# The Mystery Of XCOM's Random Shooting Percentages Explained

Even though the game is nice enough to tell you the odds every time you squeeze the trigger in XCOM, there's still an underlying feeling of "how the hell does this work", or sometimes "WHY THE HELL DID THAT JUST MISS".

The answer lies in numbers, and those numbers were last week very helpfully explained by Neil Brown, who in a couple of blog posts breaks down not only the facts behind shooting percentages, but also follows it up with an interesting piece on "save spamming", and how the game's "Iron Man" mode is about the only way, however imperfect it is, to stop people cheating a probability-based system.

If the detailed explanations and images are bit much, just stick to the graphs and know that "rapid fire" is a move that's statistically a lot better off than the game makes it sound.

Randomness vs Canniness, or Programmers vsSavescummers [The Sinepost]

Probability in Games: XCOM[The Sinepost]

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Yes, a lot of people don't understand probabilities, myself included (even though it is part of my job). Monty Hall Problem is a classic maths problem that can be used to illustrate this. You can look it up, Mythbusters even tackled it to try and explain it.

I have extensive training in stats, the Monty Hall problem still does my head in. Its just so counter-intuitive.

My reply to thom appears to have gotten posted down below due to a bug in the commenting code of this site.

I took a Maths course in stats!
I got 80 or something and have never used that knowledge ever again.
UNTIL THIS POINT
MY UNIVERSITY FEES ARE FINALLY PAYING OFF

While I love the game, and it's addictive as hell, I can't help but feeling the game mechanics should be updated for today.

I know there's the classical method that the game determines probabilities by, but other variables should also be considered, such as distance, elevation (I know there's a perk for being above an enemy), and other factors that doesn't result in a Sniper class who's less than 10 metres from a stationery, hulking target only having a 70% chance of hitting.

Snipers using their rifles actually get a malus to the chance to hit when they're within a certain range. Press 1 to select fire, then press F1 when you're targetting the right enemy to see the breakdown of buffs and penalties to the roll which determine the final scoring chance.

Want to hit every time? Get a Support with a light plasma rifle and a SCOPE. Base chance to hit at corporal seems to be ~92% (based on the MP stats).

Is there an equivalent to F1 for X360?

Press the Left Stick. It says "LS for more info" when there is information available

Is this a troll post? Distance, elevation (even without the perk, the perk just adds an EXTRA bonus), class/weapon type and cover all have effects on hit chance.

The reason a sniper will have a low hit chance in close range is because sniper rifles are so unwieldy and unfit for close range combat, so they actually receive a negative adjustment to accuracy for when enemies are close. Think about it, in real life if you had an aggressive enemy running up into your face or popping around a corner 2 metres away, what's going to have a higher chance to hit:
a) A burst of SMG/automatic rifle bullets fired from the hip, or
b) A semi-automatic or bolt-action sniper rifle which requires you to first pull the hefty thing up into firing position, then line up the shot carefully before firing a single bullet?

Well I think it's hard to explain which is why it confuses people. It's not really very confusing when you consider the host has prior knowledge. Given this there is 2/3rds chance that one of the other two doors has the car. Since the host removes one of those doors the probability is 100% x 2/3 vs 100% x 1/3. Double the odds.

What confuses people (and me) is how someone knowing something can affect the probability of a random selection.

We're talking about the Monty Hall problem, yes? I got the answer wrong the first time I encountered it, but when I read the explanation afterwards it wasn't that hard to understand.

Remember, we're not changing the results, the door that the prize is behind was already determined beforehand. The probability that you chose correctly never changes either.

I'll try to explain it the way that makes the most sense to me (all percentages will be rounded off for simplicity):

- There are 3 doors, A, B and C. Each door has an equal chance of having the prize behind it, meaning each has roughly a 33% chance of having the prize.

- You pick door A. Since each door has a 33% chance of having the prize, the chance that you chose the correct door is 33%, while the chance that you chose incorrectly and the prize is behind one of the other two doors is the remaining 67%.

- Think about that last point carefully for a second. We just divided the doors up into two sets:
i) Door that you chose: {A} (33% probability of having the prize)
ii) Doors that you didn't choose: {B, C} (67% probability of having the prize)

- Now the host of the show eliminates one of the doors that you DIDN'T CHOOSE, one that he knows definitely DOESN'T have the prize behind it. The probability of that set of doors containing the prize doesn't change, what changes is the NUMBER of doors in the set. You end up with this:
i) Door that you chose: {A} (33% probability of having the prize)
ii) Doors that you didn't choose: {B} (still 67% probability of having the prize)
iii) Doors that do not contain the prize: {C} (0% probability of having the prize)

I hope that helped, and didn't just confuse people even more!

I found this table on the Wikipedia page to be the best thing ever for understanding the problem. http://en.wikipedia.org/wiki/Monty_Hall_problem#Solutions

It's still very hard to convince someone who doesn't understand. The best way that I've found is to expand the problem to 100 doors (or even 1000). You pick one door out of 100. The Game Show Host opens 98 doors and they are all empty. Would you switch to the remaining door that you didn't pick originally or stay with the original choice.

Yay for tree diagram!

I'll stop "cheating the system" when they fix the glitches that are game breaking :)

Stats don't explain my dudes missing with 100% shot chance. All it results in is me swearing loudly.

That's because the game alters the numbers without telling you, which this article doesn't address. Some dude on the official forum delved into the code and found that the game will change numbers behind the scenes.

For example, IIRC playing on Easy mode will automatically give you a +25% to hit above what is displayed on the screen. And if you miss x number of shots in a row, it will take pity on you and give you a bonus that increases if you keep missing up to y%. And in your case, there physically isn't a 100% chance to hit in the code, I believe the maximum chance to hit is hardcoded somewhere in the 90ish% region (based on difficulty), the game just shows 100% for some stupid reason.

So yeah, basically, there's no 'real' randomness, it's all tinkered with by the developers, even after the pseudo-random number generator is involved.

This 'problem' has seriously effected my thoughts on the game. It's so infuriating that I have all but given up on the game until some mods come out to fix the issue.

The whole purpose of this feature is to stop people from save-scumming, so it's working as intended. It's not a "problem" or an "issue". The real issue is people reloading the game every time they miss a shot, taking the same shot over and over again, and expecting a different outcome each time.

If it was a little more realistic, eg, not missing when 2 squares away from a target, then people probably wouldn't 'save scum'. And even if they do, isn't that their choice. It's not like it's a MP game so the cheating needs to be eliminated.
I'm more inclined to cheat because the system they have implemented to reduce cheating, is shit.

Yup I agree.

I find it infuriating that all 6 of my guys have above 85% chance to hit, yet they miss every shot 2 rounds in a row.

I have had a lot of fun playing the game, but there are a lot of flaws in the game design :(
Not to mention some terrible bugs that make it very difficult to even play at times. :O

I agree. I had never heard of it. Quick look on the net. The initial explanation seems fairly straightforward.2:1 But THANKS for entertaining me. V. interesting. Am going to read a bit more on it.

WTF??? BUG --- meant to be a reply to IanU

It's an interesting article, but I kind of feel like it's largely a wasted effort. Why do developers need to stop players from "ruining" their own experience? If I give you a toybox, you're free to play with it however you want. If you think that behaving in a certain way is less fun, don't do it.

As for random numbers, it's a broken system anyway. Why should the game just arbitrarily say "Nope, you miss. Critical hit from the enemy. You're dead."? If the game is pulling BS moves, then I don't really see why it's a terrible thing for the player to reload and try again.

Randomness is fine for paper games where you have no other option, but I don't think it's applicable to video games. The classic games that use random systems are generally loved for reasons other than their gameplay. The warm fuzzies you get from the overall experience hides how arbitrary and frustrating the actual game can be.

Bring on the mods!!!
http://xcom.nexusmods.com/