Firstly, if you are backbetting a nonpartner, you just need to know when to split and when not to.
Only split the following in this situation:
9,9 v 2-6
8,8 v 3-7
7,7 v 6
3,3 v 5-6
2,2 v 5-6
(If DAS)
9,9 v 2-6, 8
8,8 v 2-7
7,7 v 4-6
6,6 v 5-6
4,4 v 5-6
3,3 v 4-6
2,2 v 4-6
Secondly, if the controller of the box is your partner betting table min, and you are placing a much bigger wager behind, it can be good for your partner to make the following splits (but for you not to follow unless the play is included in the above list):
9,9 v 2-6, 9-A
8,8 v 2-A
7,7 v 2-A
6,6 v 2-A
3,3 v 2-A
2,2 v 2-A
(If DAS)
9,9 v 2-6, 9-A
8,8 v 2-A
7,7 v 2-A
6,6 v 2-A
4,4 v 5-6
3,3 v 2-A
2,2 v 2-A
The above lists are taken from Andersen's BTTILS, pp.254-5.
You need to make sure, in the case of 'sacrifice splits' (those where your partner makes a suboptimal play for your collective benefit) that the ratio of the rider's bet to the controller's is sufficiently large to justify the sacrifice. You can do this in at least a couple of ways. Refer to Appendix E in Wong's _Professional Blackjack_ to find for X,X v Y the EV associated with splitting. Compare this to the EV with optimal play. The difference is the cost of the sacrifice split. Now, approximate the EV for playing X v Y by averaging the EVs for different two-card combinations that give the player a total X. Compare this with the EV from playing one hand with total X,X. This will tell you the gain from only playing one hand of total X, rather than one hand of total X,X. Once you have the controller's loss from the sacrifice split, call it L, and the gain for the rider, call it G, you can take the ratio |L|/G to determine the minimum bet ratio (between rider and controller) necessary to justify the sacrifice split. For instance, if the gain to the backbettor is .02 of money wagered, and the loss to the controller is -.06 of money wagered, the bet ratio would need to be greater than 3:1 (.06/.02 = 3) before the sacrifice split would be worthwhile.
Another way to find the minimum bet ratio would be to gain access to the bj21 Green Chip pages. A POM some time ago presented the minimum bet ratios for various sacrifice splits.