When designing Invasion maps remember basic laws of probability. *UPDATED* THERE ARE TWO SECTIONS TO THIS THREAD. BOTH ARE EQUALLY IMPORTANT TO UNDERSTAND. I KEPT THEM IN SPOILERS SO YOU CAN GET TO THE COMMENTS MORE QUICKLY. First of all you have to realize that when designing a map in Halo, YOU CANNOT INCLUDE SKILL. Spoiler Planning a map to be balanced with skill in the equation is wrong. Firstly, you do not know the skill of the players. This is why handicaps increase with multiple deaths, and increase with kills. They're looking for the middle ground. The better player will always win though, because the handicapped player won't receive the handicap they need without falling behind in the first place. Skill is preserved. When designing a map for balance, you must understand that the final outcome has to be balanced for teams of equal skill. You can't handicap a team so that they have a greater chance of winning than any of the other teams. I know this seems like common knowledge, but I have come across people that DO NOT UNDERSTAND THIS. This knowledge is a pre-req for understand the next section. There, first section done. That wasn't so bad? Well, unless you like numbers and walls, here's section two. This is a really important section though. It is what decides if an invasion map is balanced. Spoiler First things first. In invasion, winning a battle, does not guarantee winning a war. Winning the final battle guarantees it. As such, the following argument does make sense, so make sure to read it thoroughly. The more times a task is repeated, the less likely the same exact outcome will occur. Therefore, you need to use this equation WHENEVER designing an invasion map, meant to be balanced. x^y=0.5 You must replace the variable y with the number of stages in your invasion map. You then solve for x. Written another way, x equals y roots of 0.5. That x is the number you want to achieve in each individual stage. It is the percent of times attacker should win a stage. Unless playing a one stage invasion game, it should NEVER be anything less than or equal to 50%. Ever. Even on a two stage game. Example, in a three stage game: First Scenario: 2000 teams of completely equal skill verse. Map designed so EVERY stage has a 50% chance of being won. First stage is played by teams 1000 times. Attackers win half of them, and defenders win half. 500 Defenders are already done playing, they've already won. Second stage is played 500 times, by the remaining attackers. Half of them win. Half of the Defenders win. We now how 750 games won by defenders. There are STILL 250 attackers who aren't even done playing yet. Third stage is played 250 times, by the remaining attackers. Half of them win. That means 125 attackers would ultimately win. 875 defenders would win. That is really unfair. Second scenario: 2000 teams of completely equal skill verse. Map designed so EVERY stage has a 79.370% chance of being won. Stage one. 1000 team play. 79.370% attackers win. That means 793.7, rounded to 794, attacking teams win. 206 defending teams have already won the match. Stage two. 794 teams play. 79.370% attackers win. That means 629.42, rounded to 629, attackers win. 165 defenders win the match and are done, bringing the total to 371. Stage three. 629 teams play. 79.370% attackers win. That means 499.2327, rounded to 499, attackers win. 130 defenders win. That brings the defender total to 501. If you do the math without rounding the number is even closer. The final number of attackers winning is 499.9990059530 attackers. DEFINITELY EVEN ODDS. ---------------------------------- Now figuring out an exact percentage is really difficult, seeing as you're not going to manage to get 1000 equal teams to test your map. So what you should do is try it your best, and just keep in mind while you're playing that attackers should have the advantage. There is barely a way you can keep it at 80%, let alone 79.370%. Try and establish a middle ground. Seeing as I don't know if you are stuck with an invasion game of exactly 3 waves maximum, I'll give you a table of waves to percentage of attackers winning a stage. I'll also give a list of margins to aim for, and how close the margins will get you to 50%. 1 Stage: 50% - Strive for 50% 50%-50%. 2 Stage: 70.71% - Strive for 65%-75% 42.25%-56.25% 3 Stage: 79.370% - Strive for 75%-85% 42.1875%-61.4125% 4 Stage: 84.09% - Strive for 80%-90% 40.96%-65.61% 5 Stage: 87.06% - Strive for 83%-93% 39.39%-69.57% If you haven't noticed, as you get further away from 1 stage, it gets more and more difficult to nail the 50% with 10% margins. So if your goal is to create a five stage infection game, practice nailing three stage games first. So are you still with me? You are? Good. Because now we are going to get REALLY technical. I'm going to let you on in a little secret. You can have stages with different percentages. GASP. Who would have thought? This little twist is the equivalent of making the gametype asymmetric. It may be uneven on individual terms, but if you put the whole thing together there's a 50-50 chance. This method require an extensively greater amount of work. And obviously doesn't work with 1 stage games. I'm going to hand you some new equations. These are a little different. 2 Stage xy=.5 3 Stage xyz=.5 4 Stage xyzw=.5 5 Stage xyzwn=.5 x,y,z,w, and n are any specific stage's percentage. The point is, as long as all of the percentages multiplied together = 50%, the map works. Solving for which work is a little more difficult though, unless you're fine with being forced into a few numbers. So here are a few tips to help you figure out the numbers. Remember, if you don't mind the margin, you can fudge the outcome percentages a little bit without too much of a problem existing. A two stage game has the easiest equation to figure out. Just divide .5 by the percentage you want, and it will give you a second percentage. That second percentage is y. Your percentage is x. Ex. I want attackers to have a 95% chance of winning the first stage. I don't care what the second stage is. I divide .5 by .95 and get 52.63%. I have to aim the second stage to be as close to 52.63 as possible. For other stages you have to be much more careful. Your first division will determine the rest of your decisions. Your goal is to get as close to one as possible, while not going too far over. Each choice in division has to be higher than the answer your calculator gives you. To get your final percentage, take your final calculations result, as any number divided by itself = 1. Ex. I'm doing a five stage game. I start by deciding I want a stage with a 70% chance of winning. .5/.7 = around 71%. That means for my next decision, it has to be WELL above 71%. So I go with 80%. .71/.8 = around 89%. For my next decision, it has to be above 89%. I decide 95%. .89/.95 = around 94%. I need to do one more decision to get the final numbers. I go with 97%. .94/.97 = around 97%. So far I had a stage with 70%, 80%, 95%, and 97%. Because 97% was my final answer, I add that in as the fifth stage. So I have: 70%, 80%, 95%, 97%, and 97%. When I multiply these all together I get... 0.5005588. I think that's pretty close, and I rounded a few numbers along the way. That's the MOST efficient technique I can discern to making these maps balanced. So IF YOU WANT, I suppose you can have a game with a stage where there is a 50% of the attacker winning. It's just that all the other stages you have to make sure the attackers are guaranteed a win. These two sections are important for understanding balance in an Invasion game. DO NOT design won without understanding this first, as it greatly lowers the chance of you balancing it correctly. I will now answer any question and discuss this topic with you. If anyone can write scripts here, I would appreciate it if they could turn those two equations I have at the top into calculators. I realize it's near impossible to get those percentages exactly. That's not the point. I do not want posts about how you are supposed to figure out how to get them. That's your job. I'm just giving you them. One important note brought up: Remember that objects given to attackers in previous situations will affect future situations, so when designing later rounds, keep the old ones in mind. UPDATE UPDATE UPDATE UPDATE UPDATE UPDATE: Following this method WILL make your Invasion games longer. Here's the proof. I first show that the game is fair. Then I show you the chances of a match going a certain length. Broken into a graph with 50% chances of winning a round, here are all possible point outcomes. This includes the idea that winning as a defender grants no points. I also give the chance of each happening. W/L says whether or not the first team won. Basing percentages on the 80% attacker win round. T is tie, obviously. 3-3 26% T 3-2 7% W 3-1 8% W 3-0 10% W 2-3 7% L 2-2 2% T 2-1 2% W 2-0 3% W 1-3 8% L 1-2 2% L 1-1 3% T 1-0 3% W 0-0 4% T 0-1 3% L 0-2 3% L 0-3 10% L Chance of team 1 winning: 33% Chance of team 2 winning: 33% Chance of a tie: 34% So as you can see, this method is very fair. Equal chance of winning, losing, and getting a tie for each team. But, let's compare this to the 50% strategy. 3-3 2% T 3-2 2% W 3-1 3% W 3-0 6% W 2-3 2% L 2-2 2% T 2-1 3% W 2-0 6% W 1-3 3% L 1-2 3% L 1-1 6% T 1-0 12.5% W 0-3 6% L 0-2 6% L 0-1 12.5% L 0-0 25% T Chance of team one winning: 32.5% Chance of team two winning: 32.5% Chance of a tie: 35% Now, seeing as a rounded all of my calculations, I can say for a fact that those numbers are actually 33.333...% in every case. But let me give you some new numbers that might make you think my method is superior. Going with method 1, my method: Chance of the game going for 6 rounds: 42% Chance of the game going for 5 rounds: 20% Chance of the game going for 4 rounds: 29% Chance of the game going for 3 rounds: 6% Chance of the game going for 2 rounds: 4% I realize that that equal 101%, remember rounding, so these are fairly close to correct number. Notice that there is an extremely high chance of a game going on for a long time. Chance of the game going for 6 rounds: 8% Chance of the game going for 5 rounds: 12% Chance of the game going for 4 rounds: 30% Chance of the game going for 3 rounds: 25% Chance of the game going for 2 rounds: 25% Notice that there is a greater chance of the game being shorter in the 50% method.
You do realize that the basic fact that the Attackers are given a huge numerical advantage to the end will weight your equations somewhat. And no matter how many mistakes the Attackers make, they can keep coming, but if the Defenders make even one it is pretty much game over. I think your suggested stats are probably a little extreme (but brilliant none-the-less.) I actually hadn't thought of most of this information, but i really had no intention to make an Invasion map. Until now!
Soooooo... for an Invasion map to be balanced and fair.... attackers need to have a 50% at the first stage (maybe) and then need to almost guaranteed to win with the other stages. Here lemme break it down. First stage: Attackers: 50 chance Defenders: 50 Second stage and futher: Attackers: almost guaranteed or guaranteed Defenders: Almost never to never I don't get how that is fair in any aspect. Please elaborate in English. Math is my worst subject and when laid out in numbers you have confuzzled me beyond the furthest measure. Okay answer this question if you disagree with or do not get any of what i just posted above (I made it bigger just for this reason) Are you saying that attackers and defenders being even at the start and then the attackers basically winning almost every time is fair for Invasion and therefore should be set up as such?
Kind of. If the attackers make a bunch of mistakes, then they take to long and lose. They can't afford mistakes at all at a 50-50-50 game, but with the advantages if gives the result of being able to make two big mistakes. On the other hand, defenders, no matter what, can afford two big mistakes, as long as they survive the third wave. Attackers can survive two big mistakes in the first round, but like defenders, one more mistake and it's game over. That's the idea behind the numbers. To answer you basically, no. I'm saying that's one way of being fair. I'm sorry, but if math's your worst subject you'll probably have some trouble understanding this. I'll try and make it as easy to understand as possible. If there is a 50% of winning the first stage for attackers, and 50% for defenders, then if the defenders win they've already won the game. If the attackers win then they've got to do that again... twice. So the chance of an attacker winning is 50%*50%*50%, or 12.5%. If you give the attackers an advantage, then they could still win the as fairly as the defenders.
Thank you for elaborating my friend, I understand now. Now when I make my first invasion map I will take this into mind.
Well first of all, im not sure how bungie is going to do win/loss in invasion because they said it is now round based, as in each team gets a chance to attack and defend in the same game. so depending on the details of the scoring of these rounds, it could just null your whole post.
If it is this is still very important. One team has to win twice to win. So this keeps balance between rounds.
on the recent spire video posted on b.net, it shows that you get a point for each tier that you win on offense, with a max of three points per round (assuming each map has only 3 tiers). 2 rounds, an opportunity for each team to be on offense and score points. so based on that, i would think it should just be 50/50 even chances on each tier. because whoever progresses further on their attacking turn wins, so you dont need to win on all 3 tiers to win.
Or one team has to get farther than the other team. Now on to some serious stuff. Initial round The defenders start the round at a high point overlooking what they will be defending for the coming round; cover should be sparse, without much armament. Their odds would be almost equally weighted towards each side should the teams be equal, but they are not. The attackers begin far back, giving the defenders precious moments to take defensive positions before the onslaught. Attackers blitz through, overwhelming the defenders and quickly taking the objective. This gives the attackers the momentum they need to break the defenders lines at successive objectives, and gives the defenders time to plan the defense of successive objectives. Main rounds The attack is in full swing and the defenders are on the run. If the attackers make one wrong move, the defenders gain a significant advantage and the only way to take the objectives is either with one strong push, using all the might of the attackers to take the objective, or else by sabotage, sneaking behind the enemy line of defense to bring down the objective. If the attackers continue forward, they continue receiving reinforcements at each objective, but only in the face of increasing enemy opposition. Final round Here the assault comes to a grinding halt; the defenders do not move farther back, and the objective is in their midst. Only once the defenders lines break entirely, can the objective be captured. Defenders are overwhelmed, but have a smaller area to defend. Vehicles might be enough to reform the lines, but only for a moment before falling. The attackers must do everything right to take the final objective There's no fun in making the later rounds easier because then the defenders have no chance once the first objective is taken, which is usually while they are most disorganized. Instead, the first round should be easiest, a mere speed bump, while the later rounds have heavier vehicles and weapons, and the defense becomes stronger. Even Bungie admitted that Invasion on Boneyard was terrible when the defenders had DMR's on the first round to pick off the attackers across the wasteland. The height difference in the first round of Boneyard really belonged in the final round where attacking is supposed to be more difficult. /walloftext tldr: final round weighted towards defenders, starting round weighted towards attackers, gameplay escalates, attackers try to keep momentum
First of all, excellent post, redearth! It was well planned. (At first I raged, I thought you were saying there wasn't skill in halo. Then I lol'd.) I agree with everything that you said. It's difficult to discuss things like this when we use organic details about advantages such as where people are positioned and how much time they have. It's vague, relative, at the mercy of the observer as to the true value of it. It can't be measured by the naked eye, only with a calculator when recording the win-loss ratio on a tier-to-tier basis. When Bungie provided Spartan vs. Elite Slayer, they were creating a statistical experiment. Both my friend and I felt like the elites always won, or at least they did nine times out of ten. As it turned out, the actual statistic was six times out of ten. This is also not about difficulty. The arduous state of a challenge may work independent of the probability of success. Playing the campaign on heroic or legendary might be challenging, but you'll almost certainly complete the level. If we're going to go into the feel of a basic invasion match, I agree the first tier is relatively easy on the attacker's part, relatively difficult on the defender's part. And the rest of the game is a struggle for both, but mathematically, we're talking about the odds of success. What redearth is supplying doesn't make it so the game doesn't escalate. In fact, what he's describing is exactly the way Bungie makes their Invasion matches work. And "Now on to some serious stuff"? That's pretty belittling if you ask me, after all the numbers he crunched.
I better understand the math behind what you're saying now, but there are a few problems with it. Foremost, your viewpoint is from a purely ideal perspective; in a real game situation the teams that win the first round have a greater chance of winning the second round because they are better. Unless the measurement for who wins the second round is taken from only the set of those who win the first, the precentage to pass that part will be much higher. If the sucessive rounds are designed correctly, a negligable portion of those who lost the first round would have been capable of winning the second. Here the theory breaks into two sections depending on if the teams switch sides. In a situation where the attackers and defenders do not switch, there should of course be equal wins for both attackers and defenders. Keeping with the idea of escalation, the first rounds should play quickly for attackers who win, and end the game only in situations where the defenders are much better than the attackers. The final level then has an equal chance of favoring either side, but because a number of the attacking groups who would lose have already been eleminated, the precent of attackers who succeed here will seem higher. In the other scenario, each team plays as both attackers and defenders; here the game is more of a race to complete the take the most objectives, and stop the other team from doing so. This situation should have an extremely low chance of reaching the last round, let alone beating it. the greater number of rounds and increased difficulty are good to create a score karting and allow one team to excel. I have heard the second situation is what bungie has planned for Halo: Reach which makes this entire thread irrelevant. I'll post some nice math you might be interested in tomorrow
I understand completely what you're saying. I guess I rather should have said that the percentages should take into calculation the entire match, and not just one stage at a time. I assumed that went without saying, but I suppose it does make sense to say. Obviously a team who dominates in the first round will come into the second round a little more powerful. I'll update with that note you brought up. I did not hear about the switch though, in that you would be almost completely right, and any game played is right off the bat balanced. Nonetheless, you should still consider the theory, as to give each team a 50% chance each game for success, making individual rounds fair. Both teams, skill the same, should both have the same chance to get 3 points in one round. That's my personal belief. Nonetheless, as long as defenders don't get a point for defending it can be taken any other way. And lastly, you can always create a custom old style invasion, in which this does occur. Not so much belittling if you ask me, he was right. That is serious stuff. That's taking what I supplied, and pushing it a step farther. I think he has a little better idea on this than me. And that was in no way number crunching. That was basic algebra.
i my opinion, no math involved, i feel like the first tier should be tilted a bit in the attackers favor, cause i dont think a 0-0 game would be any fun. second tier would be an equal playing field, while the third tier would be more in favor of the defenders. while watching the full game on spire, this seemed to be more or less the case. both teams passed the first tier without a terrible amount of trouble, but one team got stopped on the second tier. then the other team made it to the third tier but didnt even touch the core thing.
I haven't read all the replies, but the simplest solution is to have both team plays as both attackers and defenders. Two different invasion sequences, so that no matter what, the probability of winning is exactly 50%, regardless of advantages given to attacking or defending teams. in the beta, invasion games only had one sequence, but custom options can allow us to have teams switch sides and play through two invasion sequences. How do i know? This.
please do read the replies, for your own benefit. in the game, you will switch in matchmaking, gaining a point for each tier that you clear.
I just want to add that there will be 3 phases available to edit, I don't think it goes to five. Also, the different variations that can be set up for each phase are: Territories (like in Boneyard and The Spire), CTF (stealing the core), and Assault.
Wow that was nice (and I didn't notice it at first) I was referring to being done answering some little question someone asked in a post, and being entirely focused towards the OP after that. Now back to stuff about invasion. It's not just that the team is better, but the defenders are less prepared to fend off the attackers if they move to the second objective quickly. Even if the second objective might be greatly in favor of the defenders, if both teams stopped to fight, the attackers have a quick chance to run in and take the objective before the defenders get settled in.
Oops. I apologize for misunderstanding, pyro6666. Also, this conversation is pretty useful to me. If I can get into a place where I can orchestrate big-team-battle custom games, I'll need to use some of this knowledge. Thanks again for posting, redearth.
Omg to much reading for this early in the morning. I read a thread like this on Bungie.net that said each round the attackers should have a 80% chance at victory. But here's my view on it, In the Beta we had one invasion game and I'll give you my stats off over 200games of it, Very rough estimates:Out of 200 games: First Round attackers won 80% of the time, 2nd Round attackers wont 90% of the time, Last round attackers won 50% of the time.(excluding tank over core games >) My opinion if the teams are even and fairly good teams, First Round Attackers lose 95% of the time, 2nd Round Attackers win 70% of the time, last round attacks win 30% of the time.(this is for the one level we had on the beta) But for actually what I think should be the % should be 1stA60%-D40% 2ndA60-D40% 3rd50%-50% So its a fair chance for either team to win but attacking should get a slight advantage in the first couple of rounds. You realize that Defenders can only get 1 point and then they win the game.