first or second they made it work - because they were better than the other team. Not because their captain made a genius call at the toss, or the other captain made a bad one. This sort of **** goes on so much in all sport. A captain is a genius when he's revolving his bowlers in limited overs cricket and they happen to take a wicket. It's like the way good teams appear to be 'lucky'. Australia used to be lucky because it looked like they were bowling on a bowler-friendly pitch and batting on a batting-friendly pitch.
In sport there is apparently no such thing as coincidence. Everything has to be apportioned to inexperience, lack of concentration, great captaincy, good/bad form and the like. The same happens with any major decision they make. People can't just look at the big picture and balance the pros and cons, no a lot of the commentators are too stupid to do that - so instead we have this preposterous situation where they go purely by instinct or the end result and that is followed through by many on these forums. There are no grey areas, marginally good or bad decisions. It's black and white, right and wrong. A lot of it reminds me of Deal or No Deal the way decisions that are essentially as justifiable as each other are made into something else, and a whole load of bull**** is trotted out.
In the end scoreboard maths should dictate 99% of a declaration. Virtually all of the other factors end up being fluff, like on Deal or No Deal.