Abstraction and Aggregation in Wargame Modeling

“All models are wrong, some models are useful.” – George Box

Models, no matter what their subjects, must always be an imperfect copy of the original. The term “model” inherently has this connotation. If the subject is exact and precise, then it is a duplicate, a replica, a clone, or a copy, but not a “model.” The most common dimension to be compromised is generally size, or more literally the three spatial dimensions of length, width and height. A good example of this would be a scale model airplane, generally available in several ratios from the original, such as 1/144, 1/72 or 1/48 (which are interestingly all factors of 12 … there are also 1/100 for the more decimal-minded). These mean that the model airplane at 1/72 scale would be 72 times smaller … take the length, width and height measurements of the real item, and divide by 72 to get the model’s value.

If we take the real item’s weight and divide by 72, we would not expect our model to weight 72 times less! Not unless the same or similar materials would be used, certainly. Generally, the model has a different purpose than replicating the subject’s functionality. It is helping to model the subject’s qualities, or to mimic them in some useful way. In the case of the 1/72 plastic model airplane of the F-15J fighter, this might be replicating the sight of a real F-15J, to satisfy the desire of the youth to look at the F-15J and to imagine themselves taking flight. Or it might be for pilots at a flight school to mimic air combat with models instead of ha

The model aircraft is a simple physical object; once built, it does not change over time (unless you want to count dropping it and breaking it…). A real F-15J, however, is a dynamic physical object, which changes considerably over the course of its normal operation. It is loaded with fuel, ordnance, both of which have a huge effect on its weight, and thus its performance characteristics. Also, it may be occupied by different crew members, whose experience and skills may vary considerably. These qualities of the unit need to be taken into account, if the purpose of the model is to represent the aircraft. The classic example of this is a flight envelope model of an F-15A/C:

This flight envelope itself is a model, it represents the flight characteristics of the F-15 using two primary quantitative axes – altitude and speed (in numbers of mach), and also throttle setting. Perhaps the most interesting thing about this is the realization than an F-15 slows down as it descends. Are these particular qualities of an F-15 required to model air combat involving such and aircraft?

How to Apply This Modeling Process to a Wargame?

The purpose of the war game is to model or represent the possible outcome of a real combat situation, played forward in the model at whatever pace and scale the designer has intended.

As mentioned previously, my colleague and I are playing Asian Fleet, a war game that covers several types of naval combat, including those involving air units, surface units and submarine units. This was published in 2007, and updated in 2010. We’ve selected a scenario that has only air units on either side. The premise of this scenario is quite simple:

The Chinese air force, in trying to prevent the United States from intervening in a Taiwan invasion, will carry out an attack on the SDF as well as the US military base on Okinawa. Forces around Shanghai consisting of state-of-the-art fighter bombers and long-range attack aircraft have been placed for the invasion of Taiwan, and an attack on Okinawa would be carried out with a portion of these forces. [Asian Fleet Scenario Book]

Of course, this game is a model of reality. The infinite geospatial and temporal possibilities of space-time which is so familiar to us has been replaced by highly aggregated discreet buckets, such as turns that may last for a day, or eight hours. Latitude, longitude and altitude are replaced with a two-dimensional hexagonal “honey comb” surface. Hence, distance is no longer computed in miles or meters, but rather in “hexes”, each of which is about 50 nautical miles. Aircraft are effectively aloft, or on the ground, although a “high mission profile” will provide endurance benefits. Submarines are considered underwater, or may use “deep mode” attempting to hide from sonar searches.

Maneuver units are represented by “counters” or virtual chits to be moved about the map as play progresses. Their level of aggregation varies from large and powerful ships and subs represented individually, to smaller surface units and weaker subs grouped and represented by a single counter (a “flotilla”), to squadrons or regiments of aircraft represented by a single counter. Depending upon the nation and the military branch, this may be a few as 3-5 aircraft in a maritime patrol aircraft (MPA) detachment (“recon” in this game), to roughly 10-12 aircraft in a bomber unit, to 24 or even 72 aircraft in a fighter unit (“interceptor” in this game).

Enough Theory, What Happened?!

The Chinese Air Force mobilized their H6H bomber, escorted by large numbers of Flankers (J11 and Su-30MK2 fighters from the Shanghai area, and headed East towards Okinawa. The US Air Force F-15Cs supported by airborne warning and control system (AWACS) detected this inbound force and delayed engagement until their Japanese F-15J unit on combat air patrol (CAP) could support them, and then engaged the Chinese force about 50 miles from the AWACS orbits. In this game, air combat is broken down into two phases, long-range air to air (LRAA) combat (aka beyond visual range, BVR), and “regular” air combat, or within visual range (WVR) combat.

In BVR combat, only units marked as equipped with BVR capability may attack:

• 2 x F-15C units have a factor of 32; scoring a hit in 5 out of 10 cases, or roughly 50%.
• Su-30MK2 unit has a factor of 16; scoring a hit in 4 out of 10 cases, ~40%.

To these numbers a modifier of +2 exists when the attacker is supported by AWACS, so the odds to score a hit increase to roughly 70% for the F-15Cs … but in our example they miss, and the Chinese shot misses as well. Thus, the combat proceeds to WVR.

In WVR combat, each opposing side sums their aerial combat factors:

• 2 x F-15C (32) + F-15J (13) = 45
• Su-30MK2 (15) + J11 (13) + H6H (1) = 29

These two numbers are then expressed as a ratio, attacker-to-defender (45:29), and rounded down in favor of the defender (1:1), and then a ten-sided-die (d10) is rolled to consult the Air-to-Air Combat Results Table, on the “CAP/AWACS Interception” line. The die was rolled, and a result of “0/0r” was achieved, which basically says that neither side takes losses, but the defender is turned back from the mission (“r” being code for “return to base”). Given the +2 modifier for the AWACS, the worst outcome for the Allies would be a mutual return to base result (“0r/0r”). The best outcome would be inflicting two “steps” of damage, and sending the rest home (“0/2r”). A step of loss is about one half of an air unit, represented by flipping over the counter or chit, and operating with the combat factors at about half strength.

To sum this up, as the Allied commander, my conclusion was that the Americans were hung-over or asleep for this engagement.

I am encouraged by some similarities between this game and the fantastic detail that TDI has just posted about the DACM model, here and here. Thus, I plan to not only dissect this Asian Fleet game (VGAF), but also go a gap analysis between VGAF and DACM.