Bronzium draw statistics
Author: Oberon
Guild: BaseDeltaZero
Posted: 22 May, 2018
Updated: 4 June, 2018
So, you’ve got a bunch of ally points?
You have several hundred thousand to spend. You’ve been putting it off because you haven’t been able to figure out exactly how to automate spending them and you just know you’re risking repetitive strain injury if you attempt to spend them all?
Is it worth it? What worthwhile things are you likely to win?
In this analysis I cover give you an indication of the percentages of the basic categories you might get. In future analyses I’ll go in to more detail about gear and shards.
… so I’ve risked RSI for you
Tbh I only manually spent and recorded results for about 414,750 worth of ally points. Once my arms recovered I managed to automate both the spending and recording of the remaining 649,000 ally points. Ally points were spent sporadically since April 2017 from one account that varied from 1.5 to 2.5 million GP over that time, and since April this year for an account at just under 1 million GP.
I’m assuming that the true proportions of the various bronzium prizes proportions haven’t changed over time, and that the RNG is not adjusting the probabilities based on for example GP, how often you buy crystals or any of the other sneaky ideas I’ve heard.
| A(1.5-2.5M GP) | B(1M GP) | |
| Gear | 2,198 | 877 |
| Credit | 250 | 97 |
| Training droids | 216 | 105 |
| Shard | 289 | 140 |
| One star character | 34 | 13 |
| Two star character | 23 | 3 |
| Three star character | 6 | 1 |
| Four star character | 1 | 2 |
| Total | 3,017 | 1,238 |
| Duration A: 13 months, B: 2 months | ||
Estimated proportions - similar for both accounts?
You just use the data to estimate proportions and compare them, but we only have the sample proportions. To compare the two samples we need multinomial confidence interval estimates for the proportions and to see if they overlap for the two accounts.
… and they do. We can’t rule out the possibility that the true proportions are the same for each account. Sweet.
Estimate true bronzium prize proportions
If we combine the data from both accounts:
| type | N | Proportion |
| Gear | 3,075 | 0.7227 |
| Shard | 429 | 0.1008 |
| Credit | 347 | 0.0816 |
| Training droids | 321 | 0.0754 |
| One star character | 47 | 0.0110 |
| Two star character | 26 | 0.0061 |
| Three star character | 7 | 0.0016 |
| Four star character | 3 | 0.0007 |
| Total | 4,255 | 1 |
This is certainly consistent with my own experience - mostly gear, some shards, credit and training droid, and every now and then a full character (or their weight in shards if you already have them). To give you an idea of how accurate the estimate can be there are 95% confidence intervals on the next plot.
We can be pretty confident about the all but the character proportions. They are so small that the confidence intervals are proportionally huge. With 95% confidence we can only say that the true proportion of one star characters is greater than for 3 and 4 star characters – but they’re probably a pretty good guide.
You tried to get a shard and missed 10 times in a row?
Knowing the estimated true proportions is helpful. However when you’ve made a huge number of attempts and missed them all, you want to be reassured that it’s possible and you aren’t just being scammed. Of course CG could help with this but they don’t, so here’s what you can expect.
| type | Misses |
| Gear | 0.4 |
| Shard | 8.9 |
| Credit | 11.3 |
| Training droids | 12.3 |
| One star character | 89.5 |
| Two star character | 162.7 |
| Three star character | 606.9 |
| Four star character | 1,417.3 |
In case you’re wondering why there are fractional attempts, it’s the expectation or average number of misses before a hit. It explains why many of you might not have won a four star character.
You tried to get a 4* character and missed 3000 times in a row?
Confidence intervals are important, ’kay? The expected number of misses helps you understand what the long term outcome might be, but what about your mate that got a four star character about 40 attempts after the last one, when you haven’t gotten one in more than three thousand attempts? (true story, similar happened in data account A compared to B). Unfortunately for you (and fortunately for your mate), this is not unexpected behaviour:
Summary
Say you have 250,000 ally points - or 1000 attempts - available. What useful stuff will you get? In terms of gear - dunno, that’s for another time. But you get around 100 shards and maybe ten one_star characters and a two star character. Is that worth the work? Probably not - time for you to figure out how to automate ally point spending!