Air to Air probabilities

[Courtenay]

I just had a combat where a +3 plane got shot down by a -2 plane. I wanted to see what the chances of that happening are. (I sometimes feel that the -2 plane has the advantage here; it certainly wins often enough. ) I looked at the A2A CRT and started adding up numbers in my head. I realized that was silly -- computers are much better at adding up numbers than I am. So I made the following table:

A2AProbs.jpg (327.11 KiB) Viewed 813 times

I hope I have not made any uncaught mistakes; checking, I found two adjacent boxes with errors. I hope there are no more such mistakes. Here are my copies of the CRTs, just for people to check.

A2ACRTs.jpg (236.97 KiB) Viewed 813 times

[Orm]

Thank you for sharing. Much appreciated.

[paulderynck]

There's an old saying:"Statistics are for losers" that could easily be expanded to: "Probability and statistics are for losers".

Not meaning this as an insult to anyone, but when General You experiences bad luck it seems always to be worsened in proportion to the unlikelihood of its occurrence, which in turn gets multiplied by increasing numbers of same.

[rkr1958]

I just had a combat where a +3 plane got shot down by a -2 plane. I wanted to see what the chances of that happening are. (I sometimes feel that the -2 plane has the advantage here; it certainly wins often enough. ) I looked at the A2A CRT and started adding up numbers in my head. I realized that was silly -- computers are much better at adding up numbers than I am. So I made the following table:A2AProbs.jpg

I hope I have not made any uncaught mistakes; checking, I found two adjacent boxes with errors. I hope there are no more such mistakes. Here are my copies of the CRTs, just for people to check.A2ACRTs.jpg

Looks great! Would it be possible to attach your spreadsheet? I'd like to get a copy if I may.

[rkr1958]

Took me a second to figure out the difference between the friendly & unfriendly; but it has to do with PIL survivability and whether or not the plane is shot down over a friendly or unfriendly hex or sea area?

Also, I find it interesting that if one is facing a twin engine fighter then the chance of losing the PIL is the same whether or not one if flying over a friendly or unfriendly hex.

[Courtenay]

Yes, friendly and unfriendly is whether you are flying over your controlled hex, or over opponents controlled hex or ocean. The reason that the twin-engine penalty has the same probability of a pilot kill over friendly or unfriendly territory is that the only way for a twin-engine penalized plane to get a kill is to roll a natural AX, adjusted down to DX, and all AXs in the bottom half of the table are AX PXs, whether over friendly or unfriendly territory.

[Courtenay]

Here is the spreadsheet. Note that it OpenOffice.

[rkr1958]

Here is the spreadsheet. Note that it OpenOffice.

Thanks! Downloaded and converted (equations) to EXCEL, which I've attached for those interested.

Tables.
Pretty sure numbers match with your openoffice spreadsheet. Will keep checking.

A2AProbs-EXCEL.png (159.15 KiB) Viewed 720 times

EXCEL Spreadsheet.

A2AProbs-EXCEL.zip

(17.36 KiB) Downloaded 9 times

[rkr1958]

Courtenay, thanks for doing this. I find the numbers a bit surprising.

For example,

(1) Facing -4 air-to-air your chances to get cleared on that round (51%) are slight better than a coin flip.

(2) Chances of getting cleared on that round (28%) are the same facing +1 as +2,+3.

(3) Same with facing +4,+5 and +6,+7 at 19%.

(4) Even at the best odds at +8, your opponent has a 10% chance of getting cleared (for that round) and at the worse odds (-9) you have a 10% chance of getting cleared (for that round). While not great definitely far from certain at the best/worst.

[rkr1958]

Thought I'd jazz up the table a bit and export it to pdf. Will definitely become one that I often consult before, during and even after air-to-air combat. Armed with these probabilities I feel that I can make a more informed, but not necessarily better decision.

A2ACRT-EXCEL-2.png (181.66 KiB) Viewed 684 times

pdf

A2ACRT-EXCEL-2.pdf

(132.99 KiB) Downloaded 15 times

[davidc]

Thanks guys
Very useful

[rkr1958]

Update thanks to an excellent observation made by Courtenay. Twin engine & night penalty are the same.

Combine.

a2a-friendly-unfriendly.png (186.72 KiB) Viewed 603 times

Friendly.

a2a-friendly.png (92.07 KiB) Viewed 603 times

Unfriendly.

a2a-unfriendly.png (91.61 KiB) Viewed 603 times

PDFs (zip file) of friendly & unfriendly together and separate (3 PDFs).

a2a.zip

(227.5 KiB) Downloaded 16 times

I Made them separate so that I could get a larger print font when I printed to the tables out.