Is wiki wrong about MEA?

I've been using the asin(Vbot/Vbullet) formula for ages. But in my mind it should be atan(Vbot/Vbulet). Am I right?

It is not a big deal to over estimate MEA with asin. but the over estimate could be as bad as 30% for bullets with fire power equal to 3.

asin formula is when your opponent move perpendicular to your head on angle atan formula is when your opponent move perpendicular to your hit angle ;)

However, the first one is greater, therefore the max (of them).

I am arguing that the asin(Vbot/Vbullet) formula has an assumption in its derivation, which leads to the overestimation of the angle. The easy way to see that use of the asin is wrong is to assume that bullet speed is equal to the bot then asin gives 90 degrees, but you will never hit the bot this way, by symmetry MEA in this case is 45 degrees. Note that atan does it automatically.

The thing is, if the bot moves slightly away then it increases the bullet flight time, allowing the bot to reach a higher MEA than just an orbit or chord.

Personally, in DrussGT I use a precise MEA since it gave better results. But if you have some limitation on whether the bot can exceed the calculated MEA (for example you log them to bins) then the asin is better, otherwise bots could potentially move to angles you can't shoot at.

Are you using precise MEA to scale? or just to cut. From the version history I think it is the latter, but Understanding DrussGT says former ;)

Both.

I've just calculated it. If it is correct moving away helps.

            latVel = Math.sin(angle) * 8;
            advVel = -Math.cos(angle) * 8;
            timeToHit = distance / (bulletSpeed + advVel);
            mea = latVel / (distance - (timeToHit * advVel) / 2) * hitTime;

This is the formula. It thinks that the bot is moving at full speed and with brute force search I got these results:

Bullet Power 1:

LatVel: 7.762365810207972 AdvVel: -1.9353751647973414

Bullet Power 2:

LatVel: 7.6504380477042835 AdvVel: -2.338973637781894

Bullet Power 3:

LatVel: 7.468643411977614 AdvVel: -2.8669435963624013

Distance doesn't change anything if it isn't zero.

timeToHit is not taking in account that the bullet moves at some angle too, i.e. we need to use bulletSpeed*cos(MEA). In above we assume that 'a' is angle between line connecting bots and the velocity of the target.

The last line is not precisely correct as well. There should be no factor of 2, and you forgot the atan. It should be

 mea = atan( latVel / (distance - (timeToHit * advVel)) * hitTime );

But the last thing could be simplified a bit if you notice that

latVel = bulletSpeed*sin(MEA)

Moving away is always bad idea from the MEA prospective within robocode physics.