So by now, I’d be surprised if anyone hear hasn’t heard phrases like “sim gonna sim” or “ the sim screwed us”. I went with less colorful words for the latter, but you can use your imagination to spice it up if you like. After NOLA lost again last night, I was at the point where I just couldn’t comprehend what the hell is going on anymore. I mean probability is a fickle thing. It doesn’t truly feel like we can understand it one game at a time. It really shines when you play it out over the course of hundreds and thousands of times. That’s when it truly represents a more accurate number. Still, repeatedly losing games where your chances are much better than a coin flip sting. Doing so over and over and over starts to feel like a big f you. I decided I wanted to see if I could put together something that reflected what the odds were of the loses we’ve had this season. I’m no math wiz and haven’t taken a class in about four years now, so some of what I did might be wonky or not totally accurate. Still, I think the gist of what I was going for should come through.
First, let’s start with what we were testing at each game. This is not a 100% accurate measure of if you will win or not, but I don’t think there is any better way to measure it so that’s what I’m going with. Over our 5 loses, we tested at a win percentage of 82, 87.4, 69,5, 40 and 60. This is not necessarily in the correct order. Also, the 40 and 60 are rough estimate. They could be plus or a minus 1 or 2%, so fairly accurate.
I set up a number generator with a range of 1 through 100. I then ran it 100 times for each of the five games we lost. If a number came up that was less than our chance of losing, that would count as a loss. For example, with an 82% chance to win, any number that was 18 or less would count as a loss. In theory, we should expect there to be 82 results that would lead to a win and 18 results that would justify a loss. You might be asking, “but what about a tie?”. Ah, you are correct. I didn’t have a great way to represent ties. In truth, they happen so infrequently that I think we can largely ignore them altogether. Sidenote: I’m somewhat convinced ties cause the index to breakdown and we have to resim them anyways.
Let’s take a look at each of the five games. I marked down each score that would represent a loss. The only thing to mention as far as possible tricky outcomes was our third game where we tested at 69.5% (nice…kinda). Three 31s came up, which fall right in an awkward spot. If it wasn’t a half a percent, it would have been simple enough. I decided to count two out of the three as a loss to not inflate the winning percentage. Over the five sets of one hundred “simulations”, we came out with a net of +5. With a sample size of 500, that means we were within 1% accuracy of what we should expect.
![[Image: u7q5D9N.png]](https://i.imgur.com/u7q5D9N.png)
Our calculated win percentage came out fairly close to the tested win percentage, which is what we would expect to see. Now let’s dive in to see the odds of losing all these games. I decided to run two different results. The first include all five games, the second excludes the game where we were favored to lose. While it makes to sense to look at all five losses, it seemed worth looking at the numbers for the four games we were favored. After all, it isn’t crazy to see expect a loss when you aren’t favored to win right…right?!?!
To calculate the odds of losing all the games combined, we multiply the percentage of each loss. For example, the odds of us losing the first two games would be .09 x .11. That comes out to 0.0099, or just under 1%. When doing that for all five games (based on calculated win %), we wound up at a 0.00083 chance of losing every game. To put that number into a slightly better perspective, you could run the sim 1000 times and only expect all those losses to happen 8 times. If you are curious about what it looks like for the tested instead of calculated, it comes out to 0.00166. Now let’s see if it changes much by removing the game we could have expected to lose. The results came out to 0.00138 (0.00277 for tested), which is slightly less impressive than before. It looks like the more games you add, almost no matter what the chance of winning, it will make things less likely to come about. Taking that into consideration, maybe it isn’t the most accurate way to try and say how unlucky the sim has been to us. On the one hand, it does show the extreme unlikelyhood of losing them all. On the other hand, any team could probably make the argument that all of their losses happening again are unlikely. That’s a fair rebuttal. Without knowing every team’s % that they tested at, I can’t run the numbers. I’ll take a slight turn then.
What are the odds that we would lose two of those games in any combination? This might be understating how unlucky I think we’ve been. It does help balance out the idea that the more games included, the less likely it would happen again. Let take a peek. (I won’t tell you how many boxes I originally thought I needed because woof)
![[Image: rKHYpcI.png]](https://i.imgur.com/rKHYpcI.png)
I found this really interesting. Even the worst pair of games you could look at, the outcome would theoretically only happen roughly 25% of the time. Okay that’s fair, these things happen. Seeing it happen over and over again is where it starts to hurt. I averaged out the results for all combinations. For calculated, it wound up at 9.7% likely, where as tested was 8.8%. Those numbers are quite elevated too, considering the fact it also has the game we could have expected to lose. For reference, that came out to just over 6.3%. We see a majority of combinations come in at around 5% or less. The really drastic combo of course is the two games where we were so highly favored, coming in at around 1-2%.
Thanks for following along to this point. So I guess the big question is: what did we learn from all this? Probably not much. Pretty much everyone is convinced the sim is against them at some point in time (expect the evil Otterman Empire I’d wager). You can bend numbers to reflect your viewpoint too, so I’m sure I’ve done that some. I was more so curious about just how truly unlucky my team seems to be this season and I think this has at least given me so glimmer of hope in that regard.
If this needs to be under statistical analysis, my apologies. I didn't feel like I had enough graphs and math work to justify it there.
First, let’s start with what we were testing at each game. This is not a 100% accurate measure of if you will win or not, but I don’t think there is any better way to measure it so that’s what I’m going with. Over our 5 loses, we tested at a win percentage of 82, 87.4, 69,5, 40 and 60. This is not necessarily in the correct order. Also, the 40 and 60 are rough estimate. They could be plus or a minus 1 or 2%, so fairly accurate.
I set up a number generator with a range of 1 through 100. I then ran it 100 times for each of the five games we lost. If a number came up that was less than our chance of losing, that would count as a loss. For example, with an 82% chance to win, any number that was 18 or less would count as a loss. In theory, we should expect there to be 82 results that would lead to a win and 18 results that would justify a loss. You might be asking, “but what about a tie?”. Ah, you are correct. I didn’t have a great way to represent ties. In truth, they happen so infrequently that I think we can largely ignore them altogether. Sidenote: I’m somewhat convinced ties cause the index to breakdown and we have to resim them anyways.
Let’s take a look at each of the five games. I marked down each score that would represent a loss. The only thing to mention as far as possible tricky outcomes was our third game where we tested at 69.5% (nice…kinda). Three 31s came up, which fall right in an awkward spot. If it wasn’t a half a percent, it would have been simple enough. I decided to count two out of the three as a loss to not inflate the winning percentage. Over the five sets of one hundred “simulations”, we came out with a net of +5. With a sample size of 500, that means we were within 1% accuracy of what we should expect.
Our calculated win percentage came out fairly close to the tested win percentage, which is what we would expect to see. Now let’s dive in to see the odds of losing all these games. I decided to run two different results. The first include all five games, the second excludes the game where we were favored to lose. While it makes to sense to look at all five losses, it seemed worth looking at the numbers for the four games we were favored. After all, it isn’t crazy to see expect a loss when you aren’t favored to win right…right?!?!
To calculate the odds of losing all the games combined, we multiply the percentage of each loss. For example, the odds of us losing the first two games would be .09 x .11. That comes out to 0.0099, or just under 1%. When doing that for all five games (based on calculated win %), we wound up at a 0.00083 chance of losing every game. To put that number into a slightly better perspective, you could run the sim 1000 times and only expect all those losses to happen 8 times. If you are curious about what it looks like for the tested instead of calculated, it comes out to 0.00166. Now let’s see if it changes much by removing the game we could have expected to lose. The results came out to 0.00138 (0.00277 for tested), which is slightly less impressive than before. It looks like the more games you add, almost no matter what the chance of winning, it will make things less likely to come about. Taking that into consideration, maybe it isn’t the most accurate way to try and say how unlucky the sim has been to us. On the one hand, it does show the extreme unlikelyhood of losing them all. On the other hand, any team could probably make the argument that all of their losses happening again are unlikely. That’s a fair rebuttal. Without knowing every team’s % that they tested at, I can’t run the numbers. I’ll take a slight turn then.
What are the odds that we would lose two of those games in any combination? This might be understating how unlucky I think we’ve been. It does help balance out the idea that the more games included, the less likely it would happen again. Let take a peek. (I won’t tell you how many boxes I originally thought I needed because woof)
I found this really interesting. Even the worst pair of games you could look at, the outcome would theoretically only happen roughly 25% of the time. Okay that’s fair, these things happen. Seeing it happen over and over again is where it starts to hurt. I averaged out the results for all combinations. For calculated, it wound up at 9.7% likely, where as tested was 8.8%. Those numbers are quite elevated too, considering the fact it also has the game we could have expected to lose. For reference, that came out to just over 6.3%. We see a majority of combinations come in at around 5% or less. The really drastic combo of course is the two games where we were so highly favored, coming in at around 1-2%.
Thanks for following along to this point. So I guess the big question is: what did we learn from all this? Probably not much. Pretty much everyone is convinced the sim is against them at some point in time (expect the evil Otterman Empire I’d wager). You can bend numbers to reflect your viewpoint too, so I’m sure I’ve done that some. I was more so curious about just how truly unlucky my team seems to be this season and I think this has at least given me so glimmer of hope in that regard.
If this needs to be under statistical analysis, my apologies. I didn't feel like I had enough graphs and math work to justify it there.
![[Image: rqph9tT.jpg]](https://i.imgur.com/rqph9tT.jpg)
![[Image: 6HEXEeb.png]](https://i.imgur.com/6HEXEeb.png)
![[Image: unknown.png]](https://cdn.discordapp.com/attachments/735279101711220767/761677188524277830/unknown.png)
![[Image: HtYhYYf.png]](https://i.imgur.com/HtYhYYf.png)
![[Image: 68.png]](https://cdn.discordapp.com/attachments/722696337912496132/759304283312881684/68.png)
![[Image: 018p.png]](https://i.postimg.cc/WbJGDCCK/018p.png)
![[Image: XSfVUgo.png]](https://i.imgur.com/XSfVUgo.png)
