So the past few days I've been talking about how for Warlocks and Hunters, there really isn't that much of a chance for victory in the Guardian Games at this point. I've had some friends tell me that isn't true, but being the true Warlock I am I decided to prove them wrong!
So what did I do? I made two programs using recursive functions (i.e. functions that call themselves with updated data) in order to see the probability that each class would win the games. I included the possibilities of ties, although I'm not sure if Bungie allowed that. Maybe some other factor would split a tie? Who knows!
Anyways, The way I did this was through two different methods of 'victory'. Because the actual system to determine the overall winner is unknown, I made assumptions for two possible systems:
- All-or-Nothing: In this system, only the winner gets a point for the day. I believe this is the probable system, as only the victors are shown on the plaques in the main square, but who knows. The maximum point total possible is 28. (7 per week the first two weeks, 14 the last)
- Placement Tiers: In this system, each place is given a pre-defined number of points. I used 1st = 3, 2nd = 2, and 3rd = 1. The maximum point total possible is 84 (21 per week the first two weeks, 42 the last)
So, with this out of the way, let's move on to the current results.
Currently, Titans are in the lead (as everyone knows) with 8 first place wins, 1 second place entry, and 0 losses.
Hunters have 1 first place win, 1 second place win, and 7 losses. (Honestly, a little surprised by this)
Warlocks have 0 wins (sigh), 7 second place wins, and 2 losses. I would say something motivating, but instead of playing the actual event I made programs so I can't really say anything, now can I?
So what does this all mean? Well naturally as the programs have more concrete data the numbers will change. I created them to take in the current stats and then essentially create "timelines" of every possible scenario.
Eat your heart out Osiris.
The only time that the data stops short, is when it is impossible for other teams to win. This is when a team has over 50% of the points, as by that time it's impossible to beat them. For the All-or-Nothing system, this is 15 points. For the Tiered program, it is 43. It's best to add these earlier stops as it improves the recursive algorithm's efficiency since continuing those routes won't change the results.
Here are the probabilities that after today, April 30th, each class will win:
|Total Number of Outcomes:||364813||–|
|# of Titan Victories||296641||81.31|
|# of Warlock Victories||17097||4.69|
|# of Hunter Victories||27695||7.59|
|# of Titan/Warlock Ties||9072||2.49|
|# of Titan/Hunter Ties||13762||3.77|
|# of Warlock/Hunter Ties||546||0.15|
|# of Complete Ties|
As you can see, it is near impossible for Warlocks and Hunters to win at this point. It's possible, I want to stress that, but an 81% chance of victory? Yeah, that's pretty good. Also not gonna lie, kinda sad that there weren't any possible complete ties. My logic might be wrong on that, but I've double-checked and it seemed fine.
Alright, onto the tiered probability.
|Total Number of Outcomes:||945966||–|
|# of Titan Victories||702705||74.28|
|# of Warlock Victories||142678||15.08|
|# of Hunter Victories||51189||5.41|
|# of Titan/Warlock Ties||25807||2.73|
|# of Titan/Hunter Ties||8757||0.93|
|# of Warlock/Hunter Ties||2870||0.3|
|# of Complete Ties||11960||1.26|
For those curious, the reason the number of possible outcomes increased so much here is because in the All-Or-Nothing system, only 3 possible outcomes for each day could occur (each class achieving victory). In this system with accounting for 2nd place, 6 possible outcomes occur each day.
Titans still have the highest chance of winning with 74%, but Warlocks have a higher chance in this system due to getting 2nd so much. Also interestingly enough, this system allows for complete ties! I guess we passed that point in the All-Or-Nothing system.
So, why did I make this? I don't know, I'm a nerd and a Warlock on the inside. Plus I had some free time at work…
Anyways. I hope whoever reads this enjoys the numbers. I may post some updates in the future to reflect new probabilities. As we get closer to the end of the games, it'll become clearer who is going to win. If say Warlocks win all of next week, the numbers will change drastically! Titans haven't hit the magic 15 or 43 yet, so it's still up for grabs. I know a lot of us are tired of bounties and are taking a break from the game, but for those who are still playing or maybe just interesting in the standings, I hope that this helps!
Also. Warlocks. Please. I'm begging you. Turn in some medals. ;-;
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