Talk:Showdown Update/@comment-36249842-20190724133330/@comment-34918040-20190726003216

@ SunnyTomato:


 * "believe in what you feel most comfortable"

Again, it's not a question of belief. Anecdote ≠ data. To be a bit more drastic: You can either run against a wall because some people told you it will let you through, or accept that the wall is made of solid matter and get a ladder.


 * "[statistics] doesn’t paint the full picture"

The words of some commentators may have been a bit rude, but generally they were right: It does. I believe there is a profound misunderstanding about the purpose and the methods of statistics, but perhaps I didn't explain it clearly enough. You can click the links if you want to know more, it's all here, but I'll try to put the main things in this comment.

If you have random processes, you almost never know the full picture. It's rare that you can collect the data for a whole population, say, the hight of the inhabitans of a village. The purpose of statistics is to infer conclusions from a smaller sample to the whole population. If you want to know the average height of the inhabitants of New York, you can't ask them all. You'll have to take a representative group, large enough to paint a small version of the full picture, but with the same ratios and relations.

Some processes are per se infinite: If you flip a coin, you can theoretically continue until infinity. Pro Kit Boxes are the same. There is no end, so you have to find ways to get the desired small version of the full picture. If you only open 5 boxes, the content can deviate so much that you can get completely different results than provided in the official drop rates. But there's a universal law that states the average of the results obtained from a large number of the same experiment will be close to the expected value, and will tend to become closer as more trials are performed: the law of large numbers. And the expected value of this law is exactly the drop rate we all know.

Here's an example with real data:



It shows the average relative frequencies of common, rare and legendary cards in Random Boxes. The official drop rates are marked with broken lines. You can see that at the left, the real outcomes deviate very much from the official values. Example: A player looking for legendary cards (drop rate for this period was ) could think that theoretically, every 100 / 2.61 ≈ 38th card will be legendary. In fact, the first 2 legendary cards even came after 40 revealed cards, which made the "legendary" line jump beyond the drop rate, and the player would be happy. But then, a streak of 78 non-legendary cards occured which was far off the expected 38. A player starting with such a streak would surely think that the box is rigged. But it isn't. Look at the right part of the chart: The lines become straight, no matter what happens. Already after 200 cards, they had approached the broken lines quite well (this is why we have set the "acceptable" sample size for boxes to 200, marked by the yellow light in statistics tables). Outliers do not influence the average any more as the sample size grows larger.

Or, if you have collected the height of 800 people from New York, you can even ask a basketball team passing by and include their heights in the sample. It won't change the average height much.

The law of large numbers is universal. But that's also why we can't rely of some opened boxes from a single player. The current sample size for Random Boxes is 845 cards. You can include some unlucky streaks form other players, it won't matter.

This is why statistics DO show the full picture. It's only a smaller version, but it looks the big one. Our limits for a "good" sample size is 600 cards, and 1,000 for "excellent" which is extremely high if you consider that rough predictions usually can already be made after 200 cards.

That's also how we detect deviations. If Gameloft changes something without telling us, it usually takes us only one to three weeks to notice and adapt the values. Or, in case of the, it only took us one day to prove that the drop rates were bullshit.

And now to the "golden rule": If there was such a rule, it would have been reflected in the drop rates. It was possible that it existed. That's why we designed a test which would clearly indicate if the rule was right. But it wasn't.

By the way, you can't take anecdotes from some players into account and say that that they disprove statistical results (which they don't because unlucky streaks are included in our data), but then say that some players who got all their cards from scratch are only anecdotes which cannot be taken into account. See what I mean?

As I have already suggested: Start counting and writing down your own results. Not just the bad ones, but all, and over a larger period of time. That's what the statistics project does. I can assure you will find that V8 Engines come no matter what the status of your inventory is.

By the way, as some players said that the "golden rule" may not apply to part cards (as proven in here, but will hold for engines, I started another experiment today: I upgraded a car with my remaining 4 V8s and will fuse or use any V8 engine that comes from boxes, at least until the end of this update. My inventory will not have any V8 engines in the, constantly. Let's see what happens.