The Effect of Allocated Bombers on Airfield Raids: A Statistical Analysis

[nedcorleone1]

I should start out by saying that though this is a statistical analysis, I did not do hundreds of tests (that would take me a lifetime). I wanted to test the effect of the number of 'allocated bombers' against the number of 'engaged bombers' and the number of 'destroyed SU air units.' Its a somewhat interesting result.

Definitions
'allocated' - The aircraft of a particular type the player set before launching a raid
'engaged' - The aircraft that actually was engaged in combat

Constants:
Turn 1
Game Version - 1.04.36
Difficulty Level - Custom - GE=100, SU=90 (for all options)
Weather - Clear
Scenario/Turn - '41 Germany
Location - 7 SAD Airbase (X53,Y41)
Airplane Doctrine - 10% (the rest default; value taken from ComradeP's 'First Turn' post)
Total SU aircraft attacked - 139
3 Sets - Increased 'allocated bombers' only
Each set consisted of 10 trials

Set 1:
Total GE 'allocated bombers': 74
Total GE 'allocated fighters': 69
Average GE '% engaged' bombers: 40%
Average GE '% engaged' fighters: 62%
Average SU '% destroyed' total aircraft: 38%

Set 2:
Total GE 'allocated bombers': 120 (+62% Increase)
Total GE 'allocated fighters': 69
Average GE '% engaged' bombers: 54% (+14% Increase)
Average GE '% engaged' fighters: 59% (-3% Decrease)
Average SU '% destroyed' total aircraft: 68% (+30% Increase)

Set 3:
Total GE 'allocated bombers': 162 (+119% Increase)
Total GE 'allocated fighters': 69
Average GE '% engaged' bombers: 58% (+18% Increase)
Average GE '% engaged' fighters: 45% (-17% Decrease)
Average SU '% destroyed' total aircraft: 95% (+57% Increase)

Graph:


Conclusions:
There is a very linear correlation between the number of 'allocated' bombers vs. the average number of SU aircraft destroyed (with an R^2 value of 1.0 and a fairly steep slope of m=0.6478). This was interesting as I was expecting a slightly exponential result. Why? Well if you increase the number of available bombs reaching the target, the effects of the increased saturation could be 'additive' but apparently this is not the case. I suppose this 'effect' is reflected in the fairly steep slope of the curve.

There is a near-linear relationship (R^2=0.92) between the number of 'allocated' bombers to the number of bombers that actually engage in combat though the slope of this curve is very flat (m=0.2061).

What does this mean? Increasing the number of 'allocated' bombers shows a very nice linear relationship with inflicted damage, however, this linear relationship is NOT seen with the number of 'engaged' aircraft. A slight increase in the number of bombers actually 'engaged' in combat greatly increases the amount of damage caused.

Also, the number of 'allocated GE fighters' never changed, however, as the number of 'engaged GE bombers' increased, the number of 'engaged GE fighters' actually DECREASED in what looks like an exponential way. Not sure what is going on there.

[ComradeP]

Is this for turn 1?

In my air base bombing tests thus far, I don't necessarily see a relation between the number of bombers and the number of destroyed planes. Sometimes 60 bombers destroy as many planes as 250. That's one of the odd things about air base bombing missions as the Germans after turn 1: even if you send an air armada over, you might very well have an unfavourable loss ratio (close to 1:1) or destroy few planes (less than 10).

The number of fighters mostly seems to be important because you need it to be close to what the Soviets are sending as CAP if you want to avoid casualties from interceptions. With good escorts, generally the only losses will be from AA or crashes/operational losses.

[nedcorleone1]

Yes this is for turn 1. I just added that to the post. The point of this exercise was to get a feel for the dynamics of the game regarding air. Of course there are way too many variables, many of which go on behind the scenes, to take into account and make direct correlations of cause and effect. But this gave me a somewhat basic understanding of what is going on. I just think it is interesting that the correlation between 'allocation' and 'engagement' is not linear BUT you see a very nice linear correlation with regards to inflicted losses (a quite steep one at that). Granted this does not shed any 'new' light or any sort of novel explanation to what most of the veteran players around here already know.

I should post the full data set to show GE and SU losses by 'fighter' and 'bomber' respectively. The data range is so small (for GE losses) that it would be misleading for me to even go into those details (just for curiosity's sake... a >100% increase in 'allocated' bombers resulted in twice the amount of average losses but we're talking about going from a 1 bomber loss to a 2 bomber loss average so it is virtually meaningless). I may try to extend this type of thing to other testable situations such as the various difficulty levels (see how the correlations change as the AI gets a bonus), ground combat between various unit types, etc. but for now this is all I wanted to do.

[larryfulkerson]

I applaud your efforts to analyse the application of bombers to raids ( in a really serious way I might add ) and would like to encourage you to analyse other stuff as well.  I'm glad to see someone else who takes this much effort to see what's going on under the hood.  Thanks for the illumination you provide.  I'd be ever so glad to help if you need someone to "test" a specific situation for something sometime.  The more data the better I think.

[randallw]

The thing to remember for turn 1 is the Axis side gets some special bonus, so it may not be a good compilation of stats to see the game's process of the normal week to week results.

[nedcorleone1]

You know I was wondering if the bonus was being illustrated by the very steep nature of the 'average SU destroyed' curve. I'll do a turn 2 with the same conditions and see how that changes.

[nedcorleone1]

Okay, well I wanted to do a 'Turn 2' analysis with the same data set but the 7th SAD airbase moves or disappears. I'll have to start from the bottom up on a '42 scenario and find a similar situation with which to compare. I did however extend the current turn 1 analysis by looking at a -24% decrease in 'allocated' bombers to get a better feel for the low end of the linear fit curves and I got back an interesting result.



Clearly, the average percentage of 'engaged' bombers is NOT linear. Extrapolation would put 0% bombers engaged at around a little over 40 'allocated' bombers. Obviously this would probably not happen in the game but suffice to say that below 40 'allocated' bombers, not very many are going to get through.

The fighters, still 'allocated' at 69, showed a HUGE drop in the amount that were actually engaged. Not sure what was going on there. So essentially the trend was as the number of 'allocated' bombers decreased, the amount of 'engaged' fighters increase but that only holds true up until a certain point. I'd be curious to hear from a developer how the mechanics behind this and if there is a fighter/bomber ratio and how it varies. The thing to learn from this is that you can 'allocate' too many fighters and you won't ever see the benefits of it. Save yourself some mileage. It looks like about a 1.2:1 fighter/bomber ratio is not very efficient whereas a 1:2 or more ratio would be more efficient.

Last but not least, the average SU aircraft destroyed is STILL LINEAR (R^2 is about 0.99). Remember this is turn 1 so the Germans are getting a huge bonus. I wish to test this in the future by comparing the slope and linearity of the 'average SU aircraft destroyed' with the non-bonus one. Should be interesting to say the least.

I really wish I could come up with some more helpful conclusions but at this point I cannot. I need to do some further testing beforehand so I don't look like an idiot spouting off some theories.

[Scook_99]

Definitely need more data. On turn 1, I find the 1st strike on an airbase is the most effective, so don't go cheap. I also find huge variations on the numbers: I have had 200 bomber missions hit less than 10 aircraft, and I have had 10 bomber missions hit over 60 aircraft. I would need to turn the details up to 4 or better to get a closer look, but I don't think I have the patience, or the need to know that badly.

[nedcorleone1]

Well the mileage will vary for everyone, especially since a certain level of randomness is built into the game engine. However, you must remember that the values reported are averages expressed as a percentage. I guess I could post the MIN and MAX values for people to get a feel for the spread but it wasn't anything overly interesting so I didn't. Anyhow, just by looking at the curves you can see that there is some very nice correlation (linear for inflicted losses and a logarithmic like character to the percent 'engaged' bombers. That is pretty darn good for only 4 points and 40 trials. I will admit that the 'engaged' fighters curve looks very odd and I would have to either know more about the underlying formulas (is there a Russian 'engaged' fighters dependency on the amount of German 'engaged' bombers and does this tie in with the number of German 'engaged' fighters?) or just collect more data. Anyhow I want to do a similar test for Turn 2 as well to see the magnitude of the German bonus. That should be very interesting to see. Maybe for those who are interested or whatever I'll post the full data set when I'm done so you can analyze it or draw other various correlations or feel free to just ask me as well.

Flappy

[randallw]

The game shows a size ( in weight ) of bomb loads for aircraft, along with accuracy, blast radius, and other info on the weapons carried by the planes....this should factor in how airfield attacks end up, I hope.  ( There's also a durability rating for aircraft which may factor in how often they are destroyed outright compared to just being damaged? )