**Expected Value Models**

**—EMV & EOL—**

**Expected Monetary Value**

EMV () = E (A_{i }) = ΣA_{i }_{j }(p_{j })R_{ij }

*i*refers to the matrix's rows and

*j*refers to the columns.

Alternatively, we can make use of the decision tree:

**Expected Opportunity Loss**

*and the actual outcome resulting from choosing*

*S*_{j }*given that*

*A*_{i }*S*occurs. Referring now to the opportunity loss matrix, the formula for expected opportunity loss (EOL) is:

_{j}EOL () = E (A_{i }) = ΣA_{i }_{j}(p_{j })OL_{ij }

EOL can also be depicted with a decision tree, of course. (Exercise left to the reader.)

Note that for a given probability distribution, the expected payoffs (EMV and EOL) for every action alternative A_{i } always add up to a constant. In our case, they always add up to 4.2. Thus, the Max EMV corresponds with the Min EOL.

The 4.2 value represents the Expected Value given Perfect Information (EVgPI), and is obtained as follows:

We obtain the expected value of the above lottery ( the EVgPI ) thusly:

EVgPI = Σ_{j} * p_{j}* (

**)*

*R*_{ij}The Expected Value of Perfect Information ( EVPI ) Is then:

**EVPI = EVgPI - EMV***

If the above lottery is solved using opportunity losses instead of monetary values, we get:

**EVPI = EOL***