Here is my hypothesis on measuring the value of good innings in test cricket based on 'when' it is played. This hypothesis is based on an intuition that 4th innings century makers have been unjustly glorified as 'match winners' as opposed to more deserving first innings century makers. Ideally I wanted to pull some data from "stats-guru" database to back the hypothesis. But time constraints and inability to pull the data the way I want to has left me with the cop-out option of just stating the hypothesis and have a kind soul prove or disprove the hypothesis. This hypothesis is not earth shattering or by any means new. It is in fact very obvious to most and in general used as an axiom by most test cricket captains. I state this only to counter-point a new trend in cricket analysis that seems to glorify 4th innings centuries. So here goes
1. Team that bats well in their first innings of the test match is less likely to lose the test match. (Note that this is very different from saying "...more likely to win the test match").
2. The above point can be proven by analyzing data of all test matches played so far. We should find that the team with the higher first innings score would have a greater likelihood of *not* losing the match. As a corollary we should also find that the greater the gap between first innings scores the lesser the instance of team scoring higher having lost the match. For e.g. In instances where delta between first innings scores of two teams is 50 (lets call this variable 'X') or less - let us hypothetically say that the percentage of instances where team scoring higher in first innings loses the test match only 8% of the time (let us call this percentage 'B'). The assertion I am going after is that B is super inversely proportional to X. This data is hard to get and holds the key to whether my theory has any merit or not.
3. Restating 2 to narrow down to the point I want to make - As X (per definition above) increases - the ability of each subsequent innings of that test match to change/reverse the course of that test match decreases. For example When X = 100 let us say that the probability of 3rd innings of the match changing the course of the match is N. Hypothesis here is that the probability of 4th innings changing the course of the test match is actually N/2 or worse. Further hypothesis is that as X increases 3rd innings becomes more and more irrelevant and 4th innings a mere formality to be closed out.
Now up until now #1, #2 and # 3 above are bleeding obvious. Now lets get down to the merely obvious.
4. Following from #1 above - teams should look to maximize the first innings score as much as possible in order to give them the best shot of winning a test match.
5. Following from #2 if a team is faced with a choice of picking Player-1 who will reliably perform well in the first innings of a match Vs Player-2 who will reliably perform in the second innings of a match. The team should always pick Player 1 to firstly maximize there chances of not losing the match and secondly to set themselves up for a win.
6. Following from #3 it is true that in those very rare instances where a player's 4th innings score manages to change the course of the match they have a higher probability of being noticed purely because the event is a low-probability one and so happens very rarely. However, it can be argued (not always) that the player is "curing" a situation as opposed to "preventing" the situation. And if he had batted well in the first innings things would actually have been much better (statement is based on assumption that the said player isn't hitting a century in both innings but 'woke up' in the 4th innings to play well). Sort of analogous to doing well in your arrears exam as opposed to the actual exam. Yes arrears has infinitely more pressure but you shouldn't be writing one in the first place. And you can't be regarded as a good student just because you do consistently well in arrears.
But the direction we are trying to get to is that the most important phase of the test match is the team's first innings. That is what should be called as the "crunch time". And a player who consistently plays well under those circumstances should be regarded as a player who is more effective in winning the match for the team by playing well "when it matters". This is the player who should be regarded as a match-winner
Needless to say - I am stating this as hypothesis based on casual and random filtering and sorting of cricinfo data. I do realize that this may be completely wrong.
P.S: In support of the hypothesis some of the types of data I wanted to pull outside of what was mentioned in #2 are as follows:
a. what % of the matches won by a team had centuries scored by some batsman in the first innings of the match? (knowing fully well that 'century isnt the only definition of good innings but merely a decent indicator)
b. what % of the matches not lost by a team had centuries scored by some batsman in the first innings of the match?
c. what % of the matches lost by a team had centuries scored by some batsman in the first innings of the match?