Set-off is used to describe the practice by a payor of deducting from an amount due to a creditor amounts due by the creditor to the payee. To give a simple example, Bob owes John £500, but John owes Bob £150, so Bob chooses to pay John only £350, deducting the £150 he is owed. While this may sound simple at the outset, it is more complex in practice. What happens for example if John disputes his debt to Bob? What if the debt is for an uncertain amount? What if the debt is from a completely different deal? What if there is litigation between Bob and John over the £500 and another claim over the £150. What if the £500 is due today, but the £150 is due in the future? What looks simple at the start can become much more complex in practice.
Generally, where the claims are liquidated, (i.e., for a fixed amount, a sum-certain), and both are due, the law favors set-off as an efficient and fair mechanism. There are various different types of set-off; however, it should be noted that there is considerable inconsistency in the use of language with respect to “set-off,” particularly in case-law, which can be very confusing (and it would be fair to suggest that the judges are themselves confused.):
Inside litigation, where the plaintiff brings a money claim and the defendant counterclaims or seeks off-setting in respect of the value of its liquidated claims against the plaintiff – in other words seeking to have the monetary claim reduced by the counterclaim, this is generally referred to as “equitable set-off.” Courts developed a tradition of hearing these counterclaims for set-off because it was considered unfair and not equitable to allow one party to recover ahead of the other, and indeed there was a concern that a claimant who received his award first might “take the money and run,” and because it was regarded as more efficient. For equitable set-off to be available there must be some relationship between the claims. Thus the English courts have held:
“… it is not every cross-claim which can be deducted. It is only cross-claims that arise out of the same transaction or are closely connected with it. And it is only cross-claims which go directly to impeach the plaintiff’s demands, that is, so closely connected with his demands that it would be manifestly unjust to allow him to enforce payment without taking into account the cross- claim…”
Federal Commerce & Navigation Co Ltd v Molena Alpha Inc.,  QB 927 (“The Nanfri”)
Outside (or prior to litigation), when a first party deducts from payments due to the second party the liquidated amount of that second party’s liability, i.e., subtracting from what it pays from what what it believes it is owed, so as to pay the net amount, this is often referred to as “legal set-off.” Both inside and outside litigation, when the amount a party wants to set-off is un-liquidated, i.e., the second party’s liability to the first exists, but the amount is not established or fixed, the term “abatement” is used.
Complicating things further is that the term “legal set-off” is also used in English (and Australian, Singapore, Irish, etc.) bankruptcy law to refer to the right in the relevant bankruptcy code for a party who owes a bankrupt money, but is also a creditor, to set off the liabilities of the bankrupt party against its liabilities to the bankrupt.
Set-off presents a tricky problem in arbitration. Because an arbitration takes place under a contract, the arbitration agreement, and both parties must agree to arbitrate the claims at issue, generally to seek set-off or to defend set-off in an arbitration requires that both the underlying claim and the set-off claim arise under the same agreement. If the core claim and the set-off claim do not arise under the same agreement, the arbitral tribunal may lack jurisdiction to hear both.