http://rappelz.blankweb.com contains a database of attempts at creature taming. This page contains some analysis of that data.

## Investigation periodEdit

I'm using data from Epic 6. The relevant date ranges are:

Epic 6 Prologue: Navislamia: 20 May 2009 to 13 Oct 2009

Epic 6 Solus Aurum: 14 Oct 2009 to 23 Feb 2010

Epic 6 Resurrection: 24 Feb 2010 to 30 Jun 2010.

30 June 2010 is merely a convenient round date a few days before I started this analysis.

Over the period 20 May 2009 to 30 June 2010 I haven't noticed any references in patch notes about any tweaking of the taming success rates. We'll return to this issue later.

- RedTiger announcement; I'm currently working on another possible factor in taming success rates, which involves character vs. creature level. Visit the "
__http://rappelz.wikia.com/wiki/Talk:Some_Analysis_of_Taming_Success_Rates__" Talk page for more information. Although, there is not really a lot of info on this page, I'm currently looking for other members who can contribute more data to this finding.**

- RedTiger announcement; I'm currently working on another possible factor in taming success rates, which involves character vs. creature level. Visit the "

## Do all Tier 2 pets have the same success rate?Edit

I'm starting with Tier 2 pets because they seem to be the tier for which the success rates are nearest to 1/2. The further the success rate is away from 1/2, the greater the number of trials required to accurately estimate it. That is, Tier 2 is the tier where we'v got the most chance of coming up with some sensible analysis from this relatively small data set.

It isn't yet clear whether success rates may vary by server, so I've used data for the Tortus server, since this seems to be the largest subset. Here is the data for 10+4 tamers, the most prolific group for that server, for 20 May 2009 to 30 June 2010.

ACTUAL | Blue Pixie | Octopus | Orc | Red Pixie | Siren | Skeleton | Wolf | Yeti | Total |
---|---|---|---|---|---|---|---|---|---|

Success | 36 | 21 | 25 | 37 | 10 | 18 | 43 | 21 | 211 |

Fail | 39 | 26 | 32 | 40 | 22 | 23 | 36 | 25 | 243 |

Attempts | 75 | 47 | 57 | 77 | 32 | 41 | 79 | 46 | 454 |

Success Rate | 48.0% | 44.7% | 43.9% | 48.1% | 31.3% | 43.9% | 54.4% | 45.7% | 46.5% |

The success rates do vary by pet. We'd be surprised if they were all exactly equal. The question is: Is the variation we're seeing just the normal level of variation we'd expect if the true underlying success rate is constant for all pets, or is the variation large enough to make us suspect the true underlying rates differ.

Adopt the null hypothesis that the true underlying success rate for all Tier 2 pets for 10+4 tamers is 211/454, the average rate experienced. On this assumption, we calculate the expected numbers of successes and fails to be the following.

EXPECTED | Blue Pixie | Octopus | Orc | Red Pixie | Siren | Skeleton | Wolf | Yeti | Total |
---|---|---|---|---|---|---|---|---|---|

Success | 34.86 | 21.84 | 26.49 | 35.79 | 14.87 | 19.06 | 36.72 | 21.38 | 211 |

Fail | 40.14 | 25.16 | 30.51 | 14.21 | 17.13 | 21.94 | 42.28 | 24.62 | 243 |

Attempts | 75 | 47 | 57 | 77 | 32 | 41 | 79 | 46 | 454 |

Now we carry out a chi-squared test. The test statistic sums (Observed - Expected)^2/Expected for the 16 cells of success vs fail by the 8 pet types. The test statistic evaluates to 5.48. On 7 degrees of freedom, the probability of getting a statistic of 5.48 or greater is 60%, so there is nothing to suggest we should reject the null hypothesis.

The analysis could be repeated for other levels of tamers on the Tortus server, or for other servers, subject to the requirement for the data set being large enough to ensure the assumptions inherent in the chi-squared test are met. Here is the comparable data for 10+3 tamers on Tortus.

ACTUAL | Blue Pixie | Octopus | Orc | Red Pixie | Siren | Skeleton | Wolf | Yeti | Total |
---|---|---|---|---|---|---|---|---|---|

Success | 38 | 7 | 18 | 40 | 21 | 15 | 14 | 14 | 167 |

Fail | 51 | 10 | 20 | 53 | 16 | 20 | 29 | 18 | 217 |

Attempts | 89 | 17 | 38 | 93 | 37 | 35 | 43 | 32 | 384 |

Success Rate | 42.7% | 41.2% | 47.4% | 43.0% | 56.8% | 42.9% | 32.6% | 43.8% | 43.5% |

Proceding as in the previous example, the chi-squared test statistic evaluates to 5.05. On 7 degrees of freedom, the probability of getting a statistic of 5.05 or greater is 65%. This is clearly not signficant, so we accept the null hypothesis.

**Layman's Translation**: On this data, we don't have any good reason to suspect the taming success rates differ for the different Tier 2 pets. The apparent differences between the success rates is almost certainly just random statistical variation. If you toss a coin 20 times it's actually fairly unlikely you'll get **exactly **10 heads. Similarly if tamers attempt the number of tames shown above, it's pretty unlikely that the raw success rate for each type of beast will be exactly equal. This is how randomness works. Live with it.

So, from here on we'll assume the underlying taming success rate is constant for all Tier 2 pets. This allows us to amalgamate all the Tier 2 data to slice it by other factors, such as server. If we try to determine whether the success rate for Orcs varies by server, we run into the issue of insufficient data for most servers. This is less of a problem if we asks whether the success rate for Tier 2 pets varies by server. But before going there, we'll revisit the issue of whether the taming rate has changed over time.

## Has the Tier 2 pet taming success rate varied within Epic 6?Edit

The most likely point for the taming success rates to be tweaked was at the the release of a new chapter, either Solus Aurum or Resurrection, since new higher tier pets were added at these points. Hence we'll start by testing whether the success rate has varied between the 3 chapters of Epic 6.

We'll again start with the data for data for 10+4 tamers on Tortus server, this being a good large pool. Here's the data for all Tier 2 pets combined.

ACTUAL | Navislamia | Solus Aurum | Resurrection | Total |
---|---|---|---|---|

Date range | 20-May-09 to 13-Oct-09 | 14-Oct-09 to 23-Feb-10 | 24-Feb-10 to 30-Jun-10 | 20-May-09 to 30-Jun-10 |

Success | 61 | 122 | 28 | 211 |

Fail | 69 | 147 | 27 | 243 |

Attempts | 130 | 269 | 55 | 454 |

Success Rate | 46.9% | 45.4% | 50.9% | 46.5% |

Adopt the null hypothesis that the true underlying success rate for all Tier 2 pets for 10+4 tamers is 211/454, the average rate experienced. Proceed as before, calculating the expected numbers of successes and fails on this assumption, and then calculate the chi-squared test statistic. The chi-squared test statistic evaluates to 0.58. There were 3 date subdivisions so the test statistic has 2 degrees of freedom, and the probability of getting a statistic of 0.58 or greater is 75%. This is clearly not signficant, so we accept the null hypothesis. That is, the underlying success rate appears to be constant for the 3 releases in Epic 6.

We can repeat this exercise for other subsets of the data. Here is the data for 10+3 tamers on Tortus server.

ACTUAL | Navislamia | Solus Aurum | Resurrection | Total |
---|---|---|---|---|

Date range | 20-May-09 to 13-Oct-09 | 14-Oct-09 to 23-Feb-10 | 24-Feb-10 to 30-Jun-10 | 20-May-09 to 30-Jun-10 |

Success | 50 | 75 | 42 | 167 |

Fail | 72 | 89 | 56 | 217 |

Attempts | 122 | 164 | 98 | 385 |

Success Rate | 41.0% | 45.7% | 42.9% | 43.5% |

The chi-squared test statistic is 0.66, which is still nowhere near significant on 2 degrees of freedom, so the variation we're seeing is completely consistent with the underlying success rate being constant over the 3 releases.

This also suggests there have been no significant changes to success rates within chapters. For example, if the success rate has risen considerably half-way through the Navislamia chapter, we would have expected the average Navislamia success rate to be lower than the other two releases. Either there have been no changes to success rates over time, or the changes are too small to detect, and hence hopefully too small to effect the subsequent analysis. Also, in response to a question as to whether there could be an increased taming rate event, GM itoki wrote on the Rappelz forum "I don't think it's possible to globally increase tame rate for an event." This suggests taming rates cannot be easily altered by regular patches, so it is reasonable to assume the taming rates are constant within each chapter.

So, now we're running with the assumptions that the Tier 2 taming success rate are

- constant by pet; and
- constant over time within Epic 6.

## Do tier 2 success rates vary by server?Edit

I haven't seen any previous discussion of the possibility of taming rates varying by server. If I was building a game like Rappelz with the intention of selling it to distributors like Gala-Net then I'd want to makes taming rates one of the paramters that Gala-Net could adjust to try to find the levels that maximise their income. If I was working a company like Gala-Net trying to maximise income from the game I might set different taming rates for different servers to try to ascertain whether it impact on my income, but my initial reaction is that there would be other more productive things to do. So my initial feeling was that there probably wasn't going to be any difference between taming rates on the "standard servers", though I wouldn't have been surprised if the Unicorn (PVE) and Pantera (PVP) servers adopted different tame rates better suited to their special properties.

So, I was surprised to find their do seem to be differences between tame rates on the standard servers.

I've only looked at the USA servers here. It's quite plausible that servers in other countries might adopt different taming rates.

Here are the data for Tier 2 pet taming attempts by 10+5 tamers subdivided by server. I have omitted the servers where the number of successes and fails wasn't large enough for the normality assumptions underlying the chi-squared test to be reliable.

ACTUAL | Tortus | Bahamut | Naga | Fenrir | Yeti | Salamander | Lydian | Total |
---|---|---|---|---|---|---|---|---|

Success | 164 | 22 | 18 | 29 | 272 | 41 | 265 | 811 |

Fail | 213 | 13 | 16 | 30 | 338 | 26 | 318 | 954 |

Attempts | 377 | 35 | 34 | 59 | 610 | 67 | 583 | 1765 |

Success Rate | 43.5% | 62.9% | 52.9% | 49.2% | 44.6% | 61.2% | 45.5% | 45.9% |

The chi-squared test statistic 12.6 on 6 degrees of freedom, corresponding to a probability of 4.9%. This suggests there are statistically significant differences between the data for the different servers. The 2 most significant contributors to the test statistic are the high success rates on Salamander and Bahamut. For both these servers, the data is predominantly from a single tamer, but in both cases the tamer concerned has a record of contributing over an extended period with nothing to suggest unreliability. (By contrast, elsewhere in the data it is possible to find tamers who contributed a significant amount of taming data on a single day and never contribute again. This raises concerns that they might be contributing their past 5 years data as if all those attempts were made on the day they contributed data, when in fact much of the data relates to earlier Epics when tame rates differed from Epic 6.)

Here is the corresponding data from 10+4 tamers. The need to exclude servers with insufficient data leads to a slightly different list of servers.

ACTUAL | Tortus | Bahamut | Naga | Fenrir | Yeti | Tanda | Salamander | Lydian | Total |
---|---|---|---|---|---|---|---|---|---|

Success | 211 | 17 | 46 | 40 | 141 | 19 | 253 | 200 | 927 |

Fail | 243 | 7 | 39 | 31 | 210 | 12 | 283 | 230 | 1055 |

Attempts | 454 | 24 | 85 | 71 | 351 | 31 | 536 | 430 | 1982 |

Success Rate | 46.5% | 70.8% | 54.1% | 56.3% | 40.2% | 61.3% | 47.2% | 46.5% | 46.8% |

The chi-squared test statistic 18.9 on 7 degrees of freedom, corresponding to a probability of 0.4%. This strongly suggests there are statistically significant differences between the data for the different servers. The 2 most significant contributors to the test statistic are the high success rate on Bahamut and the low success rate on Yeti.

I've produced similar calculations for 10+3 and 10+2 tamers. The 10+3 data fails to find significant statistical differenced between servers, while the 10+2 data does find signficant differences, mainly due to a low success rate on Tanda and a high success rate on Salamander. It is disconcerting that the different tests are not consistently picking the same servers as unusually high or unusually low. This suggests there may be some issues with the accuracy of the data being submitted to the database. The next obvious step is dig deeper into the data to try to identify particular tamers whose data submissions appear unreliable.

## Do we have enough data to fit the formula for probability of success?Edit

The short answer is "no".

Other pages have discussed the formula for probability of success. Apparently prior to Epic 5 part 2, the probability of success for a x+y tamer, (that is, level x with a +y skill card) took the form

b * (1+.03*(x+y))

where b is a base rate that varies by the Tier of the pet. The 3% figure was apparently displayed in-game on the taming skill and on the skill card. These locations no longer mention a particular figure. When a figure used to be explicitly stated in-game and is no longer explicitly stated, this might be indicative that it used to be a fixed parameter, but is now a variable parameter that the game distributor can vary. Apparently a Gala-Net Game Master has advised that the tamer skill level now only gives a 2% boost rather than 3%, and there has been unconfirmed speculation that the same is true for the skill card boost, so the current formula might be

b * (1+0.02*x + 0.03*y) or b * (1+0.02*x + 0.03*y)

We assume the formula is of the general form b+mx+ny and use least squares regression on all the available Tier 2 taming data to find the best fitting values of b, m and n. Since we've shown success rates to vary by Server, we'd better try it for a particular server. I've tried this for Tortus and the results are that there isn't enough data to produce a reliable answer. In fact, using different methods such as least squares, weighted least squares regression or maximum likelihood produces different answers, which is usually a sign of inadequate data. Each resulted in either m or n being fitted as slightly negative, which is not reasonable.

Part of the difficulty is that most of the data is of the 10+y form with very little data from tamers below level 10. (1386 of the 1626 attempts were at skill level 10.) But even if we try to fit a linear model of taming success as a+ny for the 10+y tamer data, we still get unreasonable answers, because over this range the success rates vary little. For example, if the true formula were say 0.4*(1+0.02*(x+y)) then from a 10+0 to a 10+5 tamer the success varies from 0.48 to 0.52, and we don't have anything approaching the level of data required to detect that small a difference.

One corollary is that if the number of attempted Tier 2 tames you expect to make over your game life is of the order of 1600 or less, then you shouldn't waste too much time seeking out a high level tamer, since on average, you aren't going to get a significantly greater number of successes by doing so.

## What's the cheapest way to get better data?Edit

Though no one much cares about success rates on Tier 1 pets, they are probably the cheapest way to generate enough data to acccurately determine the loadings for taming skill and skill cards. Tier 1 cards cost 8000 rupees and can be bought in unlimited quantities from merchants, and you can recover 2000 rupees on each succes by selling the tamed cards back to the Merchant.

If you want to help, go buy 20 or 30 tortus scrolls, go taming, record your results and contribute them to the database cited above. If you are a level 10 tamer, don't do all your tames at that level. Drop down to a lower level for some tames. We'll be able to fit a more reliable model with data spanning the whole range of levels rather than just having a heap of 1+0 data from non-tamer classes and separate heap of 10+y data from tamer classes.