Meta-Analysis of sword and bow use in 1st & 2nd Ed.
Date: Fri, September 03, 2004
Topic: The Game Engine

This article compares the average damage done per round by swords vs. bows under various rules systems. It demonstrates how the weapon specialization rules of Unearthed Arcana are biased in favor of bows and those of Second Edition are biased in favor of swords. It suggests a few rule changes, compatible with either edition, to bring weapon specialization into balance. It is intended for DM’s, but can be used by players to pick the weapon that takes best advantage of their PC’s individual stats under each rule system.

A Meta-Analysis of sword and bow use in First and Second Edition
By: Kirt
Used with Permission. Do not repost without obtaining prior permission from the author.

Typically some fighters in any party have to engage in melee (“tank” characters) and will always use a sword in close combat. Other characters are there to assist the front-line fighters (forward “support” characters), such as rangers, fighter/thieves, fighter/clerics, and fighter/magic-users. These support characters face a choice: to engage in melee with swords, or to hover just out of melee and use bows at close range. First Edition AD&D presented a basic conflict in bow vs. sword use.

First Edition
Bows fire faster (2 bow shots per round vs. one sword attack; PHB1 p.38), while swords do more damage (d8 vs. d6; PHB1 p.37). Dexterity increases chances of hitting with bows (PHB1 p.11), while Strength increases both hit probability and damage with swords (PHB1 p.9). Because of these different variables, the choice of sword vs. bow in First Edition depends on the attributes of the PC. For example, a First Edition, first level fighter proficient in sword and bow, with Str. and Dex. both 16, will do on average 1.375 points of damage per round against AC5 with a sword, but 2.1 points per round with bow. Thus, bow is clearly the better choice. On the other hand, a fighter with Dex. 15 and Str. 18/25 does 2.25 points per round with sword and only 1.75 points per round with bow, making sword the preferred weapon when possible.

[These calculations of average damage per round include the chance of hitting, which is why a target of AC5 is specified. All calculations are shown in the Excel spreadsheets accompanying this article.]

First Edition thus sets up the bow vs. sword choice as a Dexterity vs. Strength paradigm. Low-level PC’s of high Strength and low Dexterity are always better off using a sword, while those of low Strength and high Dexterity are always better off using a bow. For characters with both stats high, or both low, the optimal choice depends on the actual numbers involved. Str. and Dex. both 18, for example, favors bow, while both stats at 19 favors sword. Regardless of the confusion “in the middle”, I believe that the association of high strength with sword and high dexterity with bow is part of the Original Intent of the AD&D combat system. Furthermore, I believe it was the Original Intent to make the choice of weapon balanced, that is, different situations or characters would favor different weapons. In other words there should not be just one best weapon in all situations.

Additional rules allowing multiple attacks at higher levels and weapons specialization often weaken or even destroy this Original Intent. Game designers likely do not think about how their rules affect the balance between bow and sword, but in the three cases I have studied (First Edition, Unearthed Arcana, Second Edition), the additional rules skew the balance, sometimes extensively. This article explains how each of these systems is biased in favor of one weapon. At the end of the article, I give some suggestions for rules modifications that allow the original idea of balance to hold at all levels and across all degrees of weapon specialization.

The basic idea of the balance between sword and bow holds in First Edition at low levels, that is, levels 1 through 6. When a fighter becomes 7th level, however, he is allowed to increase his melee attacks to 3/2 rounds, while his missile attack rate remains the same (PHB1 p.25). This happens again at 13th level, when melee attack goes to 2/1, while missile attack remains at 2 per round (ibid). Part of the original balance between sword and bow is that while a bow does less damage, it gets more attacks. By allowing higher-level fighters more sword attacks but not increasing their bow attacks, the relative value of bows is obviously diminished. What 13th level fighter would choose 2 attacks per round with a bow when he could get 2 attacks per round with a sword? If players have Robin Hood or Legolas in mind for their characters, they either have to abandon their ideal or play at a disadvantage.

Thus we see that in First Edition, the choice of bow becomes less optimal at higher levels. At 7th level, bow is still better with Dex. 17 or greater and Str. 16 or less, but the “attribute-space” over which bow is better has been greatly reduced from that of lower levels. By the time 13th level is reached, bow is the better option only at Str. of 3 to 5. At any Str. of 6 or higher, sword is always better, even Str. 6 with Dex. 19. This effect is delayed for rangers, who do not get multiple melee attacks until 8th and 15th level, but it is still eventually present.

Unearthed Arcana
Unearthed Arcana (effectively Edition 1.5) introduced the idea of weapon specialization. By spending an extra weapon proficiency slot upon character creation, a PC could become specialized in sword; by spending two extra proficiency slots, a PC could have double specialization in sword or specialization in bow (UA p.18). The fact that this could only be done at character creation made it costly, for a fighter could spend three of his initial four slots to get sword double specialization or bow specialization, while a ranger could spend all of his three slots and receive no other weapon of proficiency. Once the choice was made, it could not be altered or amended, and it was not possible to specialize in both sword and bow (due to the number of slots required). However, this cost was worth it for the benefits received.

For melee weapons, the most important benefit was advancement in multiple attacks. Melee weapons shifted up one attack rank category, so that fighters with sword specialization receive 3/2 attacks at 1st level, 2/1 at 7th, and 5/2 at 13th (UA p.18). A secondary benefit was an additional +1 to hit and +2 to damage with the weapon (ibid). Thus, a first level fighter could increase his damage per round with sword by 98% to 241% just by spending an extra slot for specialization. The largest gains happen at the lowest strengths, but even at Str.19, damage per round effectively doubles with specialization. For rangers, weapon specialization apparently allowed a earlier increase in multiple attacks, since specialists increase their attacks at 7th (ibid) while unspecialized rangers would increase at 8th.

As impressive as the gains were for sword, however, the gain for bows was more so. At “point blank range”, defined as less than 30 feet, a bow specialist gains +2 to hit and +2 to damage with bows. A bow specialist is allowed to add strength bonus to damage at point blank range. And, as if that weren’t enough, the bow specialist is allowed double damage on all hits at point blank range! The double damage is computed after the +2 for specialization but before any strength damage bonus, so a single arrow hit from a specialist at point blank range does 6-16 points before strength bonus (UA p.18). In addition, a bow specialist at any range is allowed more attacks at higher levels, to 3 shots per round at 7th level and 4 per round at 13th (ibid).

Thus, while the sword option had been viable because of strength damage, bow specialists remove that advantage because they get strength damage as well (and don’t incur a penalty for low strength!). Whereas in First Edition only melee attacks increased in frequency at higher levels, UA assured that a bow specialist at any level would always get more attacks than a sword specialist. The only thing recommending a sword, then, is that it does on average one more point of damage than an arrow, but even this advantage is removed by the bow specialist’s double damage ability. Thus, everything in the system favors bows. Swords are only a better option at extreme high Str. and low Dex., where the adjustment on to-hit rolls would be significant.

Indeed, doing a comparison, we find that under the UA rules, it is only better to be a sword specialist at low levels if Dex. is 3 or 4 and Str. is 18/51 or higher. At 7th level and higher a specialist always does more damage by using a bow.

Of course, being a bow specialist requires one more slot than being a sword specialist. A more fair comparison would be between a bow specialist and a sword double specialist. Double specialization with a sword increases to hit and damage bonuses to +3, +3, but confers no other benefit (UA p. 18). This paltry gain does allow sword to be better than bow at low levels for Dexterities up to 5, depending on Strength. At a Dexterity of 3, sword is better if Strength is greater than 7. As before, however, bow is always better at level 7 and above.

Thus, it is safe to conclude that for any normal PC stats, bow specialization will always yield more damage under UA rules. This is definitely not balanced.

Second Edition
Second Edition changed many aspects of the bow-sword balance. In general, these changes remove almost all benefits to specializing in bow. At the same time, they allow bows in general to do more damage without specialization. Thus under Second Edition rules, bows start out being preferable at low levels and no specialization, but they become less desirable at higher levels.

One perhaps unappreciated change between First and Second Edition is the to-hit bonus for high Dexterity. Under First Edition, Dex. 17 gives +2 to hit with missile attacks, while Dex. 18 and 19 give +3 (PHB1 p.11, DD/LL p.7). In contrast, Second Edition has both Dex. 17 and 18 give +2, while +3 is not achieved until Dex. 19 (PHB2 p. 14).

In Second Edition, all characters that use bows use “strength bows”, or bows with “pull” appropriate to their strength, whether they are specialized or not. This includes low Strength characters, who receive penalties to damage. Thus, while to-hit with bows is based on Dextarity, damage from bows is affected by Strength in the same way as any melee weapon (PHB2 p.73). Bows rated for exceptional strength are more costly, but easily within the range of 2nd level fighters - 500 gp maximum for the most expensive, an exceptional strength composite long bow (PHB2 pp. 73, 68). This damage adjustment applies at all ranges, not just point blank.

Second edition introduced “sheaf arrows”. These are heavier, shorter-range arrows that do more damage, that is, d8 (PHB2 pp. 73, 68). Thus bows in Second Edition can have the same base damage as swords, if characters buy sheaf arrows, which cost only twice as much as normal (“flight”) arrows (PHB2 p.68)

Second Edition makes weapon specialization easier for PC’s, by allowing them to spend WP slots at any level, not just at character creation (PHB2 p.52). However, weapon specialization is more restricted by class. In UA, weapon specialization is specifically permitted for fighters and rangers and not specifically prohibited from multi-class characters (UA p.18), while in Second Edition it is restricted to single-class, pure fighters only (PHB2 p.52). In Second Edition, there is no such thing as double weapon specialization, but sword specialization costs two slots and bow specialization three, as before (ibid).

Sword specialization yields the +1 to hit and +2 to damage, as before. Bow specialization yields only a +2 to hit at point blank range, no damage bonus. And that is the only bonus for bow specialization. While sword specialization allows an increase in multiple attack rate, and specialization in any other missile weapon does the same, bows are expressly limited to two attacks per round (ibid). Why a player should spend two extra WP slots to specialize in bow with the only benefit being a +2 to hit at point blank range is not readily apparent (bow specialists do get the ability to shoot before initiative, but this does not affect damage).

To summarize, in Second Edition, bows and swords start out doing equal damage (base d8 plus Strength bonus). Bows start out with more attacks than swords, whether specialized or not. Thus, at first level and unspecialized bow is almost always better, unless extreme high Strength and low Dexterity affect the to-hit rolls sufficiently. However, a character gains multiple attacks with sword as level increases, but not with bows. And while specializing in sword yields benefits to hit, damage, and in number of attacks, specializing in bow only affects hit rolls. Thus in Second Edition as level increases or specialization is added, the optimal weapon shifts from bow to sword.

To add detail to what was related above, at low levels and no specialization, bow does more damage than sword at all Dexterities above 5. At Dexterities of 5 or less, sword can do more damage, providing Strength is high enough. This persists through mid-levels, up to 13th level. At 13th level, unspecialized sword users get two attacks per round, that is, the same number as bow users. At that point the balance shifts completely, and sword is better in nearly all cases. Bow remains better at Dexterities of 16 and above, and for Strengths of 8-15 and 17 (but not 16).

For specialized users, the transition to sword being better happens earlier. At low levels, bow better at all Strengths only above Dex.16. At Dexterity 16 and below, whether or not bow is better depends on Strength. At 7th level, when sword attacks twice per round, bow is only better at Str. of 3 and Dex. of 16 or higher. At Dex. of 19, bow is better up to Str. of 7. At 13th level, a sword specialist always does more damage than a bow specialist, regardless of their stats.

In conclusion, bow is only a preferable weapon in Second Edition at low levels and with no specialization. Since sword specialization only costs one more slot, bow may be a choice for low-level characters with high Dex and low Str., but it should be abandoned upon reaching 7th level.

My Suggestions
Given that First Edition and Second Edition favor swords, and UA favors bows, I wanted to see if I could devise an alternative that provides the balance I believe was originally intended. It was my explicit goal to create a system in which at all levels and all degrees of specialization, there would always be a balance between sword and bow, such that bow was preferable at high Dex. and low Str., and sword preferable at high Str. and low Dex. I wanted to achieve this result using the mechanism of bows being a lower damage but higher attack frequency weapon. The following rule suggestions succeed in providing all of this.

I like the idea of Strength-rated bows and adding Str. damage to bow shots. But used alone, this places too much emphasis on Str. for bow-users, without a corresponding emphasis on Dexterity. It leads to perverse situations in Second Edition, where a character of given stats might favor a sword, but an increase in Str. actually favors bow because the extra Str. damage counts more for bows, since they have more attacks. For example, in Second Edition, a first level character with Str. 17 and Dex. 15 does more damage per round with a sword than with a bow. But should that character find a way to increase Str. to 18/25 without changing Dex., she would actually do more damage with a bow!

Thus, the system I suggest places more emphasis on Dexterity for bow users, and limits the effects of high Strength in bow use. High-level bow users are allowed multiple attacks (ultimately up to 6 bow shots per round), but their Dexterity limits how many of these they may actually take. Strength damage bonus is allowed, but has a maximum that increases with increasing bow proficiency.

I do not suggest that “sheaf arrows” be allowed as an item that can be commonly purchased. In terms of game balance, they are a cheap way to make arrows do as much damage as swords. In terms of realism, most mass-produced arrows would be used for hunting or war, and most archery units would want greater range, not greater damage, on their weapons. Thus there would be little call for sheaf arrows outside of places that cater to adventurers. I suggest that sheaf arrows be a special item rewarded to PC’s for good roleplaying of connections with NPC fletchers or elves. Much like elven chain, they can be found or received as gifts, but not purchased. A PC with a NWP in fletcher could make them.

Finally, here are my specific suggestions:

Dexterity 18 allows +3 to hit with missile weapons (as in First Edition).

There are four levels of proficiency with swords: non-proficient (0 WP slots), proficient (1 slot), specialized (2 slots), and double-specialized (3 slots). Effects of these levels are as described in UA.

There are four levels of proficiency with bows: non-proficient (0 WP slots), proficient (1 slot), skilled (2 slots), and specialized (3 slots). Effects of these levels are as described below.

Non-proficient (0 slots)
A character non-proficient in bow receives the non-proficiency penalty appropriate to his or her class and may not apply racial bonus to bow use. To-hit is normal at point blank and short range, -6 at medium range and -10 at long range. Rate of fire is limited to 1 shot per round, regardless of level. A strength-rated bow may be used, but only up to Str. 15 (that is, penalties to damage for low Str. but no bonuses).

Proficient (1 slot)
A character proficient in bow receives no penalty to hit for bow use and may apply racial bonuses. To-hit is normal at point blank and short range, -3 at medium range and -5 at long range. Rate of fire is 2/1 at 1st level, 3/1 at 7th, 4/1 at 13th and 5/1 at 19th. These may be limited by Dexterity (see below). A strength-rated bow may be used, but only up to Str. 18 (maximum damage bonus +2).

Skilled (2 slots)
A character skilled in bow may apply racial bonuses. To-hit is +1 at point blank, normal at short range, -2 at medium range and -4 at long range. Damage is +1 at point-blank range. Rate of fire is increased by 1/2 attack per round over proficient users, thus 5/2 at 1st level, 7/2 at 7th, 9/2 at 13th and 11/2 at 19th. These may be limited by Dexterity (see below). A strength-rated bow may be used, but only up to Str. 18/00 (maximum damage bonus +6).

Specialized (3 slots)
A character specialized in bow may apply racial bonuses. To-hit is +2 at point blank, +1 at short range, normal at medium range and -3 at long range. Damage is +2 at point-blank range. Rate of fire is increased by 1 attack per round over proficient users, thus 3/1 at 1st level, 4/1 at 7th, 5/1 at 13th and 6/1 at 19th. These may be limited by Dexterity (see below). A strength-rated bow may be used, but only up to Str. 20 (maximum damage bonus +8). A specialized character who starts the round with an arrow nocked and drawn and a target in sight may fire (once) before initiative. This counts as one of his attacks for the round.

Dexterity limits to rate of fire:
Dex. 3-5 Maximum rate of fire 1 per round
Dex. 6-15 Maximum rate of fire 2 per round
Dex. 16 Maximum rate of fire 3 per round
Dex. 17 Maximum rate of fire 4 per round
Dex. 18 Maximum rate of fire 5 per round
Dex. 19 Maximum rate of fire 6 per round

Dexterity limits to rate of fire apply to every round. For example, a skilled, level 7, bow user gets 7/2 shots, or 3 some rounds and 4 others. A Dex. of 16 would limit this fighter to 3 shots per round, in any round, however.

Cost of Strength Bow
A purchased strength bow will cost normal list price up to Str. 17.
Str. 18 (+2 damage) costs 2x list price.
Str. 18/01 to 18/75 (+3 damage) costs 3x list price.
Str. 18/76 to 18/90 (+4 damage) costs 4x list price.
Str. 18/91 to 18/99 (+5 damage) costs 5x list price.
Str. 18/00 (+6 damage) costs 6x list price.
Str. 19 (+7 damage) costs 10x list price.
Str. 20 (+8 damage) costs 15x list price.

Fabrication of Strength Bows
Successful creation of a Strength Bow up to Str. 18/00 requires a proficiency check as Bowyer/Fletcher (PHB2 p. 58). Bows rated for Str. 19 require two slots in Bowyer/Fletcher. Bows rated for Str. 20 are made of metal (like heavy crossbows) and require two slots in Bowyer/Fletcher and one slot in any of Armorer, Blacksmith, or Weaponsmith.

Notes on Excel Spreadsheets
Use the link included in this article to download the Excel spreadsheet file with details on my calculations. There are five pages. The “Conclusions” page gives color charts for all systems (First Edition, Unearthed Arcana, Second Edition, My Suggestions), levels, and degrees of specialization, showing graphically whether sword or bow use is better.

The other four pages detail for each system how much damage is done per round, on average, for bow, sword, and bow vs. sword. At the top are three matrices referring to dexterity to-hit bonus, strength to-hit bonus, and strength damage bonus for all combinations of Str. and Dex. Beneath that are charts in vertical groups of three, showing average damage in actual points per round for sword, bow, and the difference between sword and bow. In the sword-bow table, positive values indicate a sword does more damage, negative values that a bow does more.

Damage values are computed using the form
(number of attacks per round)*(chance to hit)*(average damage).

Chance to hit is based on AC5 for the level in question. It has a maximum value of 95% regardless of adjustments, since a natural 1 on a d20 is always a miss.

Average damage is based on 3.5 (d6) for arrows in First Edition, UA, and my suggestions, 4.5 (d8) for sheaf arrows in Second Edition, and 4.5 (d8) for swords in all systems. These values hold except where there is a (-1) penalty to damage for low Strength (Str. 3-5) with no offsetting proficiency bonus. In this case the minimum damage is 1, not zero, so the average damage is (11/3) for d6 (ones count as twos) and 4.625 for d8 (ones count as twos).

MS Excel Spreadsheet: Article Enhancement


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