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I'm looking for a way to get out of the typical classic "warhammer/shield cleric" and just want to swap it with spear/shield.

What I mean is a spear in my right hand and shield in the left, pretty much like a warhammer and shield. No homebrew. It's honestly just for the looks.

Can I do that, and how would I do that? What are the pros & cons?

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    \$\begingroup\$ As you might have gathered from the answers, your character's race is a factor, also another potential factor is your cleric's domain. If you want further detail you might consider editing your post to include race and domain. \$\endgroup\$ – Jack Sep 9 '18 at 16:30
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    \$\begingroup\$ It worth mentioning that spear is the favored weapon of Talos (the early version of your question described a Tempest domain cleric), so it would be natural for your cleric to wield it. \$\endgroup\$ – enkryptor Sep 9 '18 at 18:33
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There are no restrictions on what weapons you can wield in 5e

As long as you have a free hand, you can use any weapon. The usual limitation on a character is not being particularly effective with weapons they dont have proficiency with, but clerics by default have proficiency with spears. As such, the only disadvantage you'll have by wielding one is sacrificing the extra damage of other weapons and damage type differences.

A spear, when compared to a warhammer (assuming you are using a shield), only loses 1 damage per hit on average. Piercing instead of bludgeoning will only come up against certain monsters that are vulnerable or resistant to those damage types.

Also, the spear comes with the added benefit that it can be thrown making it better in certain situations. If you want to switch for flavor reasons, don't worry too much about the mechanics. Shield and spear is good enough for your cleric.

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    \$\begingroup\$ i would only add that the cleric might chose to use a weapon if it agreed with the symbolism of his chosen deity/pantheon. it's a social/psychological restriction, not a game mechanic restriction \$\endgroup\$ – SteveED Sep 9 '18 at 20:28
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Spear is fine

Unless you're a dwarf, elf, or some other race that gives weapon proficiencies, clerics can only use (with proficiency) simple weapons anyway (excluding domains that grant martial weapon proficiency), which means that with a shield you can only wield a one-handed weapon that has at most a d6 damage die. So at that point, whether you pick a spear over a mace (the typical default cleric weapon, unless you're a dwarf, then it's a warhammer) makes no difference in terms of damage output.

The spear does piercing damage, so if you are fighting a creature with vulnerability to bludgeoning damage like a skeleton, then the mace or warhammer would be better, but that's very situational (more of interest if considering choices for backup weapons).

However, if you are a dwarf or an elf and could therefore could pick a warhammer or longsword, which uses a d8 damage die, then it is the mechanically better option over a spear, but D&D doesn't have to be all about min-maxing. You'd still be fine with a spear of that's what you want your character to use.

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    \$\begingroup\$ Your statistics are wrong; not only does a d8 have a 25% chance of rolling a number higher than a d6 ever could, but it also has a lower chance of rolling a low number (e.g. 12.5% chance of rolling 1 to the d6’s 16.7% chance). I don’t, off the top of my head, know how to translate that into a “a d8 is better than a d6 \$x\%\$ of the time,” but it’s a non-trivial question. Far better to just say that the d8 is, on average, 1 better than the d6 (average damage on a d8 is 4.5, average damage on a d6 is 3.5). \$\endgroup\$ – KRyan Sep 9 '18 at 15:26
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    \$\begingroup\$ @KRyan it is better 56.25% of the time. You can just draw a table of 1-6 vs 1-8 and see which values are better. Each cell has an equal probability since each die is independent. 27 of the 48 cells have a higher value. 6 have the same result and 15 have the d6 with a higher number. \$\endgroup\$ – David Coffron Sep 9 '18 at 15:47
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    \$\begingroup\$ Then again, we can't just look at th e 56 % figure, since there are the cases where the d8 rolls lower. And if we take the difference of "d8 higher than d6" (56,25 %) and "d8 lower than d6" (31,25 %), we get exactly 25 %. Which makes sense: 75 % of the time, the d8 rolls <= 6, and within those rolls, the d6 and the d8 have the same odds. \$\endgroup\$ – ilkkachu Sep 10 '18 at 10:26
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    \$\begingroup\$ Really, E(d8-d6) and SD(d8-d6) is probably what you want. \$\endgroup\$ – Yakk Sep 10 '18 at 14:38
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    \$\begingroup\$ Unless you want to actually include a lot of math in the answer itself, I would recommend just sticking with "d8 is better damage than d6" in some manner, or "on average d8 deals 1 more damage than d6" as mentioned by another answer. Claims like "25% better damage" are harder to define and prove. \$\endgroup\$ – Kamil Drakari Sep 10 '18 at 15:03
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You'll deal slightly less damage than with a Warhammer (or the same as a mace), but as far as I can see that'll be the only noticeable difference. So just go for it.

A spear only costs 1gp, so you can buy one with your starting gold and drop the warhammer. Alternatively if there's no shop option, you can pick up a spear as your "simple weapon"-option instead of a crossbow.

Beyond that, for Clerics their choice of weapon is mostly flavor. They focus mostly on spells, with a weapon as backup, so you can grab whatever you think is most flavorful for your character concept.

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    \$\begingroup\$ Spears can be thrown \$\endgroup\$ – András Sep 9 '18 at 16:01

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