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SBFord
Associate Editor - News ManagerThe CitadelPosts: **20,740**MMORPG.COM Staff Epic

In the second part of Becoming a Designer, Matt Miller talks more about what aspiring developers need to do to make their dreams come true. Read on and then offer your ideas in the comments.

A couple people asked in the comments about the time restriction. I’ve seen design tests at other companies that are rigidly timed, with websites that track the minute you download the test to the minute you submit it. We didn’t do that at Paragon. We simply asked the candidate when they felt they would have enough time to devote to the test, and scheduled email delivery of the test to that time period. They would then complete the test and return it. When the HR department delivered the test for “grading” (not a real thing), we were told how long the applicant had the test for.

Read more **Matt Miller: Becoming a Designer - Part Two**.

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## Comments

1,393Member Common115Member Uncommon45Member UncommonHere's my shot it:

1. Average damage is 100, assuming the target lives to see all 5 ticks (with no hit point info, I think we have to assume target has more than 100hit points and I will assume this from now on).

2. Average is 50 + 5(0.5)10 = 75

3. Average is 50x0.5 + 60x(0.5

^{2}) + 70x(0.5^{3}) + 80x(0.5^{4}) + 90x(0.5^{5}) + 100x(0.5^{6}) = 58.1That's what I get anyway. It took me like 15 min to do that and I screwed it up at least once. I know I screwed it up at least once because the first way I did it was different, and then I changed it. It's entirely possible that both my first approach and this one are wrong, but I feel better about this one.

"Well sure, the FrinkiacVII looks impressive - DON'T TOUCH IT - but I predict that within 100 years computers will be TWICE as powerful, ten THOUSAND times larger, and so expensive that only the five richest kings of Europe will own them." -Prof. Frink

45Member Uncommon"Well sure, the FrinkiacVII looks impressive - DON'T TOUCH IT - but I predict that within 100 years computers will be TWICE as powerful, ten THOUSAND times larger, and so expensive that only the five richest kings of Europe will own them." -Prof. Frink

956Member Uncommon100

75

50+5+2.5+1.25+0.625+0.3125= rounded to 60

3,099Member UncommonI would have said "just under 60" for the last one, then asked if they needed more precision.

( the average number of ticks would be 1/2 + 1/4 + 1/8 + ... which converges to 1, so if there were an infinite number of ticks it would be 60, maxing out at 5 ticks would be a little less than that; since there aren't a lot of situations where you'd need an exact answer, so I'd start with the ballpark figure in a conversational interview and only break out the calculator only if a more exact answer was requested )

3,099Member Uncommon16,342Member EpicOn the math question, it depends on when the mob dies. For example, if the initial 50 damage kills it, then the attack does 50 damage in total, as the later ticks will never happen.

Assuming the mob survives to take all of the damage, parts (1) and (2) are trivial, so I'll ignore them.

For part (3), the answer is clearly 50 + 10 * (expected number of damage ticks that occur). So the real question is computing that expected number of damage ticks.

The probability that tick i occurs is 2^(-i). By a well known series,

$$sum_{i=1}^{infty} 2^{-i} = 1.$$

If there are n ticks possible, then we only want the first n terms from this series. But the series can also break down as:

$$sum_{i=1}^{infty} 2^{-i} = sum_{i=1}^{n} 2^{-i} + sum_{i=n+1}^{infty} 2^{-i}$$

from which

$$sum_{i=1}^{n} 2^{-i} = sum_{i=1}^{infty} 2^{-i} - sum_{i=n+1}^{infty} 2^{-i}$$

$$= sum_{i=1}^{infty} 2^{-i} - 2^{-n} sum_{i=1}^{infty} 2^{-i}$$

$$= 1 - 2^{-n}$$.

So if the mob has h health and does not heal or take damage from other attacks, we let

$$n = min{ max{0, lceil {h - 50 over 10}

ceil }, 5 },$$

which caps the number of ticks at whichever is less of 5 or the number it would take to kill the mob. Then the expected value of damage that the mob takes is $60 - 10 * 2^{-n}$.

45Member UncommonMy initial answer was wrong for part 3. It should be:

Average is 50x0.5 + 60x(0.5

^{2}) + 70x(0.5^{3}) + 80x(0.5^{4}) + 90x(0.5^{5}) + 100x(0.5^{5}) = 59.68If the tick that does the 10 points that get you to 90 hits, you get a swing at another tick, if that last tick misses, you still did 90 points, and if it hits, you did 100 and stopped. My weighted average failed to take that into account the first time. Sorry about that.

Doing the math, you get caught up in exponents and sums and indices,etc. I had to visualize it by drawing a numberline and breaking it up into chunks to get it right. If you didn't account for/use the whole number line, you did it wrong, or such was my thinking anyway. My original post assumed there was a 6th coin flip (and what's worse, if you failed it, my original math assumed that you did a total of 0 damage for missing the 6th flip, which would have been a disaster had there been fewer flips in the first place).

Probability and statistics questions are always harder than you think. I TOTALLY won a goat that first time. Thanks Monty -- er, I mean Matt.

"Well sure, the FrinkiacVII looks impressive - DON'T TOUCH IT - but I predict that within 100 years computers will be TWICE as powerful, ten THOUSAND times larger, and so expensive that only the five richest kings of Europe will own them." -Prof. Frink

2,677Member Uncommon1,393Member Common16,342Member EpicI'd hope that the damage numbers were after accounting for such effects.

38Member2,057Member Uncommondesign. Knowing what will be fun, gratifying, immersive, engaging. It's one of the paradigms of the "promote to incompetence" phenomenon in business. Usually even when people are promoted for doing a good job in one area, the next one up is at least related to what they used to do. Game design is an amalgam of creative thought, formulas, and intuition that only certain people possess. Qualities that aren't usually learned through education or even experience in the field, but through introspection and philosophical dialogue.

We have good games coming out all the time, but look at all the mmo failures. It's because people doing design simply don't possess the right qualities, people who do possess them would be considered as line-jumping, or undeserving, or not having paid their dues, because those people don't do programming or asset modeling, and they don't have BAs in finance or business management.

6Member1: 100

2: 75

3: The first 50 points of damage is always going to happen.... so just move on to the ticks of damage to figure this out. The 1st tick does an average of 5 points of damage, because it does either 0 points of damage or 10 points of damage [(10 + 0) / 2 = 5]. That 1st tick averages to 5, because it ALWAYS gets a chance to occur. The 2nd tick of damage averages out to 3.333, because it has three different "states". It could do 0 damage in the case where the 1st tick doesn't even happen, 0 damage because it got a chance to occur yet failed its own 50% chance, and finally a state where it does apply 10 damage. So the average there is [(10 + 0 + 0) / 3 = 3.333]. For each tick after that, you just add on another "state" that could occur and divide from 10 to find the average damage that tick applies to the total.

50 + 5 + 3.333 + 2.5 + 2 + 1.667 =

64.5Does that make sense at all?

19MemberThe first two are pretty easy. 1. is 100 and 2. is 75. 3 is tricky. Is tick has a 50% chance of occuring, so each subsequent tick is half as likely to occur as the previous one. So 50% > 25% > 12.5% > 6.25 > 3.125. Luckily, it's easy to count from there since we're working with an easy number (10). So simply multiply the % chance of that tick of occuring with 10 to get the average damage of that tick.

So, in the end, 3. comes out to 59.6875, which could be safely rounded to either 60, 59.7, or 59.69 depending on how accurate you wanted to be. I find it a bit interesting that the average damage added beyond the first two ticks amounts to so little.

I'm not sure I could have figured this out in the middle of a phone interview. I'm not entirely sure I'm correct either, but I'm confident in the answer. You'll give us the correct answer in your next article, won't you?

4Member1. 100 (assuming no other factors)

2. 75 (ditto)

3. Hoo boy. I figure I did this the hard way and made a copy+pasted array in Excel to generate the results 1323 times; with an average that hovered around 59-60 (truncated to the nearest whole number for the final average). I'm sure there are more mathematically elegant ways to accomplish what I did; I just did what I knew would work.

Prior disclaimers apply to this too.

Edit: extended excel model out to 15,876 rolls, for an average of 59.73419.

Another (simpler) way of doing it:

100

Then you use a weighted average to get a result of 59.688.

3,099Member UncommonThe problem with your reasoning is that the three states ( 0, 10/0, 10/10 ) are not all equally likely: no damage on the first tick happens happens half the time, 10/0 and 10/10 split the other half of the possibilities (making the average damage 2.5 rather than 3.333)

The average damage on each tick is half of what it was on the previous tick (think of the previous tick as just being a coin flip as to whether or not to proceed).

( I feel that the mechanic in question 3 is more natural to think of in terms of "what is the average number of ticks until damage stops" because the limit of 5 ticks, although in the same pattern as previous two questions, is just an artifical limitation in this mechanic - adding that 5-tick limit is actually more coding than simply having a "50% chance of expiring each tick" )

33Member UncommonIf a power does 50 Points of damage, followed by 5 “ticks” of 10 points of damage, what is the average damage the power deals?

Since you're saying "Average" and not "Average per tick" or anything, I would ofc say 50+5*10 = 100 damage per power cast.

If a power does 50 Points of damage, followed by 5 “ticks” of 10 points of damage, but each tick only has a 50% chance of applying damage, and if it fails to apply damage no further ticks occur, what is the average damage the power deals?

50+ 0.5*10 + 0.25*10 + 0.125*10 + 0.0625 * 10 + 0,03125 * 10 = 50+5+2,5+1,25+0,625+0,3125 = 59,6875 dmg.

I want to become a game designer myself and reading your column is so interesting for me, thank you

I'm the hardcore player, the one that rushes lvl cap before you even finish the starting area.

16,342Member EpicThat actually works pretty well most of the time, due to the Central Limit Theorem. Where it fails is if you have very large (or infinite!) variance. For example, modify the third case such that every tick does twice as much damage as the previous one and the ticks keep happening until one fails. Still have any failed tick immediately end the damage, and a 50% chance that each tick occurs. In this case, the expected value of the damage is infinite, even though the damage in any particular trial is always finite. Of course, that assumes that the mob never dies no matter how much damage it takes, and also that your system can handle arbitrarily large numbers without any sort of overflow error.

2,413Member UncommonWell, you guys might be working on the question(s) posed.... and the third one is interesting since it involves probability - I suggest reading

The Unfinished GamebyKeith DevlinBut I didn't get that far since what caught my eye was this quote from the article:

There was a great question on the content designer’s test that tasked the designer with creating 20 missions/quests to take a character from level 1 to 20. There was a variety of enemies that could be used in the test, but all they were was a name and a level range. The designer was also required to “spice things up.” They had four different “objective types”, Click object, Collect Drop, Escort NPC, Kill NPC. They were required to have no two quests out of the 20 have the same objective or combination of objectives. If you had a mission to escort an NPC and then kill a boss at the end, you couldn’t have another mission using Escort NPC and Kill NPC as the only objectives. You could add Collect Drop and it would make it different enough, but then you cross that combination off the list of usable combos as well."Combination of Objectives"??? Really?

I call Bullshit.

Why?

You start with 4 choices {a,b,c,d}

Let's say "a" is "Click Object" and "b" is "Collect Drop"

By your description a quest to

Collect Drop and then Click Objectis the same asClick Object and then Collect Drop?a,b and b,a are the same which is correct.

So, how many Combinations are possible from four objects (tasks in this case)?

a

b

c

d

a,b

a,c

a,d

b,c

b,d

c,d

a,b,c

a,b,d

a,c,d

b,c,d

a,b,c,d

which gives you 15 combinations total - not 20.

You can confirm this using the formula for combinations

Total = (4!/(1!(4-1)!)) + (4!/(2!(4-2)!)) + (4!/(3!(4-3)!)) + (4!/(4!(4-4)!)) = 4 + 6 + 4 + 1 = 15

The only way to get to 20 would be to allow missions such as

Click Object 1 and then Click Object 2which is cheating to say the least.Nothing says irony like spelling ideot wrong.

2,677Member UncommonI took "spice things up" as coming up with my own objectives.

Use inventory item, Use ability at location, Use ability on NPC, Deliver item, Lure NPC to location, etc

3,099Member UncommonI assumed that either there were actually supposed to be more verbs in the list or that "combination" should have been read as "permutation" or "sequence" (so that kill NPC, escort NPC was considered different than escort NPC, kill NPC). I was wondering if "kill NPC", "kill NPC, kill NPC", "kill NPC, kill NPC, kill NPC", etc could have been used.

There's one other possible quest combination you could add: no verbs (no a,b,c,d - just accept quest and turn in quest - eg: breadcrumb quests), rounding the combinations off to a nice 2

^{n}( but since you posted that, I find myself now wondering about my reaction to imperfect communication - rather than stop and ask for clarification, I would have just charged ahead with what I assumed was intended.)

10,026Member EpicAnother good article Matt. Thanks.

There seems to be a limited number of activity categories (fetch, kill, transport, puzzle). The interesting thing to me in a game is how well that is hidden in the story or plot of the encounter. This is one thing I think TSW does very well. Their questing system feels more like plot and event participation than it does a checklist quest.

45Member UncommonHow is that cheating? It sounds like a perfectly reasonable mission to me. I mean, sure you're allowing a person to write missions that go a, aa, aaa, aaaa, aaaaa, etc, but those missions suck and the person submitting them would be told they were a terrible mission writer. The whole point of the exercise was to make 20 different missions with a limited set of useable objectives. I would also point out that I think "defeat NPC then collect drop then defeat other NPC" is perfectly fine, and sounds like storyline to me (defeat badguy, take his magic sword, use it to defeat the dragon, etc) whereas click glowwy, then click other glowwy, then click other glowwy, then click other glowwy is a mission I'd never do. Of course, this is a slippery slope, because I would also argue that in many cases the ordering matters from a contextual perspective (defeat NPC then click object feels like "defeat the boss and defuse the bomb" whereas click object, then defeat boss feels more like "steal supergun then use it on boss"). Whether or not I would lose points for using the same mission objective combination twice in that case is debateable, but I would defend it if it fit the storyline I had in mind, and I think having a storyline in mind, and an interesting, non-repetitive one at that, is the bigger picture.

While we're on the subject, probably the worst mission-like thing CoH ever had in this vein was the infamous "Lehionnaire" badge, though it wasn't technically a mission. In order to get the Legionnaire Badge, you had to defeat 100 Warrior bosses. Unfortunatley they never spawned in great numbers anywhere so it was a tfrustrating waste of like infinite time to get it. They eventually fixed it by making them spawn more.