[The article below is reprinted from April 1997 edition of *The International TNDM Newsletter*.]

**Numerical Adjustment of CEV Results: Averages and Means
**by Christopher A. Lawrence and David L. Bongard

As part of the battalion-level validation effort, we made two runs with the model for each test case—one without CEV [Combat Effectiveness Value] incorporated and one with the CEV incorporated. The printout of a TNDM [Tactical Numerical Deterministic Model] run has three CEV ﬁgures for each side: CEV_{t} CEV_{l} and CEV_{ad}. CEV_{t} shows the CEV as calculated on the basis of battleﬁeld results as a ratio of the performance of side a versus side b. It measures performance based upon three factors: mission accomplishment, advance, and casualty effectiveness. CEV_{t} is calculated according to the following formula:

P′ = Reﬁned Combat Power Ratio (sum of the modified OLls). The ′ in P′ indicates that this ratio has been “reﬁned” (modified) by two behavioral values already: the factor for Surprise and the Set Piece Factor.

CEV_{d} = 1/CEV_{a} (the reciprocal)

In effect the formula is relative results multiplied by the modified combat power ratio. This is basically the formulation that was used for the QJM [Quantified Judgement Model].

In the *TNDM Manual*, there is an alternate CEV method based upon comparative effective lethality. This methodology has the advantage that the user doesn’t have to evaluate mission accomplishment on a ten point scale. The CEV_{I} calculated according to the following formula:

In effect, CEV_{t} is a measurement of the difference in results predicted by the model from actual historical results based upon assessment for three different factors (mission success, advance rates, and casualties), while CEV_{l} is a measurement of the difference in predicted casualties from actual casualties. The CEV_{t} and the CEV_{l} of the defender is the reciprocal of the one for the attacker.

Now the problem comes in when one creates the CEV_{ad}, which is the average of the two CEVs above. l simply do not know why it was decided to create an alternate CEV calculation from the old QJM method, and then average the two, but this is what is currently being done in the model. This averaging results in a revised CEV for the attacker and for the defender that are not reciprocals of each other, unless the CEV_{t} and the CEV_{l} were the same. We even have some cases where both sides had a CEV_{ad} of greater than one. Also, by averaging the two, we have heavily weighted casualty effectiveness relative to mission effectiveness and mission accomplishment.

What was done in these cases (again based more on TDI tradition or habit, and not on any specific rule) was:

(1.) If CEV_{ad} are reciprocals, then use as is.

(2.) If one CEV is greater than one while the other is less than 1, then add the higher CEV to the value of the reciprocal of the lower CEV (1/x) and divide by two. This result is the CEV for the superior force, and its reciprocal is the CEV for the inferior force.

(3.) If both CEVs are above zero, then we divide the larger CEV_{ad} value by the smaller, and use its result as the superior force’s CEV.

In the case of (3.) above, this methodology usually results in a slightly higher CEV for the attacker side than if we used the average of the reciprocal (usually 0.1 or 0.2 higher). While the mathematical and logical consistency of the procedure bothered me, the logic for the different procedure in (3.) was that the model was clearly having a problem with predicting the engagement to start with, but that in most cases when this happened before (meaning before the validation), a higher CEV usually produced a better ﬁt than a lower one. As this is what was done before. I accepted it as is, especially if one looks at the example of Mediah Farm. If one averages the reciprocal with the US’s CEV of 8.065, one would get a CEV of 4.13. By the methodology in (3.), one comes up with a more reasonable US CEV of 1.58.

The interesting aspect is that the TNDM rules manual explains how CEV_{t}, CEV_{l} and CEV_{ad} are calculated, but never is it explained which CEV_{ad} (attacker or defender) should be used. This is the ﬁrst explanation of this process, and was based upon the “traditions” used at TDI. There is a strong argument to merge the two CEVs into one formulation. I am open to another methodology for calculating CEV. I am not satisfied with how CEV is calculated in the TNDM and intend to look into this further. Expect another article on this subject in the next issue.