Comparing a certainty with a distribution
The decision to settle or try a case is a comparison between two things that are not the same shape. On one side is a number you can have this month, reduced by a fee and by the costs already spent. On the other is a set of possible verdicts, each with a probability, arriving in a year or two, reduced by a bigger fee and bigger costs, and with a real chance of nothing at all.
Expected value makes them comparable by collapsing the distribution to a single number: multiply each outcome by its probability and add them up. Then discount that number for the delay, because a dollar arriving after eighteen months is worth less than a dollar arriving today. What comes out is a like-for-like comparison, and the gap between the two figures is the price of certainty.
Three modelling choices do most of the work here, and each is a place where an estimate can quietly become a decision. The probabilities are the first and the least reliable. The second is the fee structure, because most contingency agreements charge a lower percentage on a pre-suit or pre-trial settlement than on a verdict — the case has to clear the additional fee before it clears anything else. The third is whether the client bears advanced case costs when the case is unsuccessful, which turns the downside from zero into a negative number and can be the single largest term in the calculation.
Netting each branch, then discounting the whole
Every branch is netted the same way: gross award, less the contingency fee on that award, less the case costs. Costs come out after the fee in most fee agreements, which is the convention used here; some agreements deduct costs before computing the fee, which produces a different and usually better number for the client. Read the agreement rather than assuming, because on a $400,000 verdict with $45,000 of costs the difference between the two conventions is $18,000.
The unsuccessful branch is where the sign matters. If the firm absorbs advanced costs when the case fails — common, and sometimes required by the fee agreement — the branch is worth zero. If the client remains liable, it is worth minus the costs. On the default figures, that switch moves the expected value from $96,750 to $81,000: a swing of $15,750, which is 35% of the $45,000 costs, because the unsuccessful branch carries 35% of the probability.
Discounting handles the delay. Dividing by (1 + d) raised to the power of months over twelve turns a future expected value into a present one. The choice of rate is a judgement about your own circumstances rather than a market fact: a claimant with medical bills falling due has a much higher effective discount rate than one who does not need the money, and that alone can justify accepting an offer that expected value says is too low.
The indifference offer is the most useful single output for a negotiation. It answers the question in the form it is actually asked: not "is this offer good" but "what would the offer have to be". Rearranging the comparison, it is the present value of trial plus the costs already incurred, divided by one minus the settlement fee percentage — the gross figure that nets down to exactly what proceeding is worth.
Worked example: a $120,000 offer against a $400,000 claim
You are offered $120,000. Counsel's fee is 33% on a settlement and 40% at trial. You have spent $12,000 in case costs and expect $45,000 in total by the end of trial, and your agreement makes you responsible for those costs whatever the outcome. You assess a 45% chance of a full win at $400,000, a 20% chance of a partial outcome worth $150,000, and therefore a 35% chance of recovering nothing. Trial is eighteen months away and you value money at 5% a year.
- Net if you win. $400,000 × 60% = $240,000, less $45,000 of costs = $195,000.
- Net on a partial outcome. $150,000 × 60% = $90,000, less $45,000 = $45,000.
- Net if unsuccessful. No recovery and you carry the costs: −$45,000.
- Expected value. 0.45 × $195,000 + 0.20 × $45,000 + 0.35 × (−$45,000) = $87,750 + $9,000 − $15,750 = $81,000.
- Discount it. 1.05 raised to the power 1.5 is 1.0759298, so $81,000 ÷ 1.0759298 = $75,283.72.
- Net of the offer. $120,000 × 67% = $80,400, less the $12,000 already spent = $68,400.
- Advantage of proceeding. $75,283.72 − $68,400 = $6,883.72.
- Indifference offer. ($75,283.72 + $12,000) ÷ 0.67 = $130,274.21.
So the arithmetic mildly favours trial, by about 10% of what the offer nets. That is a small edge bought with a 35% chance of walking away $45,000 worse off than you are today. Whether that trade is worth making is not an arithmetic question, and the honest use of this number is to tell you that $130,274 is where the conversation should be, not to tell you to reject $120,000.
What expected value does and does not tell you
Expected value is the average outcome across many repetitions of the same gamble. An insurer facing ten thousand claims genuinely experiences that average, which is why insurers can and do reason this way. A claimant with one case experiences one draw from the distribution, and the average is not available to them. That asymmetry is the reason settlements systematically favour the repeat player, and it is a real structural feature of litigation rather than a failure of nerve on the claimant's side.
So treat a small positive advantage as an argument for negotiating rather than for trying the case. The indifference offer tells you what to ask for; the size of the downside tells you how badly you need to avoid the bad branch. If the unsuccessful branch would leave you unable to pay for something you need, the correct decision can be to accept an offer well below expected value, and no amount of arithmetic changes that.
Then test the sensitivity. The table on this page recomputes the whole comparison across probabilities of winning from 10% to 90%, and the column that changes sign tells you the win probability at which the two routes are worth the same. If that break-even probability is close to your estimate, the calculation is not telling you anything — your estimate is not accurate to that precision. If it is far from your estimate, the answer is robust to being somewhat wrong about the odds, which is the only sense in which this exercise is reliable.
Two further things sit outside the model. Appeal risk: a verdict is not money, and a defendant with resources can appeal, delay and sometimes reduce it, while a judgment accrues interest at a statutory rate in the meantime. And collectability: an uncollectable verdict is worth nothing whatever its size, so a defendant with limited insurance and no assets caps the realistic award far below what liability alone would suggest.
Break-even probability at different cost structures
| Costs to trial | Net if you win | Net if unsuccessful | Break-even P(win) |
|---|---|---|---|
| $0, firm absorbs | $240,000 | $0 | 28.5% |
| $45,000, firm absorbs | $195,000 | $0 | 35.1% |
| $45,000, client bears | $195,000 | −$45,000 | 47.3% |
| $90,000, client bears | $150,000 | −$90,000 | 66.0% |
Each break-even is (68,400 - net loss) / (net win - net loss). Who carries the case costs on an unsuccessful outcome moves the break-even probability by more than twelve points in the middle two rows, on identical facts.
Where these estimates go wrong
- Optimism about the probability of winning. Lawyers and clients both overestimate it, and the effect is well documented in the settlement literature. Ask what an experienced neutral would say, not what you believe.
- Modelling only win and lose. Most verdicts are neither. Comparative fault findings, reduced damages and partial liability are the common outcomes, which is why the middle branch is here.
- Using the same fee percentage for both routes. If your agreement steps up at suit or at trial, the trial branch has to clear that step before it clears anything else.
- Forgetting costs already spent are gone. They come out of a settlement too. Only the additional costs of proceeding are the incremental price of trial, though both figures are needed to net each route correctly.
- Ignoring the time value of the delay. Eighteen months at any meaningful discount rate removes a real amount from the trial branch, and the wait itself has non-financial costs.
- Assuming a verdict is collectable. Policy limits and defendant assets cap what any judgment is actually worth. Check them before setting the award figure.
The other numbers in a settlement decision
Once you have decided, the arithmetic continues. The contingency fee net settlement calculator shows what actually reaches you from any gross figure after the fee, the case costs and any medical liens, and lien reduction is frequently worth more than the last increment of negotiation on the gross number. If comparative fault is the live issue, the comparative negligence calculator shows how the three different rules in use change the recovery, which is often exactly what the partial-outcome branch on this page represents.
If you proceed and win, a verdict starts accruing interest: the judgment interest calculator prices what an unpaid judgment is worth as an appeal runs, which belongs in the trial branch of any serious analysis. And before any of this, confirm the claim is still live — the statute of limitations deadline calculator counts the filing window, which no expected value can survive missing.
Where the settlement would be paid over time rather than in a lump, compare like with like using the structured settlement present value calculator: a structured offer with a large headline total can be worth less in present value than a smaller lump sum, and quoting the undiscounted total is a standard negotiating move on the defence side.
One case is not a portfolio
Everything on this page assumes risk neutrality — that you would be equally happy with $75,284 for certain and a gamble whose average is $75,284. Almost nobody is, and a claimant with a single case, real bills and no ability to absorb a loss is right not to be. Use the expected value to know what the case is worth in the abstract and to set a target for negotiation, and then decide separately how much you are willing to pay for certainty. That premium is a rational choice, not a mistake.