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I have a Shiny Houndour with these IV stats:

Attack: 0
Defense: 13
Stamina: 0

I am thinking of evolving this to Houndoom, and I was wondering if it's worth having that defending a Gym, since the Defense is quite good, or is the Stamina too important for this to be worth it?

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Ability to defending at a gym based on states isn't straight forward.

As Thiebert stated, a Pokemon's stats are what matter, not so much the IVs. Houndour's level will make a much larger impact than its IVs, as they'll bear more weighting on its stats both as a Houndour and as Houndoom. For example a 15/15/15 level 1 Houndoom has far, far less stats than a 0/0/0 level 35 Houndoom.

The more Def and Stamina, the longer it takes to make the defender faint. More Attack means your defender can do more damage to the opposing Pokemon. At a first glance, it'd appear that Def and Stamina are more important, and Attack is less important but also useful.

However, with gym defence, I always assume that if the opponent attacks, they'll KO your defender and the rest of the gym should they choose. With that philosophy, the best goal is not to beat the attackers (you'll never succeed), but to deter them from attacking in the first place. Higher CP and higher motivation both deter attackers. The more stats you have, the more CP you have, with Attack having the largest influence on CP. But the more CP you have, the faster your motivation decreases. In that sense, there is an advantage to both having higher stats and a disadvantage. Higher CP is better for short-term defence, but lower CP may be better for longer-term defence.

Your 0-13-0 Houndour will have poor CP compared to other Houndours of your same level. At level 40, it caps at 2247 (compared to the max of 2529). Likely it'll be more suited for mid- to long-term defence, especially if you don't level it up. But I don't recommend Houndoom for defence.

As Thiebert said, Houndoom is a bad defender due to its poor Def and Stamina stats and weaknesses to common gym attackers. Houndoom is hence fairly poor for deterring people from attacking since it's beaten easily regardless of its stats. Technically speaking I would not recommend any Houndoom for defending regardless of its IVs. I would only include your Houndoom in the gym if you wanted people to attack it in the not-too-far future so you can get coins faster, like in a neighbourhood where gym attacks are uncommon.

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A pokemon's base stats matter far more when determining viability as a defender or attacker than it's IVs do. Houndoom tends to be much better suited as an attacker, with 224 base attack, and only 159 base defense and 150 base stamina. It's also weak to many typical gym attackers, such as Machamp, meaning it's unlikely to add much to the longevity of a gym its in.

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