unit counter: Ashigara

The Cruiser Chase

(When to Pursue)

By Bill Burch

unit counter: Baltimore

Sunk Damaged Disabled

Introduction

While my article was being reviewed by John Pack for inclusion on his web site, he made several suggestions. One of those suggestions was to include more applications of the numbers and statistics to common situations that occur in almost every game of VitP. Given that my article was very large already, I disagreed with John. But John's idea was very worthwhile so I proposed addressing these applications by adding another set of sidebar articles. John agreed and here is one of the results.

Why Pursue?

John's question about cruisers involves when to pursue a retreating group of the enemy's cruisers as the aftermath of an area combat. Though John asked this specifically from the Allied Commander's point-of-view, the answer will apply to both the Allied Commander and the IJN Commander. Why does any player want to pursue after having already won an area? Since he has already won the area, its either to cause further attrition (sinkings) or further damage to his opponent's fleet. This will (hopefully) help him in the later turns of the game.

When to Pursue (ATTRITION)

The answer to both the attrition and damage questions involve rearranging the probabilities listed in the tables within my main article and doing a few additional calculations. This calculation involves finding the exact ratio where the expected number of sinking for both sides are equal. I'll call this the critical ratio. Show below are the critical ratios for all the cruiser combinations (undamaged) possible in the game. The critical ratio is always expressed as the number of Allied cruisers to the number of IJN cruisers. In the game when the actual ratio exceeds the critical ratio, the Allied forces have the advantage and conversely when the actual ratio is less than the critical ratio then the IJN forces have the advantage for attrition.

Critical Ratios (Attrition)
Allied Cruiser
1-1-7 1-2-7
IJN Cruiser 1+0-7 1.80:1 1.40:1
1+1-7/8 2.18:1 1.69:1
1+2-7 2.72:1 2.11:1

So what's this table telling you? My old rule-of-thumb used to be to pursue with two Allied cruisers to every IJN cruiser. This was based on the general concept that a bonus shot was twice as likely as a normal shot to get a hit. Unfortunately, the critical ratios tell a little different story. Lets say two IJN 1+2-7 cruisers are retreating from an area, then applying the critical ratio gives a result of 5.44. This is telling the Allied Commander that he has to pursue with at least six 1-1-7 cruisers to have any advantage in the number of expected sinkings. If you would pursue with either four or five cruisers as I sometimes would, you are handing your opponent an advantage in attriting your fleet.

When to Pursue (DAMAGE)

When you look at the above table everything looks perfectly reasonable. All of the ratios are near the 2-to-1 ratio that would come from a quick guess or a lot of players rule of thumb. Unfortunately when I looked at the ratios from the point-of-view of expected damage, the critical ratios look completely outrageous. In VitP even the small ships (like cruisers) with only a single shot can sink or heavily damage all but the highest defense-factor ships. No matter what happens a 1+0-7 IJN cruiser takes one point of damage and sinks. Any other hits or damage points are moot and do not contribute to the game. In other words, they don't count. Take every available Allied ship and shoot at the IJN cruiser and you cannot exceed an expected damage of 1. But that little 1+0-7 cruiser can fire at a large Allied ship and get an expected damage of 1.17. This leads to the peculiar-looking and counter-intuitive critical ratios for expected damage.

Critical Ratios (Damage)
Allied Cruiser
1-1-7 1-2-7
IJN Cruiser 1+0-7 5.19:1 9.84:1
1+1-7/8 2.21:1 3.26:1
1+2-7 1.54:1 2.18:1

So what's this table telling you? Simple, its very hard for the Allied player to deal out more damage than he expects to take. Conversely, the IJN player may pursue at a numerical disadvantage and have a fair chance at damaging his opponent worse than happens to him. This is expecially true for the two 1+0-7 cruisers.

One More Step

Unfortunately, the expected damage table cannot be further simplified so you are on your own when there is a mixture of cruisers on one or both sides. But the attrition table is very well behaved and can be reduced to an equation to find out how mixed groups of cruisers match up. Here's the equation for the ratio:

2.18 * {[0.83 * (# of 1+0-7s)] + (# of 1+1-7/8s) + [1.25 * (# of 1+2-7s)]}
(# of 1-1-7s) + [1.29 * (# of 1-2-7s)]

The numerator represents the IJN cruisers and the denominator represents the Allied cruisers. If this ratio is greater than 1 then the IJN player has the attrition advantage. And if this ratio is less than 1 then the Allied player has the attrition advantage. Hope you find use for this. Good Luck!

- wcmb