Tutorial Z-Factor and Proper Late Game Balance of Power

Discussion in 'Graveyard' started by Ioannes, May 28, 2010.

  1. Ioannes

    Ioannes Oh man, I shot Marvin in the face.

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    Z-Factor, Snowballing and Proper Late Game Balance of Power in PVP Maps

    This tutorial is not like the other ones. It does not explain a technique in mapmaking but rather sheds light on a major flaw in mapmaking. It is essentially faulty balance of power. When I still played in TFT Bnet I used to find it in AOS-type maps and felt really irritated by it. The problem is: some maps work in such a way that as the game progresses strong players become even stronger and weak players cannot outmatch them. This is true not only for WarCraft - any RTS has a potential to allow snowballing. I will first explain how this happens and what features of a map enable it. Then I will discuss the effects on mid- and late-game balance of power and consequentially why it is a problem for your map and how you can avoid it.

    -I- Introduction
    -II- The Mechanics of Snowballing and the Z-Factor
    -III- The Effects of Snowballing and High Z-Factor on Your Map
    -IV-Towards a Reduction of the Z-factor and Elimination of Snowballing

    [​IMG]


    -I- Introduction


    Imagine a 1v1 game in DotA. After 15 minutes player A has 1 kill and player B has 5 kills. As a result player B has earned more gold and experience and will spend them to improve his stats, skills and gear. Better stats and items result in a tougher hero who can both withstand harder beating and deal more damage (normally or through spells). In the next encounter between hero A and hero B the odds will be slightly more in hero B's favor. From now on he will become more likely to win than player A. This means that e will gain more and more experience and equipment whereas player A will lag behind, unable to overpower the current winner and get the money needed.

    [​IMG]

    This is known as 'snowballing' because at this point player B's power grows with greater and greater speed, akin to a snowball rolling down a hill. Each subsequent encounter is easier and easier for player B, making him stronger and stronger. The tendency of the map to allow this is called 'Z-factor.' ​



    I saw this in an interview posted on the internet with the makers of Guild Wars (former Blizzard employees). In their words:

    (When I found this quote in the spring the original page was gone and I had to read from Google's cached version. I presume it is all off the interwebs now.)


    -II- The Mechanics of Snowballing and the Z-Factor

    How exactly does snowballing in AOS games work? I will show it through a simplification of an AOS game.

    Let's play TodA – 'Throwing of Dice... Anyways.' AOS simplified would look something like this:
    • 2 identical heroes fight each other
    • Each has 30 hit points and deals 4+1d4 (one four-sided die) damage at the same speed
    • Each kill is rewarded with 2 additional hit points and 1additional damage point

    Less players and identical heroes means clearer snowballing. Imagine normal armor and health and so on substituted for the above hit points (same for normal attacking, spells and 'dps' capability in general). After each fight – referred to as 'duel' here – winners get gold and XP with which they make their heroes stronger, learn higher levels of their spells, buy better items and so on, all of which ultimately increases the hero's durability and dps.

    [​IMG]
    It will be a bit worse after he spends that gold

    With identical attack speed and simultaneous hitting here it is the dice that decide the outcome of each duel. In real DotA or Battleships or any other AOS map it is player skill (and hero balancing) that decide the outcome. Therefore, let us presume that player A's skills translate into 5+1d4 instead of 4+1d4 damage per second. If you see this game being played you will see the snowballing showing up. Here are the graphs.


    [​IMG]
    Each point is the heroes' hp and dps at the beginning of an encounter (duel). You can see them growing for heroA since he started winning. As a result, killing be easy
    [​IMG]
    Player B put up some resistance at the beginning, but once he was overcome player A started snowballing freely. I have extrapolated the graphs for the same games later in the tutorial.
    [​IMG]
    In the third game player B actually got lucky and managed to get an advantage. Player A managed to overcome him, but regardless of who was on top, as long as he was on top long enough he would start snowballing.

    All the notes follow.
    Code:
    The duels in GAME 1 looks like this:
    (I'm throwing dice as I write)
    heroA: 5+1 dmg – heroB: 4+4 dmg
    => heroA hp = 22; heroB hp = 24
    
    heroA: 5+2 dmg – heroB: 4+1 dmg
    => heroA hp = 17; heroB hp = 17
    
    heroA: 5+1 dmg – heroB: 4+1 dmg
    => heroA hp = 12; heroB hp = 11
    
    heroA: 5+3 dmg – heroB: 4+1 dmg
    => heroA hp = 7; heroB hp = 3
    
    Obviously, player A wins and gets rewarded:
     +2 hp and +1 dps bringing him to 23 hp 
    
    The next encounter looks like this, starting with 32
    and 30 hp, as well as dps bases of 6 and 4 respectively
    
    heroA: 6+1 dmg – heroB: 4+2 dmg
    => heroA hp = 26; heroB hp = 23
    
    heroA: 6+3 dmg – heroB: 4+1 dmg
    => heroA hp = 21; heroB hp = 14
    
    heroA: 6+3 dmg – heroB: 4+2 dmg
    => heroA hp = 16; heroB hp = 5
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Player A wins again, earning the 2 hp and 1 
    damage per second point. Duel #3 starts with 
    hero A having 34 hp and 7+1d4 dps while player B 
    will have to suffice with 30 hp and 4+1d4 dps 
    because he couldn't earn more on his own. 
    
    heroA: 7+4 dmg – heroB: 4+2 dmg
    => heroA hp = 28; heroB hp = 19
    
    heroA: 7+2 dmg – heroB: 4+2 dmg
    => heroA hp = 22; heroB hp = 10
    
    heroA: 7+1 dmg – heroB: 4+2 dmg
    => heroA hp = 16; heroB hp = 2
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Things are looking bad for player B here. 
    Ever since he lost the first duel he has been
    spiraling down, ladies and gentlemen. Now, 
    he is recovering at his corner, fearing the 
    storm that is about to be unleashed by 
    player A's hero. I myself wonder why I'm 
    still rolling the die on my desk. Hero A has 
    36 hp and 8 base dps while hero B has 30 hp 
    and a mere half the killing power. 
    This promises to be ugly.
    
    heroA: 8+2 dmg – heroB: 4+3 dmg
    => heroA hp = 29; heroB hp = 20
    
    heroA: 8+1 dmg – heroB: 4+3 dmg
    => heroA hp = 22; heroB hp = 11
    
    heroA: 8+1 dmg – heroB: 4+3 dmg*
    => heroA hp = 15; heroB hp = 2
    *i'm seriously not cheating. 
    Duel 5: (hero A is at 38/9+1d4)
    
    heroA: 9+4 dmg – heroB: 4+3 dmg
    => heroA hp = 31; heroB hp = 17
    
    heroA: 9+3 dmg – heroB: 4+1 dmg
    => heroA hp = 26; heroB hp = 5
    
    heroA: 9+4 dmg – heroB: 4+1 dmg
    => heroA hp = 21; heroB hp = 0
    
    And, as expected, player A beat player 
    B again. Hero A will reap the rewards of 
    win once again. Did anyone notice how 
    it was easier for player A to win every 
    consecutive duel? His hero was gaining 
    more and more power. And what is worrying 
    is that the stronger he got, the faster he 
    would finish off hero B and the more easily 
    player A got the rewards, which are health 
    and killing power. 
    
    
    I will do this some more. Starting with 30/5 and 30/4, GAME #2
    
    heroA: 5+3 dmg – heroB: 4+4 dmg
    => heroA hp = 22; heroB hp = 22
    
    heroA: 5+2 dmg – heroB: 4+4 dmg
    => heroA hp = 14; heroB hp = 15
    
    heroA: 5+4 dmg – heroB: 4+4 dmg
    => heroA hp = 6; heroB hp = 6
    
    heroA: 5+2 dmg – heroB: 4+4 dmg
    => heroA hp = 0; heroB hp = 0
    
    This turned out even. Player B manned 
    up and resisted, managing to get the 
    duel to a draw. For the next duel
    
    heroA: 5+2 dmg – heroB: 4+2 dmg
    => heroA hp = 24; heroB hp = 23
    
    heroA: 5+2 dmg – heroB: 4+1 dmg
    => heroA hp = 19; heroB hp = 16
    
    heroA: 5+2 dmg – heroB: 4+3 dmg
    => heroA hp = 12; heroB hp = 9
    
    heroA: 5+2 dmg – heroB: 4+2 dmg
    => heroA hp = 6; heroB hp = 1
    
    heroA: 5+2 dmg – heroB: 4+4 dmg
    => heroA hp = 0; heroB hp = 0
    
    okay, this is the last draw I'm including... Again:
    
    heroA: 5+1 dmg – heroB: 4+4 dmg
    => heroA hp = 22; heroB hp = 24
    
    heroA: 5+4 dmg – heroB: 4+2 dmg
    => heroA hp = 16; heroB hp = 15
    
    heroA: 5+4 dmg – heroB: 4+3 dmg
    => heroA hp = 6; heroB hp = 9
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Hero A wins. Gets pumped up to 32/6 and...
    
    heroA: 6+1 dmg – heroB: 4+4 dmg
    => heroA hp = 26; heroB hp = 23
    
    heroA: 6+1 dmg – heroB: 4+4 dmg
    => heroA hp = 18; heroB hp = 17
    
    heroA: 6+4 dmg – heroB: 4+4 dmg
    => heroA hp = 10; heroB hp = 7
    
    heroA: 6+2 dmg – heroB: 4+2 dmg
    => heroA hp = 2; heroB hp = 0
    
    Player A won. Final duel for this game... 
    I can safely bet on player A with his 34hp 
    and 7+1d4 dps now. Player B needs the 
    die to give him at least 3 or 4 in order to 
    even be a match for hero A's base dps 
    of six. Tough. 
    
    heroA: 7+1 dmg – heroB: 4+3 dmg
    => heroA hp = 26; heroB hp = 22
    
    heroA: 7+4 dmg – heroB: 4+4 dmg
    => heroA hp = 18; heroB hp = 11
    
    heroA: 7+1 dmg – heroB: 4+4 dmg
    => heroA hp = 10; heroB hp = 3
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    
    Player A wins again. This time the 
    chances that player B is at least even 
    off with player A in terms of dps are 
    slim. Player B needs 4+4 to at least 
    equal player A's 7+1 dps for each step. 
    That's small chances there. 0.25X0.25, 
    to be precise, or 12.5%. Not to mention 
    outperforming hero A is impossible. 
    I will mention the percentages again later.
    
    One last time. Game 3:
    
    heroA: 5+1 dmg – heroB: 4+4 dmg
    => heroA hp = 22; heroB hp = 24
    
    heroA: 5+3 dmg – heroB: 4+2 dmg
    => heroA hp = 16; heroB hp = 16
    
    heroA: 5+1 dmg – heroB: 4+4 dmg
    => heroA hp = 8; heroB hp = 10
    
    heroA: 5+4 dmg – heroB: 4+1 dmg
    => heroA hp = 3; heroB hp = 1
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = 0; heroB hp = 0
    
    It's a draw, but with slight advantage 
    for player A. In Battleships Xfire or DotA 
    this is a kill for him.
    
    heroA: 5+1 dmg – heroB: 4+4 dmg
    => heroA hp = 22; heroB hp = 24
    
    heroA: 5+2 dmg – heroB: 4+4 dmg
    => heroA hp = 14; heroB hp = 17
    
    heroA: 5+2 dmg – heroB: 4+3 dmg
    => heroA hp = 7; heroB hp = 10
    
    heroA: 5+1 dmg – heroB: 4+3 dmg
    => heroA hp = 0; heroB hp = 4
    
    Player B wins. Fortune smiled and 
    his hero is now slightly better off than 
    hero A. 30/5 vs 32/5
    
    heroA: 5+3 dmg – heroB: 5+1 dmg
    => heroA hp = 25; heroB hp = 25
    
    heroA: 5+1 dmg – heroB: 5+3 dmg
    => heroA hp = 17; heroB hp = 19
    
    heroA: 5+3 dmg – heroB: 5+4 dmg
    => heroA hp = 8; heroB hp = 11
    
    heroA: 5+1 dmg – heroB: 5+1 dmg
    => heroA hp = 2; heroB hp = 5
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = 0; heroB hp = 0
    
    ...and player B reached a draw. He 
    must be feeling the taste of vengeance already.
    
    heroA: 5+2 dmg – heroB: 5+2 dmg
    => heroA hp = 23; heroB hp = 25
    
    heroA: 5+4 dmg – heroB: 5+3 dmg
    => heroA hp = 15; heroB hp = 16
    player A is catching up...
    heroA: 5+3 dmg – heroB: 5+4 dmg
    => heroA hp = 6; heroB hp = 8
    
    heroA: 5+3 dmg – heroB: 5+3 dmg
    => heroA hp = 0; heroB hp = 0
    
    Another draw. Let's see...
    
    heroA: 5+4 dmg – heroB: 5+1 dmg
    => heroA hp = 24; heroB hp = 23
    
    heroA: 5+4 dmg – heroB: 5+2 dmg
    => heroA hp = 17; heroB hp = 14
    
    heroA: 5+3 dmg – heroB: 5+2 dmg
    => heroA hp = 10; heroB hp = 6
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    That's a kill for player A, regardless of 
    the dice. Hit points are now equal and 
    hero A has base dps hugher than hero B, 
    so if I continue player A is likely to win.


    To reiterate, what we saw above in games #1 and #2 was snowballing. Player A started with bigger killing power than his opponent. Chance was on his side and at the beginning of the games he won duels more often than his opponent. Therefore, he got rewarded by the map and received more hp and dps – in other words, more killing power. Consequentially, with each new duel the odds were stacking on player A's side. A gap of power appeared between the players. The faster the gap grows, the higher the Z-factor of the map.

    AOS maps have high Z-factors and tend to allow for snowballing. This is due to their basic mechanics of rewards for a kill.
    [​IMG][​IMG][​IMG][​IMG]
    Cases such as these, when a player gains an advantage at the beginning, are common in AOS's I've played. When someone does get lucky it becomes clear who will have the most kills by the end. Of course, this is also about skill and managing to rise above everyone else during the first 5-10 minutes. However, as I will point out, 'skill' is not an excuse.


    -III- The Effects of Snowballing and High Z-Factor on Your Map

    In the end, it makes a map less fun.

    Ideally, the more skilled a player is, the better his chances of winning. If not, then something is terribly wrong with the map. If you did not play well you do not get rewarded with xp, items, skills, upgrades and so on (i.e. durability and killing power). Yet, this does not atone a map with an tangible Z-factor. Why?

    I think that a map that allows for snowballing reduces the importance of player skill. If a pro joins 20 minutes later (disregard Bnet ), he ought to be just as serious threat to everyone as if he had been playing since the beginning. If not, then the map restricts the display of a person's skill and this is one reason why its fun drops. And you don't want to make maps that aren't fun, do you?

    Consider this. If you are a pro but had to leave your younger brother to play your battleships for you during the first, say, 10 minutes how would it be like when you are back? Your ship will have lagged behind the others because it wasn't played skillfully, and you will be lacking in money, items, xp and so on. If there was a guy of your skill in the game who played without interruption than his ship has more durability and killing power than yours. Better yet, make him somewhat weaker than you. You have played Bships for 2 years now and he has played for only 1. And, does stupid things like blocking people's way and so on. How would you feel if his big ship quickly closed the distance to your weaker boat (yes, you gained some time because he got stuck among AI ships, but that doesn't matter because in that map you can also upgrade speed and chase down noobs, allowing for painfully high Z-factor) and sailed through you? As I thought. Don't bother mourning – your next meeting will be worse, since he now has earned gold from killing you which has improved his hp and dps.

    [​IMG]
    Good ol' battleships. Bships Xfire's Z-factor is a greater than that of some battletanks I played, though


    And so, this means that in a map with snowballing the beginning is very important, if not the most important part of the whole game. In other words, a high Z-factor places the emphasis of the whole game in the beginning. This actually makes the middlegame and the endgame somewhat unimportant. Which is a mapmaking mistake.

    Imagine. It's the same game of Battleships from above and you are having a hard time while the fortunate newbie reaps gold and xp (or shall I just say hp and dps) with ease. What chances do you have of reaching his power? Unless you seized control from your brother early enough, miserable. At one point, if your opponent has snowballed enough, no amount of skill can even the scales. No matter how hard you try you will not be able to make up for his extra 2000 health, 20 armor, 166 damage or whatever. At one point in the game you will be doomed to lose.

    Let us look at how the TodA games look like after more rounds.
    NOTE: I am ignoring rewards from creep kills. The reason is that at best both players will have creeped the same. Normally, whoever is already stronger will be creeping more, facilitating the snowballing.

    [​IMG][​IMG]

    You can see the red and yellow lines belonging to heroA become more and more steep. This is the snowballing. The change in slope is the Z-factor.

    The maths has been compromised, for your convenience.
    Code:
    GAME 1:
    Player A starts duel 6 with big 
    stats – 40/10 while Player B is hopelessly locked down at 30/4
    
    heroA: 10+1 dmg – heroB: 4+1 dmg
    => heroA hp = 35; heroB hp = 19
    
    heroA: 10+1 dmg – heroB: 4+4 dmg
    => heroA hp = 27; heroB hp = 8
    
    heroA: 10+3 dmg – heroB: 4+2 dmg
    => heroA hp = 19; heroB hp = 0
    
    Another score for Player A. Next it's 42/11 vs 30/4:
    
    heroA: 11+3 dmg – heroB: 4+1 dmg
    => heroA hp = 37; heroB hp = 16
    
    heroA: 11+3 dmg – heroB: 4+4 dmg
    => heroA hp = 29; heroB hp = 2
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Player A has spent his gold and 
    raised a skill's level. 44/12 vs 30/4
    
    heroA: 12+2 dmg – heroB: 4+2 dmg
    => heroA hp = 38; heroB hp = 16
    
    heroA: 12+1 dmg – heroB: 4+2 dmg
    => heroA hp = 32; heroB hp = 3
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Hero A is now 46/13. Scary?
    
    heroA: 13+4 dmg – heroB: 4+1 dmg
    => heroA hp = 41; heroB hp = 13
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Ugly (48/14).
    
    heroA: 14+4 dmg – heroB: 4+1 dmg
    => heroA hp = 43; heroB hp = 12
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    In fact, there is no point to keep 
    writing the duels down, since it is 
    clear that Player A has enough 
    firepower to take out hero B with 
    two hits. It continues in the table.
    
    At heroA = 72/26 things look like this:
    
    heroA: 26+1 dmg – heroB: 4+3 dmg
    => heroA hp = 65; heroB hp = 3
    
    And at heroA = 74/27
    
    heroA: 27+1 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 2
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    At heroA = 76/28
    
    heroA: 28+1 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 1
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    And finally heroB is relatively so 
    weak that he falls with one hit.
    
    
    
    GAME 2:
    Player A starts duel 6 with stats of 
    36/8 versus 30/4
    
    heroA: 8+3 dmg – heroB: 4+1 dmg
    => heroA hp = 31; heroB hp = 19
    
    heroA: 8+3 dmg – heroB: 4+2 dmg
    => heroA hp = 25; heroB hp = 8
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Player A reaps rewards and his hero 
    is now 38/9. With a dps range of 
    10-13 it won't take more than 3 
    hits to kill heroB. HeroA becomes 
    40/10 and his dps range is enough 
    to strike heroB down in 3 steps but 
    still not enough for two. Will heroB 
    fall once heroA's stats get as high as 
    42/11? Statistics demands that I check.
    
    heroA: 11+2 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 17
    
    Nope. Checking for 44/12
    
    heroA: 12+4 dmg – heroB: 4+2 dmg
    => heroA hp = 38; heroB hp = 14
    
    heroA: 12+1 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 1
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    
    How about stats=46/13?
    
    heroA: 13+2 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 
    
    heroA: 13+4 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 
    
    HeroA turns 48/14. Now heroB is 
    sure to fall in two hits. And the 
    slope of heroA's dps will become 
    even steeper. At heroA = 82/26 I 
    ought to check again
    
    heroA: 26+3 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    At 84/27?
    
    heroA: 27+1 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    At 86/28?
    
    heroA: 28+4 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Good riddance.
    
    
    GAME 3:
    Player A starts duel 6 at 32/6 and 
    player B at 32/5
    
    heroA: 6+3 dmg – heroB: 5+2 dmg
    => heroA hp = 25; heroB hp = 23
    
    heroA: 6+3 dmg – heroB: 5+2 dmg
    => heroA hp = 18; heroB hp = 16
    
    heroA: 6+3 dmg – heroB: 5+2 dmg
    => heroA hp = 11; heroB hp = 8
    
    heroA: 6+4 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    heroA has become 34/7
    
    heroA: 7+1 dmg – heroB: 5+1 dmg
    => heroA hp = 28; heroB hp = 24
    
    heroA: 7+1 dmg – heroB: 5+1 dmg
    => heroA hp = 22; heroB hp = 16
    
    heroA: 7+4 dmg – heroB: 5+3 dmg
    => heroA hp = ; heroB hp = 5
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    heroA vs heroB = 36/8 vs 32/5
    
    heroA: 8+2 dmg – heroB: 5+3 dmg
    => heroA hp = 28; heroB hp = 22
    
    heroA: 8+1 dmg – heroB: 5+2 dmg
    => heroA hp = 21; heroB hp = 13
    
    heroA: 8+3 dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 2
    
    heroA:  dmg – heroB:  dmg
    => heroA hp = ; heroB hp = 0
    
    Hero B is lagging behind again while 
    hero A is 38/9 and capable of killing 
    heroB with three hits. At heroA = 44/12 
    and heroB = 32/5 I roll 4 and 2 for the 
    1d4 bonus to heroA's dps which means 
    3 hits and lvl up. When heroA is 46/13 
    I'm rolling 3 and 4 which means another 
    2 hits distance to the reward. Note that 
    at this point heroB would need at least 
    6 hits (since his maximum dps is 5+4=9 
    and heroA's hp are 46) and no resistance 
    by heroA to make a kill. Tough. When 
    heroA is 48/14 I roll 2 and 2, again saving 
    a step. HeroA is now 50/15 and has 
    achieved minimum dps of 15+1, so no 
    rolling until 76/28. I roll 4 (woot) and 
    it's 78/29 now. Rolling 2 is displeasing. 
    At 80/30 I roll 1 so it's two rows in the 
    spreadsheet for this. 


    Here are the graphs again. People sometimes play very effectively while at other times they aren't really focused. You yourself may start really trying to outfight the huge and expensive enemy ship. To simulate for this human complication in controlling the hero I have inflated the dps lines to simulate players' potential 'top' and 'bottom' range of managing to deal damage.
    [​IMG][​IMG]
    Even if it overlaps at the beginning, due to the extremely high Z-factor, in the simplified TodA the lines quickly diverge, sending one of the players into the winners' party. I will mention the irreversible gap shortly

    It is like a game of (association) football in which there was a special rule - after each goal the opponents score, your team's goalposts move further apart. Imagine how easy it would be to score in that case, once your team has taken the lead.

    To continue with the bad news, the same thing – snowballing – is bound to happen in any map that rewards successful frags with dps. Whenever someone is a bit more successful with his hero than the others, even if we picked all players to be equally apt and have identical apm with identical accuracy, things will spiral out of control. It's like TodA with the only difference that heroA's superior dps is not due to skill but rather luck. And even if a lesser hero gains the upper hand, and then a third player becomes top, in the long run somebody's streak will prevail above all other competitors and in the end he will enjoy snowballing at the enemies' expense. I have seen balanced games but more than half of what I've played on Bnet ended up in snowballing. Yes, there were leavers, but there were other games it persisted.

    This overly simplified game shows the basics behind the high Z-factor's harmful effect. The strong become stronger and the weak stay the same. The rich become richer and the poor relatively poorer. Gaining the upper hand is impossible and at one point the top ranking hero cannot be overcome. He becomes stronger and stronger, accumulating hp and dps with increasing speed. Finally,

    Tangible Z-factor ruins the endspiel. If you suck at the beginning, especially if it is a 1v1 or 2v2 game, you will find yourself weaker and slower and in 20 minutes all your resistance will have become obsolete. :( This is why the power gap is irreversible: no amount of skill you show can make up for your hero's inferior power. Imagine the losing football team just quitting because their goalposts were so far apart that defending them was impossible.

    [​IMG]
    imagine facing this

    When a mapmaker designs a map, s/he expects that players will keep on fighting. The author and the winning side should not be surprised, then, if the losing side leaves or stops playing in mid-game and just lets his/her hero stay in the base, waiting for the AI units and structures to fall. After all, why should they keep playing and resisting?

    That's right – what difference will it make? When you know that in this map your hero will certainly die and that then will be come even more vulnerable? Because the map (DotA or Bships Xfire are not the only examples) has such a high Z-factor, it will stop being fun before it is officially over. ​

    Because the map has a high Z-factor and propensity for snowballing, players will not be stimulated to finish their games. They will not want to continue after a certain point because they know that resistance has been rendered futile and although the base and all the ancients may be standing, there is nothing to do to prevent them from falling. The map will only be fun at the first n minutes of game time and finishing it is pain and/or annoyance for 50% of the players.

    Obviously, any rational mapmaker should avoid this when designing pvp maps. If he chooses to have penalties and rewards for losers and victors respectively, he is increasing the Z-factor of the map. He is making a map in which the game is decided at the beginning and the rest is not a fair competition where both sides have a chance to win, but a slow agony for those who have been away or distracted or whatever. The latter players may be more skilled, or better motivated after playing a bit, but if the Z-factor is high then the map will allow player skill to decide victory only at the beginning and will ignore player skill and efforts later on.

    Snowballing, engendered by high Z-factor, therefore serves to stratify the player's existant ranking, to widen the gap of power between strong heroes and weak heroes, to reduce the importance of game skill and, worse of all, to decide the result of the game before it ends as designed.


    -IV-Towards a Reduction of the Z-factor and Elimination of Snowballing

    Z-factor, I mentioned above, is fostered by things like penalties for losers and rewards for victors. When ship M sinks ship N, ship M gets more gold and experience (including the 30 seconds during which he kills creeps and ship N is dead). Z-factor is also increased by the basic design of the map –if fulfilling the main objective becomes easier the more successful you are, a problem is at hand. If the map's goal is to kill enemy heroes and you become a better hero killer (more HP and damage, etc.) as you succeed, then the balance of power between players will spiral out of control. Chances of victory may have been equal at the beginning, heroes evenly matched, but when your job becomes easier the more you do it, and the other players' job becomes harder if they have been doing bad at the beginning, then there is high Z-factor.

    Thus, Z-factor is found outside your AOS map. I have all reasons to expect snowballing in upcoming SC2 maps and I bet there's poorly designed games out there ('Z' being an obvious example) who discriminate against the losing side. In fact, we can see something similar to snowballing in that country where the rich gets richer and the poor gets poorer, assuming that the rich person uses the money to become even richer. Also, we can see it in modern warfare. The fluid environment of today's battlefield, where units' dps's are by far superior to their hp it is easy to exploit an advantage. But I'm straying.

    Fixing the Z-factor is basically simple. To ensure that both sides have a chance up to the end, a good mapmaker will make sure that the losing side always has a feasible way to catch up. This way, although player A has lost to player B the first three times, he will be able to prevail later on if he mobilizes himself. Also, your AoS map can and should reward successful hero killers not with hit points and damage, but with some other valuable resource that is unrelated to hero duels. For example, items may be worth gold, but to reduce the Z-factor you may choose to reward hero kills with lumber. Your team will need the lumber for some big goal, but the reward will not in any way affect the outcome of the next duel. Generally, keeping the rewards out of the competition is the way to go.

    Popular AOS maps do this in the following ways.


    • Alternate sources of hp&dps - usually creeps, this is the most used source of gold and experience for the hero who lags behind and does not want to risk facing stronger heroes. Another good thing about creeps is that the player cannot focus on killing both them and enemy heroes. Which means that if the strong heroes are busy with each other, a weaker one may try to sneak in and reap some gold from the AI.

      [*]Teamwork - weaker players will team up and fight a strong hero. Stands to reason.
    • Autobalance - arguably. I won't risk making statements about how effective an automatic intervention is in preventing snowballing.


    There are also solutions such as in Tides of Blood or 'The Search for Illidan.' In these maps, the players are not that focused on gaining gold and experience, which breaks the cycle from the beginning.

    An almost perfect example for an AoS map with a Z-factor close to 0 is Chapter 4 of the Human campaign in 'WC3: The Frozen Throne' – 'The Search for Illidan.' There, side A and side B were sending armies against each other and the player was controlling two heroes for side A (Maiev, alone and grumpy, was on side B). It was all going according to a typical AoS, but the Z-factor was almost eliminated by two brilliant decisions by Blizz.

    [​IMG][​IMG]

    First, the goal was different from the attaining of it. The goal was to keep the enemies, Night Elves, away from a slow-moving wagon that was on its way to side A's base, because if they got close, it would start moving in the opposite direction and if it got to side B's (the Night Elf) base, the game was over. The attaining it was fighting anything that was Night Elven and that approached the wagon. The rewards were small amounts of gold that could be spent on items that helped you deal some more damage, but that was it XP gain was capped. Killing enemy units did not make the wagon move faster. Closing the distance between the wagon and base A did not make it move faster. This was the first good idea. The second one was to regulate the strength of the waves. Blizzard, in their wisdom, had decided that as the wagon drew farther and farther from the Good Guys' base (or that of the Night Elves), the good base will spawn bigger waves and the enemy base will spawn smaller waves (and vice versa). What happens is that when the wagon is in the middle of the map the armies are evenly matched, but as the wagon draws closer to the allied base, the allied spawns diminished and the closer the player was to winning, the harder it was to keep the many enemies away from the wagon. Similarly, if the player had been losing and the wagon was closing in to the Night Elves' base, he got massive reinforcements and the enemy's spawns were meagre.
    [​IMG]
    This way Blizzard had elegantly kept the player constantly occupied. Victory was always at approximately the same distance away from you and no matter where the wagon was, you had to expend a similar effort to make it go to your base.
    [​IMG]
    It was not until the last seconds that victory was decided and the wagon was safely in, because the pressure on defending it grew larger and larger the closer you were to winning. The balance of power between the two sides in this map was kept even until the very end.

    This is what maps on Bnet miss. Once you gain an advantage in DotA (I suppose: I myself never have :D ) your job of killing the enemy heroes and base is likely to be easier. You will have come closer to victory. What we should see instead is some sort of penalty, which will always push victory away from you and compel you to keep fighting until the very last moment. Or, respectively, some compensatory mechanism that will always pull victory closer to you and give you hope that you can win until the very last moment. Instead, the maps people make allow the balance of power later on to irrepairably tilt to one side, taking the chances of success away from one side and putting in the hands of the other.

    Now, I need to make a note. I have described rewarding players for success as something evil, but I am aware that it is also one of the main things that makes people play your map. You wouldn't play DotA if what it took to have a strong hero with good items was to let yourself be killed! People want to work towards victory and gain power and be superior to other players. The problem is to realize when this has gotten out of control and when does resistance in games on your map become futile. When players have started losing they do need to muster their skill and apm.

    The question arises: how easier it will be to catch up once they've mobilized against a stronger and better equipped hero? I know of no feasible way to calculate this; it is all subjective and only beta-testing can give the mapmaker the answer. However, somewhere out there there is a boundary, for most pvp maps, when the current game has been decided and the losing side need not bother playing anymore. The mapmaker's job is to make pay attention that this boundary is as close to the mechanical end of the game (e.g. death of enemy main building) as possible.



    This is developed from what has already been said here
    http://www.thehelper.net/forums/showthread.php?t=147635
     
    • Like Like x 9
  2. tooltiperror

    tooltiperror Super Moderator Staff Member

    Ratings:
    +233 / 0 / -0
    No one likes walls of text.

    Include diagrams and pictures too get a bigger audience and hold attention.
     
  3. Laiev

    Laiev Hey Listen!!

    Ratings:
    +187 / 0 / -0
    you really need a new thread template...

    i don't know what is what before i read :(

    the only thing which i really notice is the first picture


    organize it and i'll read :thup:

    PS: Posts: 1,337!!!!!!!!!11111111111oneone!!
     
  4. BlackRose

    BlackRose Forum User

    Ratings:
    +239 / 0 / -0
    I like walls of text [well just this one :p]. It's an interesting read.
     
  5. Crazy_Dead

    Crazy_Dead New Member

    Ratings:
    +24 / 0 / -0
    Use
    Indent​
     
  6. Tom_Kazansky

    Tom_Kazansky --- wraith it ! ---

    Ratings:
    +157 / 0 / -0
    yes, indeed, interesting :)

    I don't know about this until now :)
    ---
    but you need to organize the thread, this is a tutorial, right? :p
     
  7. Earlenlajnen

    Earlenlajnen Member

    Ratings:
    +10 / 0 / -0
    Interesting subject. Really good that you enlightened us about the problem.

    Personally I've never really thought about the "snowball effect" or the "Z-factor" (probably since I wasn't aware of these words).
    I've always accepted these aspects of gaming as normal and needed.
    Which they are with some moderation.
    But since i resently started playing DotA I've become more and more aware of how important the first few minutes of gaming are.
    Even though the snowball effect is really irritating it's important to keep in mind that you have to reward player that plays good.

    + rep for awsome tutorial.
     
  8. Viikuna

    Viikuna No Marlo no game.

    Ratings:
    +265 / 0 / -0
    Snowball effect, ey. I didnt read it yet, but I will. I think Ive seen some of this text from you before, though.

    Looks neat.
     
  9. SineCosine

    SineCosine I'm still looking for my Tangent

    Ratings:
    +76 / 0 / -0
    I read ALL of it.
    I don't normally like walls of text >.>
    Butthis caught my attention.

    I lol'd when I saw Shimrra's techies screenshot as an example of snowballing XD
    It was a funny moment for me.

    Good read, now I'll know what to avoid!
    Extremely awesome article, +rep!
     
  10. Blackrage

    Blackrage Ultra Cool Member

    Ratings:
    +25 / 0 / -0
    Wow, I actually never really paid much attention to the 'Snowballing and Z-factor' before reading this tutorial. I just thought that it was natural, but you proved me otherwise.

    +Rep
     
  11. Executor

    Executor I see you

    Ratings:
    +57 / 0 / -0
    Well, I think that DotAs system is really good. You grow stronger by killing, but being killed with a streak results in extra gold. The point is, that mostly the noobs leave because they don't pwn and try their luck in another game. DotAs key to turn-over the game is to kill the one 'imba' dominating hero via a gangbang and rush into the enemies base => team-play. This happens all the time, if the game lasts long enough and only one "killer hero" gets feeded.

    Okey, if the whole enemy team is feeded and plays in a team it is hard.. yes. But real game-goal of DotA is to PREVENT the enemy team growing to strong via tactical movement.

    Such methods as you suggested (one team gets nearly defeated => creep spawn increases) will annoy the most people. For example: You fight 20 min to get nearly to the enemy base, one ultimate and the game ends up again in the middle ....
     
  12. SineCosine

    SineCosine I'm still looking for my Tangent

    Ratings:
    +76 / 0 / -0
    Shimrra's techies XD

    XD
    XD
    XD
    XD
     
  13. Ioannes

    Ioannes Oh man, I shot Marvin in the face.

    Ratings:
    +50 / 0 / -0
    Yes, yes, I fixed it :)

    You did - refer to the link. Also, snowball effect is actually different from Z-factor. Z-factor is the tendency to have snowball effect. But I still fixed it and it mentions 'snowball' a lot more now.

    @ Executor: I know. I'm just using this to criticize Z-factoring and point out the evil it can be :rolleyes:.
     
  14. Earlenlajnen

    Earlenlajnen Member

    Ratings:
    +10 / 0 / -0
    This tutorial needs an approval.
     
  15. SineCosine

    SineCosine I'm still looking for my Tangent

    Ratings:
    +76 / 0 / -0
    Shimrra's techies XD
     
  16. Jedi

    Jedi New Member

    Ratings:
    +63 / 0 / -0
    Great tutorial.
     
  17. tooltiperror

    tooltiperror Super Moderator Staff Member

    Ratings:
    +233 / 0 / -0
    I wouldn't say it is actually a tutorial, though.
     
  18. SineCosine

    SineCosine I'm still looking for my Tangent

    Ratings:
    +76 / 0 / -0
    It's an article =)
    (With a hilarious moment depicting Shimrra's techies)
     
  19. tooltiperror

    tooltiperror Super Moderator Staff Member

    Ratings:
    +233 / 0 / -0
    Exactly. It's a great read, and very helpful. But I wouldn't say it is a tutorial.
     
  20. SineCosine

    SineCosine I'm still looking for my Tangent

    Ratings:
    +76 / 0 / -0
    We should have a new section for this >.>
     

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