Discussion:
In the
DPP OU Metagame Discussion Thread, several replays, counters and calculations regarding Jirachi were mentioned. This post aims to address some of those.
How likely was the replay involving a leftovers Magnezone which wasn't paralysed?
https://replay.pokemonshowdown.com/gen4ou-1056553765-4mqizakml2wlrnx2oetha69ydmva9hkpw
Modifying the simulation so that the opposing Magnezone (which was of a
mild nature) never gets paralysed, we see that the probability of the interaction in this replay occurring, after the first attack, was 14%. (Magnezone started at 81% of full health, if it starts at 94% to account for rocks and not the first attack instead, then the probability is only 9.1%). It was assumed that the Jirachi was holding a choice scarf indicated by the fact that it never body slammed, so I did not give Jirachi leftovers recovery.
Are the odds of Magnezone losing in this replay 1.0463794e-11?
No.
Even if you multiply every event in the replay together, which is 0.6^9*0.4*0.6^5*1/16*1/16*1/16 (the chances of a critical hit are 1/16), then you get a number approximately 10 000 times bigger than 1.0463794e-11. I don't know how this was calculated.
Does the nature of Magnezone make a difference here?
As indicated by the analysis in the results section, the nature of Magnezone makes a large difference, particularly if it is holding leftovers.
What if Magnezone uses thunder wave the first turn it gets a chance, then keeps using thunderbolt after that?
Tomahawk suggested on the discord that I calculate this for completeness. I have done so, but in the future I wont be modifying the simulation beyond the simple "already paralysed, keep attacking" scenario. This is because in most of the cases where different moves can be used, the problem of determining when to stop using another move, be it status, a boosting move, or a more accurate one, is not trivial to solve.
If a modest Magnezone (EVs: 32 HP / 4 Def / 252 SpA / 220 Spe) uses thunder wave in the first opportunity it gets, against the offencive Jirachi, then should it be holding leftovers, Magnezone will have a 99.7% chance of winning. If the same Magnezone is not holding leftovers, then it will have an 82% chance of winning.
This illustrates that in practice, Magnezone defeats Jirachi much more often than what is suggested, by the idealised situation in the results section.
How likely was the replay involving a specially offensive Swampert being flinched to death, given that it wasn't paralysed?
https://replay.pokemonshowdown.com/gen4ou-1356271516-z4g8j0hcpmr21ltbunjezgjwupub5nwpw
Modifying the simulation so that specially offensive Swampert is not paralysed to begin with, and starts at 81% HP (due to a single layer of spikes), and also assuming that the Jirachi was an offensive variant, we find that the probability of this interaction occurring was 45%. This is much higher than I expected, to say the least. If Swampert started at 100% HP, the odds were 37%.
Are there higher odds for a Gengar to obtain a critical hit against Jirachi in a single attack, than for Jirachi to beat specially offensive Swampert?
No.
Does Jirachi have low, but higher than needed odds to win the 1v1 against specially offensive Swampert?
Only if it is paralysed, otherwise the odds are in Swamperts favour (although it's a shaky 67% against defensive Jirachi).
Do defensive Jirachi lack the offensive power to muscle through sturdy checks, such as Heatran?
As indicted in the results section, Heatran without leftovers possess a very high chance to lose against defensive Jirachi, if they happen to be paralysed.
I ran the simulation again in the case where a Heatran without leftovers is not paralysed, and faces off against the defensive Jirachi variant I have been using, and got a win rate of 15% for Jirachi (both Pokemon start at 100% HP, Heatran uses fire blast each turn and may miss).
What if Heatran runs magma storm instead of fire Blast?
If Heatran is already paralysed, not running leftovers, and it has no HP or defensive investment, then it will lose 53% of the time against the defensive Jirachi set. It will lose 30% of the time against the offensive set. Should it possess leftovers the odds of Jirachi winning become negligible again.
Is the enough flexibility to use items other than leftovers on the Pokemon considered?
Only Heatran can get away with this reliably, and its reliability diminishes if it's paralysed.
Is the following a healthy pool of viable options against Jirachi?
Metagross, Empoleon, Heatran, Skarmory, Magnezone, Rotom, Zapdos, Suicune, Swampert, Milotic, Hippowdon, Gliscor.
This is outside the scope of the project. However we can say with certainty that either of Heatran with leftovers or Magnezone with them are good enough on their own, should Jirachi only have access to iron head and paralysis. We can also say that Swampert can be insufficient if it is paralysed, particularly if you are running an offensive varient.
Is the number of games "stolen" by Jirachi inflated in players heads by our negative bias?
This is outside the scope of the project as well.
However if I were a betting man, I would bet that the win ratio of Jirachi against the Pokemon outlined here is higher than most people expected.
In practice, are Jirachi's chances of winning much lower than those described in the results section?
Yes.
Most opposing Pokemon wont begin their turn paralysed. Opponents will also change up their moves, and generally play better than just attacking each turn. Such interactions are much harder to model than these idealised situations however, and are outside the scope of this project.
Have you tested the some of the matchups with real games, to see if the simulation is actually working?
I have run a test of 10 games involving the defensive Jirachi and the Heatran which didn't possess leftovers. The Heatran was paralysed on the first turn, and then attempted to use fire blast on subsequent turns. The results were 2 victories for Jirachi, and 8 for Heatran. Since the simulation can vary from a win ratio of 10% to 40% for sample sizes of only 10, the simulation was consistent with this test.
Greater sample sizes using Smogon's showdown simulator are needed to fully trust the results however. I plan to conduct the same test with a sample size of 100 sometime this week.
It might take an hour though, *sigh*.
Ok that's everything, thank you for reading everyone <3
