Two years of chocobo racing

Crystal Stakes (C1) results

Time period	1st place	2nd place	3rd place	4th or lower	TOTAL
Period of angst	98	78	24	15	215
Period of relative prosperity	52	28	11	3	94
Since Chocobo Circuit changes	40	24	9	6	79
Since March 2010 update	5	4	5	1	15
	195	134	59	25	413

I made some gil. How about you?

Katanas from Trial of the Magians

This post is patterned after "great axes from Trial of the Magians," but with a minimum of tedious commentary. These are explicit damage calculations that should match up closely with simplified, one-minute "paper napkin" analysis when WS damage is dropped as a damage component. It should be obvious what katanas are of interest (Kuina with STR and attack bonuses, for example). See FFXIclopedia entry for final forms of katanas.

Givens, assumptions, and simplifications for analysis

• Basic rates: 95% hit rate, 15% double attack rate, 0% haste, 40% dual wield delay reduction, 24% critical hit rate
• Store TP +5
• Blade: Jin used as the WS of interest
• At 100 TP, a critical hit rate bonus of +10% (added to base critical hit rate) exists for Blade: Jin (questionable assumption by analogy: Evisceration shown to have a critical hit rate bonus at 100 TP)
• All hits in Blade: Jin can critical hit (unfounded assumption)
  
• For WS, double attack can occur once for main hand and once for off hand (unfounded assumption)
  
• 40% "occasionally attacks twice" OAT rate for Isatu
• Effective double attack rate is the sum of the OAT and DA rates (unfounded assumption)
  

Probability distributions for required number of hits to 100 TP after Blade: Jin

TP per hit	22 hits	21	20	19	18
4.6 TP	.00245	.09330	.88770	.01654	-
4.7	.00018	.00919	.15338	.83725	-
4.8	-	.00245	.09330	.88770	.01654

Remarks: these are required to account for variability of TP return to determine average time to 100 TP. 4.6 TP (201/190 delay combo), 4.7 TP (227/190, 227/201, 232/190, 232/201), and 4.8 TP (227/232) cover all katana combinations presented in this post.

Average time to 100 TP in the long run

Weapons	Average no. of rounds	Average no. of hits	Average time (s)
Senjuinrikio/Perdu	9.081	19.842	37.87
Mozu/Perdu	9.081	19.842	37.87
Mozu/Isatu	7.780	19.955	35.71
Mozu/Kuina	9.081	19.842	38.87
Isatu/Perdu	7.815	20.045	32.98
Isatu/Kuina	7.815	20.045	33.84
Kuina/Perdu	9.497	20.752	37.13

fSTR and average pDIF (both auto-attack and WS)

Used baseline fSTR 4 and 9 for auto-attack and weapon skill, respectively (5 and 10 for Kuina), and +53 to Blade: Jin base damage from secondary modifiers (+54 for Kuina).

Used baseline average pDIF 1.452 (from 450/300 attack to defense... yes, I know that equals 1.5) and 2.552 for non-critical and critical hits, respectively. Average critical pDIF is taken to be 1.1 plus average pDIF (very rough estimate that can slightly overestimate the effect of critical hits).

Weapon	Phase	Average pDIF (no critical)	Average pDIF (critical)
Senjuinrikio/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Mozu/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Mozu/Isatu	TP	1.452	2.552
	WS	1.533	2.633
Mozu/Kuina	TP	1.506	2.606
	WS	1.586	2.686
Isatu/Perdu	TP	1.491	2.591
	WS	1.571	2.671
Isatu/Kuina	TP	1.506	2.606
	WS	1.586	2.686
Kuina/Perdu	TP	1.544	2.644
	WS	1.624	2.724

Average damage in a single cycle

Weapons	Avg. hits	Avg. TP dmg.	Avg. WS hits	Avg. WS dmg.	Avg. total dmg.
Senjuinrikio/ Perdu	19.842	758.796 + 626.823	2.9925 + 1.0925	820.638	2206.258
Mozu/Perdu	19.842	818.353 + 626.823	2.9925 + 1.0925	829.362	2274.540
Mozu/Isatu	8.499 + 11.455	685.489 + 746.999	2.9925 + 1.0925	817.325	2249.815
Mozu/Kuina	19.842	825.347 + 719.984	2.9925 + 1.0925	848.606	2393.939
Isatu/Perdu	11.507 + 8.538	767.446 + 539.427	2.9925 + 1.0925	775.131	2082.006
Kuina/Isatu	8.538 + 11.507	619.599 + 774.006	2.9925 + 1.0925	810.714	2204.320
Kuina/Perdu	20.751	769.145 + 675.347	2.9925 + 1.0925	822.067	2266.560

Remarks: Isatu effective DA rate is taken to be (40 + 15)% = 55%, which is subject to verification. Isatu's OAT rate is thought not to affect weapon skills.

Damage per second

Weapons	Proportion of total dmg. in auto-attack phase	Damage per second
Senjuinrikio/Perdu	.628	58.260
Mozu/Perdu	.635	60.063
Mozu/Isatu	.636	63.004
Mozu/Kuina	.645	61.592
Isatu/Perdu	.627	63.130
Kuina/Isatu	.632	65.141
Kuina/Perdu	.637	61.036

Remarks: Auto-attack damage proportions may be lower than what should be expected (closer to 2/3)

Some comments

It should have already been obvious that Mozu/Perdu would generally be better than Senjuinrikio/Perdu, especially in a max pDIF context. Fudo was already (barely) better than Senjuinrikio (for auto-attack damage alone)... Mozu/Kuina is the best of the non-Isatu pairings (OAT rate still in question; take with a grain of salt), particularly better than Kuina/Perdu because 4.7 TP per hit is better than 4.6 TP per hit. Kuina/Isatu still gives 4.7 TP per hit, making it a formidable combination on paper (again pending OAT rate verification).

Great axes from Trial of the Magians

[Update: forgot delay +10 on Luchtaine.]

New update, more junk to waste time on, like the new quest "Trial of the Magians." I'd take a 100-damage Bonesplitter over Perdu Voulge anyday if I didn't have to camp the same lottery spawns over and over, and a 76-damage Luchtaine that "occasionally attacks twice" sounds even better and, not unexpectedly, even more tedious to obtain. (How about compared to Fortitude Axe?) Then again, so does Bravura, but that's something I'll never bother trying to get.

With that in mind, this post attempts to answer how much better these new great axes are compared to Perdu Voulge to inform the decision on whether to get one of these new great axes. This will be determined by calculating average rates of damage for the previously mentioned great axes (except Bravura).

This post is constructed in a similar fashion to my comparison of a 33-damage Tsukumo to Senjuinrikio (in a dual-wield context).

Some basic "givens" and assumptions

• 95% hit rate
  
• 22% double attack rate
• 24% critical hit rate
  
• 0% delay reduction (literal delay reduction or haste)
  
• "Sufficient TP" to accumulate at least 100 TP in only six hits
• King's Justice used as the WS of interest
  
• WS damage based only on 100 TP (where TP modifiers apply)
• 50% "occasionally attacks twice" rate for Fortitude Axe
• 40% "occasionally attacks twice" rate for a 76-DMG Luchtaine
  
• Luchtaine CANNOT attack three times in an attack round

Points 1 and 5 together imply a 95% chance to reach 100 TP in only 5 hits after any weapon skill, because any additional hits in the WS don't affect this probability.

The TP bonus on Raging Rush is still not understood well (and probably never will be), and King's Justice has more application anyway, so I will just go with KJ here. KJ has its own problems with "spike damage," but it is not characterized well at all, so how could I really account for it?

The last two points have yet to be substantiated for 2-handed Magian weapons as far as I know. Actually, determining how the DA trait interacts with the "occasionally attacks twice" property for the Magian weapon warrants its own post. For now, I will assume that the DA rate and OAT rate are additive (so effective DA rate of 62%) based solely on this BG post. The Clopper-Pearson 95% confidence interval is (.378, .528) (n = 179) and there were no reported triple attacks, much less quadruple attacks. I also think it's safe to say that the 62% rate, if true, would not be applicable to weapon skills.

I will update this post if those assumptions are invalid.

Average time to 100 TP in the long run

Weapon	Average no. of rounds	Average no. of hits	Average time (s)
Perdu Voulge or Bonesplitter	4.505	5.221	37.84
Luchtaine	3.531	5.434	30.24
Fortitude Axe	3.247	5.571	27.28

This whole analysis is based on consideration of a cycle of TP generation to reach 100 TP immediately followed by a weapon skill (no delay between cycles). The "long run" refers to the fact that the initial cycle, starting at 0 TP, has a infinitesimal effect on the ideal average time to 100 TP, given previously stated conditions. It is possible, though, to miss the first hit on a weapon skill, so the averages do account for that.

Also, it is well established (by me) that Fortitude Axe can triple attack in a single round, and the DA trait interacts with Fortitude Axe's OAT in a way that is not obvious. (Refer to a previous post on this if you're interested in the details. I didn't provide strong evidence the OAT rate is 50% though...)

fSTR and average pDIF (both auto-attack and WS)

I will just use fSTR 6 and 11 for auto-attack and WS damage (based roughly on my own character).

As always, pDIF for 2-handed weapons is a pain in the ass to consider.

For now, I will use an attack/defense ratio of 1.5 (450/300) as an arbitrary baseline for Fortitude Axe, in the auto-attack or TP phase. Then, the ratios for Luchtaine, Bonesplitter, and Perdu Voulge are 1.52, 1.52 (attack +6 with Fire Bomblet), and 1.553 (attack +16), respectively.

Ratios for weapon skills will be based on my own equipment (attack +8 except for Fortitude Axe, which will be attack +14 to account for Fire Bomblet).

For the range of attack/defense ratios considered, at least there are no pDIF floors or ceilings to account for. Therefore, the distribution of pDIF (given attack/defense ratio) is symmetrical.

For the sake of clarity, I will not justify the following at this time (would anyone really care though?) and assert that, partly given what I just stated in the last paragraph, average non-crit pDIF is approximately equal to attack/defense ratio and crit pDIF is approximately equal to non-crit pDIF + 1.1. (This is a rough simplification, to be generous, but one based on data.)

Weapon	Phase	Average pDIF (no critical)	Average pDIF (critical)
Perdu Voulge	TP	1.553	2.653
	WS	1.58	-
Bonesplitter or Luchtaine	TP	1.52	2.62
	WS	1.546	-
Fortitude Axe	TP	1.5	2.6
	WS	1.546	-

Since KJ is the weapon skill of interest, critical pDIF is irrelevant here.

Average damage in a single cycle

Weapon	Avg. hits	Avg. TP dmg.	Avg. WS hits	Avg. WS dmg.	Avg. total dmg.
Perdu Voulge	5.221	967.698	3.268	790.366	1758.064
Bonesplitter	5.221	987.382	3.268	795.036	1782.419
Luchtaine	5.434	794.924	3.268	669.3747	1464.298
Fortitude Axe	5.571	687.882	3.268	607.278	1295.160

King's Justice has a damage modifier of STR 50%, so I added 42 to WS "base" damage (again, based on my own character). Also, I accounted for the fTP bonus from a sea gorget (first WS hit only).

Damage per second

Weapon	Proportion of total dmg. in auto-attack phase	Damage per second
Perdu Voulge	.55o	46.457
Bonesplitter	.554	47.101
Luchtaine	.543	48.410
Fortitude Axe	.531	47.481

The proportion of total damage from the auto-attack phase is one way to check to see if these calculations are remotely rooted in reality (comparing to parser output), and the corresponding figures for each weapon seem reasonable. They are rather "far" from 50%, but I haven't merited in a non-Colibri situation in a long, long time, so I can't say for sure. Note that the given double attack rate, 22%, is higher than I have used in the past. As DA rate increases, the auto-attack proportion of damage necessarily increases. (I have used either 17% or 19% in the past.) I also used a maximum critical hit rate, which would increase auto-attack damage relative to King's Justice damage.

Now, consider paper-napkin calculations. For auto-attack damage alone, I could argue that Bonesplitter is about (106/102-1)*100% = 3.92% better, but I didn't account for the attack difference, much less differences in WS damage, so 1.38% might be a better indication of how much better overall Bonesplitter is than Perdu Voulge where attack still contributes to damage (even where average pDIF is rather high as in this example).

Fortitude Axe is often touted as superior to Perdu Voulge, and a previous analysis corroborates that notion. However, that analysis presumed that Fortitude could attack up to four times in a single attack round, which we know now obviously isn't true, so the gap between the two is even less than I showed.

Luchtaine appears superior to Fortitude Axe, not only in average rate of damage (not by much though) but also in average TP fed per attack round (if that is ever a concern). Now only if there were some corroboration on the 40% OAT and how the DA trait interacts with OAT...

Conclusion

Luchtaine appears to be the best option on paper, pending confirmation on its "occasionally attacks twice" rate and how that interacts with the normal double attack trait. Now, I can show how much something is better, but whether it's worth getting one thing over another is a matter of priority depending on how much you value the marginal improvement (over Perdu, Fortitude, whataever).

The requirements for Luchtaine, including 10 of an exclusive item that drops off a Vampyr that probably requires an alliance of two parties to kill efficiently (see "Voidwalker Notorious Monsters"), seem rather onerous, so I would need some good evidence concerning Luchtaine to bother upgrading it, and I would do so only as part of "nothing better to do" activity, which means it could take a year to get it.

I didn't even consider the various final forms of Hephaestus, either, including one with 91 DMG, 482 delay, STR+4 and attack +15, which looks good until you remember that you need +29 store TP for a 6-hit setup. I might update this post to include that great axe later.

Topic generation

My motivation to post is closely related to my motivation to play, even though what I actually do when I play tends to have little direct relationship with what I post about. Considering this, until (if) I have motivation to blog again about FFXI, maybe passersby can leave something in the comments to this post about what they might be interested in having me discuss at a later time. (While I do have an idea about showing whether Poisson regression is more appropriate than a simple difference of two binomial proportions for a particular FFXI-related data set, as I do not have any intuition about what would be "better," that would be interesting only to me, really.) Perhaps to stimulate generation or recall of ideas, I will reflect briefly about this blog:

One of the things I wonder about is what a reader of this blog, whether someone who has actually perused most of it or is coming from a link from a FFXI forum, actually applies anything he/she may have gleaned from the multifarious range of topics I've discussed. In some cases, I merely describe simple facts that are, surprisingly, not widely known, like the attack bonus on Yellow Curry Buns compared to Coeurl Subs (why else would you waste your gil buying subs instead of buns?) and chocobo raising/racing information. In other cases, I apply basic statistics to data collected by other players to support or refute things about game mechanics that are either "known" from anecdotal observation or merely assumed without any legitimate evidence. Sometimes I even do probability exercises to compare tactics (optimizing Phantom Roll "algorithms") or differences in equipment as precisely as possible.

In all cases, though, what really motivated me to create these posts was irritation with ignorance. (Many times this irritation was profanely expressed.) Yeah, maybe you can't read Japanese. I can't either, but it doesn't stop me from hitting up the major Japanese wikis to see if there is any information that doesn't show up on FFXIclopedia. And considering that the core of MMORPGs is a random number generator, I would hope the savvier players would have some appreciation that applications of probability and statistics can be very useful to understand how to play the game beyond lootwhore-agonizing about poor drop rates, or just have a better understanding of FFXI and of probability and statistics in general.

The (chocobo) racing silks

I would consider this scraping the bottom of the barrel, but let's run with it for now.

I never cared about chocobo digging, as someone who hasn't even gotten around to getting all the chocographs for Hot and Cold, but anecdotes about the effect of the blue racing silks, which " enhance chocobo digging endurance," indicate that they dramatically increase the total yield above the usual maximum of 100 items per zone. The sky blue silks, which are supposed to "enhance chocobo digging skill," can give the message "Your chocobo appears to have gained valuable knowledge from this discovery" after a successful dig, but it is unclear to me whether any chocobo digging skill-ups come with that. The blue silks seem like the better value for chocobo digging.

As for Hot and Cold itself, the white and black silks give one additional digging attempt and "increase Jackpot chance," respectively. Since hitting the jackpot allegedly can only occur when your chocobo is "especially sharp today," the white ones would seem to be a better value. I myself have observed that you can receive another digging attempt when your chocobo is "especially energetic," so this status and the white silk effect are not mutually exclusive.

The green racing silks are supposed to "enhance chocobo caring ability," which sounds like it could decrease the amount of energy depleted from both care plans and active care. However, chocobo raising is not something I would expect anyone to do indefinitely, so this doesn't sound like a really good value. Besides, you can raise a maxed-out chocobo with minimal expenditure and attention anyway.

The last three racing silks pertain to a chocobo's speed (how fast it goes) and riding time. It seems as though the orange silks would increase riding time by 10 minutes for both rental and personal chocobos, which is not very useful. Rental chocobos last 30 minutes and personal chocobos with maximum endurance are supposed to last up to 45 minutes. (I'm sure it has been shown but it's something easy enough for me to test, so I will just say "supposed to" until I check it out.) If the orange silks can be shown to increase riding time by 10 minutes for both max-END personal chocobos and rentals, then what about the red silks, which have the vague description "extends riding time"?

Finally, the purple racing silks, which I bought sight unseen because I like purple, are supposed to increase the movement speed of your personal chocobo. From FFXIwiki, which provides a convenient chart showing how levels of STR and END for personal chocobos correspond to movement speed and riding time, respectively, max-STR chocobos are only +95% faster than character running speed, compared to rentals, which again run as fast as Flee.

There is at least one account indicating that a max-STR personal chocobo with the purple silks is as fast as a rental chocobo, although I'm not sure how you can really ensure that your chocobos are lined up so that they run exactly parallel. My own extremely informal testing indicates that my personal chocobo with or without the silks covered approximately the same distance in approximately the same amount of time (about 32 seconds) as a rental, accounting for positioning error and 1-second precision. If the purple silks actually work, sure, why not use them. Again, I just got them because they were pretty.

Overall, the silks corresponding to chocobo digging and Hot and Cold seem to be the most economical uses of 150 chocobucks. To the extent that you do chocobo digging, you want to optimize your yield, and for Hot and Cold, you want to minimize failure. The other ones, not so much, but if you like the colors, go for it.

The Chocobo Circuit changes

C1 frequency: C1 races are held every other hour, with the registration period starting 45 minutes after odd hours for Japan time and Eastern Standard Time. This means that the number of C1 races per day has increased from 9 to 12, C2 races from 15 to 24, and C3 races from 24 to 36. Also, it is much more convenient to register for a C1 race because the registration periods are distributed uniformly throughout the day.

So far, the sequence of alternating C1 and C2 races has held. Also, the chocobuck rewards for C1 races have increased to 120, 100, and 80 for 1st, 2nd, and 3rd place, respectively. (I have not verified these myself though.) The chocobucks were also increased for C2-C4.

The obvious consequence of this chocobuck change is that, if you win around 50% of your races on average, you will pretty much never have to farm chocobucks ever again, barring an unlucky streak of finishes 4th place or worse, and you'll be swimming in chocobucks, which would give you the incentive to use them on things other than entry fees for Chocobo Circuit (raising another chocobo, even selling items).

Now if only FFXI could "die" some more so that there are fewer Japanese players doing races...

A cynic's view of the Chocobo Circuit changes

Edit: whoops, major mistake fixed.

I'm kind of surprised that there will be changes to the Chocobo Circuit schedule in the next "major" version update, among other things. Given the skeleton crew assigned to FFXI, you have to wonder if there is any sense of priority. On the other hand, there should no longer be any surprise that SE tends to play up features that hold limited interest, at best, among the "player base" in the lead-up.

For those of you who choose not to spend time racing a chocobo in the Circuit (actually spending time earning enough in entry fees actually to be able to enter your chocobo in the races), here is an overview of what I think the stated changes actually mean:

Bigger Rewards. The amount of chocobucks rewarded to first, second, and third place winners in chocobo racing will be significantly increased.

What it actually means: They obviously forgot to mention the part where the entry fees to chocobo racing rise accordingly. Given SE's penchant for parsimony, the end result is that it will take more time to accumulate enough chocobucks to race, not less time.

Revised Race Schedule. The Chocobo Circuit schedule has undergone a full review. ...

Comment: What do you expect? Their tendency is toward being even more tight-fisted. Any careful consideration (to the extent that there actually was a "full review") is done only to ensure that any changes don't make things inadvertently easier on players.

... The C2 Chocobo Race and C1 Crystal Stakes will be held with greater frequency, and races will take place at the same time each Earth day, making it easier for players to participate than ever before.

Comment: To understand the potential implications, you have to understand how C2 and C1 races are handled under the current schedule. (You may review the details of the August 2007 update that introduced the Chocobo Circuit.)

Currently, all C1 and C2 races are handled by the blue NPC. Either C1 or C2 occurs every hour, but there are only three consecutive C1 races in an 8-hour cycle, or nine in a 24-hour cycle (with the remaining being C2). Furthermore, the sequence of C1 and C2 races follows a pattern such that there are only two C1 races that occur every day, with the third C1 race occurring every other day in its time slot (alternating with C2).

Moreover, the registration period for each C1 (C2) race is only 15 minutes, starting 15 minutes before the hour and about 35 minutes before the actual race. Also, the registration procedure is handled such that up to six PC chocobos can enter a given race, apparently, yet you, the registrant, are completely blind as to how many PC chocobos are currently registered or will eventually register, not to mention blind as to whether the scrub chocobos MegaFlare or LunarHarvester are actually in the race (they always occupy lanes 1 and/or 2). Chocobo racing seems to be fairly popular, relatively speaking, in the JP community (although sheer numbers of Japanese, given that the "market share" of FFXI is predominantly the Japanese market, provide another plausible explanation), so that it's pretty rare, especially during JP prime time, to be in a race that is completely uncontested. (That is no guarantee that you'll win, though.) Therefore, chocobo races end up being a zero-sum game where the first two finishers have net positive earnings (accounting for entry fees) while the rest are totally fucked. (Imagine how it is when there are six PC chocobos registered...)

Also, you are only allowed to register for a race only if at least 24 hours have passed since the last time you registered. Yes, this is the same kind of player-unfriendly time-limit feature that manifests with Dynamis, Limbus, and Einherjar also occurs with chocobo racing. So you can see how the combination of limited C1 races, small registration windows, competition among the JPs (at least on Fenrir), and time limits to registration makes chocobo "racing" generally pretty annoying, but I can deal with it.

Now, regarding the changes, the allegation is that C2 and C1 races will be held with greater frequency. The red NPC, which currently handles only C4 races (yes, C4 races, which have trivial rewards, are held twice an hour currently), will now handle C2 and C3 races, meaning that C3 races may occur twice an hour now.

It will probably be the case that the frequency of C1 races will be cut while the frequency of C2 races will increase, so that SE can technically be correct by saying that "C2 and C1 races will be held with greater frequency" while looking like the asshole Scrooges they are.

New Rewards. The dashing racing silks dutifully worn by jockeys will be added to the list of reward items obtainable in exchange for chocobucks. With each color offering unique beneficial effects for its wearer, there is bound to be something for every chocobo fan!

Comment: Honestly, this is kind of a nice perk and not unexpected, but I wouldn't be surprised if they made the body (and legs?) 500 chocobucks apiece with the benefits being completely incommensurate with the cost (and I don't mean there's going to be movement speed +12% on them).

Stay tuned to see if I should issue a mea culpa after tomorrow.

I suppose I should mention my chocobo racing record since I'm talking about it. I actually had a nice run going, actually approaching the 50% win rate at 149/299. Of course, I dropped my 300th race (second), which initiated an eight-race losing streak (including two 3rd place finishes and coming in second in both uncontested races) that was snapped today, so I now sit at 150-106-35-17. Starting with my 9- or 10-race winning streak (I forget which) earlier in the year, my record since then is 52-28-11-2, for a 56% win rate, which isn't that bad for a server that seems more competitive than others.