I'm still reeling from downloading the crusader_unit_prod11.xls file and seeing how systematically CA have built up the unit stats. One thing that struck me was the costing of the units.
It seems that a complicated formula is used to work out the cost of the units, based on many of its stats. This should help balance the game for MP and means that cost should not be a bad statistical measure of relative effectiveness.
However, support costs seem to be determined largely by the troop type, defined in terms of "soft" factors like whether it is tribal, guard, missile etc, with cav costing double and 20% markups for "elites". There are also some strange fudge factors: Byz infantry get a 40% surcharge on support costs; spearmen get a 50% one; crossbows and arbs pay only 75% of base support costs. You pay 20% extra for Royals and only 50% of base support for crusading knights. Now the end result is that support costs are only very weakly related to combat power. The Chiv spear and Saracen are essentially the same unit, but the Chivs cost 25% more to support than the "tribal" Saracens.
Now bear in mind that support costs are overwhelmingly important in the SP game. A spearman's price may be 150 but this is outweighed after a mere three years of paying a support cost of 50.
So if you want to know whether a unit is relatively cost-effective in the SP game, one rough assessment is to compare the purchase price as a proxy of benefits to the support cost as a proxy for costs.
For a more sophisticated assessment of costs, we could combine purchase price and support costs given some assumptions. Let's say the unit lives for 20 years and the discount rate is 5%, then we can calculate the net present value of the support cost (in excel, using the function PV(5%,20,support cost))
Some results are unsurprising. By either method, peasants are the least cost-effective units. Their price-support ratio is 1.33; by the more complicated method of comparing price to the discount net present value of both purchase and support costs, it is 0.1.
However, there are some other units very low down the list that I tend to like, eg Byz infantry at number 5, followed by hobilars and spearmen.
There is tendency for higher tech units to appear more cost-effective - their capabilities - measured by purchase price - rise dramatically, but their support costs don't keep pace. The top 20 include the Gothic knights, SAPs, PavArbs, JHI etc. Gothic knights are a steal, with a simple price/support cost ratio of 12 and the more sophisticated cost-effectiveness index of 0.49. Some of this is driven by the fudge factors mentioned before, but not all.
I'm not seriously proposing looking a the price to support ratio as better than relying on experience when buying armies in SP, but it does prompt a couple of thoughts.
One reaction: why not make support costs are simply a fraction of purchase costs?
Other thought: I wonder how the AI assesses cost-effectiveness? If it is looking at the price as a measure of the cost, rather than the effectiveness, then that may explain the high preponderance of peasants in early games.
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