Decision Tree Analysis is simply a process of analyzing an issue on the basis of a step by step basis while applying the principles of probability.
In its simplest terms think of a coin flip. Every time you flip a coin, there is a 50% probability that it will come up heads.
But if you are trying to predict the probability of two consecutive coin flips coming up heads, then you multiply the two probabilities. Thus 50% X 50% = 25%. In other words, there is a 25% chance of a coin flip coming up heads two times in a row or a 75% chance that that will not happen.
Many lawsuits can be analyzed using this same methodology.
Imagine the following fact situation:
The plaintiff was fired, and the employer is alleging just cause.
The Plaintiff’s lawyer believes that she has a good chance of beating the just cause issue and puts her chances at 75%.
Of course, that means that there is a 25% chance that just cause is upheld and the case is therefore worth zilch.
Assuming that just cause is upheld, an additional issue is that there is an employment contract which if enforceable, would limit the plaintiff’s recovery to $10,000. Given the uncertainty of the law on this issue, the Plaintiff’s lawyer thinks that her chances of defeating the contract are only 50%.
If she can both beat the just cause argument and get around the contract, the next issue is whether or not the $25,000 bonus will be included in the award. If the bonus is included, the case is worth $100,000. If the bonus is excluded, the case is only worth $75,000. Again, given the uncertainty in the law, the lawyer estimates a 50 % risk factor to this issue.
So, what are the chances that the Plaintiff will recover $100,000 at trial?
Step One : $100,000 X 75% = $75,000 ( Just cause risk )
Step Two: $75,000 X 50% = $37,500 (Termination clause risk)
Step Three: $37,500 X 50% = $18,750 (Bonus inclusion risk)
Another way is to simply multiply the probabilities as follows:
75% X 50% X 50% X $100,000 = $18,750
Thus, the chances of winning $100,000 are only 18.75%.
However, there are also the following probabilities to consider:
- There is a 25% chance of getting nothing if just cause is upheld.
- There is a 37.5 % chance of getting only $10,000 if just cause is not upheld but the termination provision is found to be valid.
- The probability that the outcome will be $75,000 is the same as it is for $100,000
The chances of getting nothing 25%
The chances of getting $10,0000 37.5%
The chances of getting $75,000 18.75%
The chances of getting $100,000 18.75%
Now assume that the mediation hits an impasse and the defendant’s last offer is $66,000. The plaintiff’s last offer is $82,500.
Assume that the plaintiff’s lawyer is on a contingency fee and that the plaintiff does not have adverse cost insurance. Also assume that the plaintiff owns a house with plenty of equity.
Note that neither of the offers actually reflect a possible court outcome. This is good because it shows that each side is already evaluating risk, however they just disagree on how to do it.
As a mediator I would have this discussion with the plaintiff.
“Well, we have certainly come a long way today, considering that before we started the mediation, the employer had offered you only $5,000, which is what we call in the trade “nuisance money”. Whether you like their number or not, $66,000 is not nuisance money.
Your ex-employer has said that the most they will pay you today is $66,000.
We know that if you are successful on all counts you will get $100,000 and if you don’t succeed on all counts, you could get either $75,000 or $10,000 or zilch.
At $66,000 you are $34,000 short of your objective. But not really. First of all, because of your contingency fee arrangement, that $33,000 difference is really only $24,750 because of the 25% fee arrangement. Moreover, that $24,750 is subject to tax withholding of 30%, which means the real difference to you of not getting an extra $33,000 is only $17,325.
Let’s take a closer look at the 25% nightmare scenario, in which you get zilch. Now, I know that with that outcome you will not owe your own lawyer anything. But I also know that your lawyer has explained to you that if you lose, the Court will in all likelihood order you to pay part of the costs of your former employer. She has told you that this would likely be around $50,000. As you have a house with real equity, your ex-employer could ultimately collect the costs award.
So here we have it. You a decent chance of getting $17,325 more money in your pocket if you win in Court. But if you lose in Court and get zilch, you have lost two amounts, the $50,000 you have to pay to the defendant and the $66,000 you could have had if you accepted their offer.
In other words, if you go to trial and lose completely (of which there is a 25% chance) you will be out $116,000.
Next, what are the consequences of losing $116,000 to you? In many cases, it would involve losing your home or a large portion of your retirement fund.
Let’s assume that odds of you getting $17,325 more in your pocket are the same as you losing $116,000.
In Vegas, only a high-risk poker player would take that bet.
So, what are my instructions?”
Using the same data, this is the conversation I would have the owner of the defendant.
“Well, we have certainly come a long way today, considering that before we started the mediation, the employee had offered to settle $250,000, which is what we call in the trade “crazy money”. Whether you like their number or not, $82,500 is not crazy money.
I fully appreciate that this settlement is real money to you as you own this company. I appreciate that you got to where you are today because in part you are a good businessman.
Let’s analyze this issue the same way you would analyze any other business problem, because that is exactly what this litigation is.
As this case stands, your lawyer has said that largely because of the issue of just cause, this trial will probably take 5 days. Since we are at the beginning of a long litigation process, your lawyer has told you that to take this case to the end of a 5-day trial will cost you around $115,000.
Now I know that if you were to win on the issue of just cause (which we agree you have a 75% chance of not achieving) then the Court would probably award you about 60% of your legal fees or $69,600. That means, that assuming you could collect that from the plaintiff, the cost of winning would be around $46,400.
Let’s look at the cost of losing. Lets even assume that it is not a complete loss and you win on the issue of excluding the bonus. That means you would pay as follows:
Costs to your lawyer $115,000
Partial costs to plaintiff’s lawyer $69,600
Even if you only lost on the issue of just cause and won everything else and the Court awarded the Plaintiff no costs, this would still cost you:
Costs to your lawyer $115,000
So, a complete win will cost you $46,400
Losing partly will cost you $125,000 to $259,600
Settling today could cost you at most $82,500
The only way you can do better than $82,500 is to win outright, which your lawyer has told you has a 75% chance of not happening.
What are my instructions?”