# Xpovos' Blog - Jul to Sep 17 (89 followers)

Aug

18

18

###### Croaker

I promised another Leap Frog update blog with graphs, so let's go.

As of this writing, we have 17 days of Leap Frog done. That has allowed us to watch the traditional exponential decay patterns establish themselves and to see in two different periods how the increased difficulty of adding a bonus achievement each week is changing the dynamic. The simple answer is pretty substantially. The first day of each new week, the first day that there is another achievement added has a dramatically larger impact on the number of croakers than just increasing the ratio. Day 8's drop was 91, compared with a total of 227 for the rest of the week. Day 15's drop was 61, ~50% higher than either of the days that has come since.

But these spikes are becoming less dramatic. 91 is a much bigger spike from 53 (Day9's drop) in terms of percentage than Day 16's drop. The exponential decays are becoming less spiky and likely converging.

I plugged the data into Excel, per usual and got our first graph using the built-in linear regression functionality. Here's what it spits out.

For those looking for some refreshers on what some of this means, check out my posts from Leap Frog 1: Xpovos' blog post - mTAhlete and Xpovos' blog post - LeapFrog: Croaked. So, our R^2 is looking pretty solid at 98%, so let's evaluate for 1. That is, how many days (x) do we need to get a value of 1 (y) for the sole survivor.

~86.8. Huuh. So basically we'd expect if the progression holds up that Leap Frog will end with a single survivor on day 87. The poor sucker who wins this will have earned on the day before 13 different achievements each with a ratio of 18.2 or higher. That seems improbable. I think in fact that our linear regression is inadequate. Excel is a good tool, but this is not the program's strong suit. Let's try a better regression analysis tool and see if we can't get a more accurate formula to evaluate.

Another way of trying to calculate exponential decay is to look at the half-life. That is, how long does it take 50% of what is remaining to turn into something else. In this case, how many days does it take for 50% of our frogs to croak? With 1759* frogs at the start, we hit our first day with less than 50% (<880) on Day 7 (half-life of 6-7 days). We're down to under a quarter now, so we get to check our math. Our first day with less than 25% of our original group (<440) was Day 16. So one half-life was 6-7 days and two half-lifes was 15-16 days. Therefore, we can estimate that our half-life is probably pretty close to 7 days, perhaps a touch over.

Next, how many half-lives do you need for Valve to release Half-Life 3? Wait, no. How many half-lives do you need for 1759 to croak down to 1?

Step one: Decay constant

But isn't that still implausbile? There are only about 200 achievements total that could be unlocked for 16.0 or better, and likely some of them will have been used even to get to that point?

Certainly. But this has always just been about random speculation. I make no assertions that the math is genuinely predicting anything. I just point out that the exponential decay model fits pretty well and predicts a much longer contest than we are currently expecting. This outpaces even my hearty 40-60 day prediction from a while back. And the fact is that math never lies. We're going to have to see a change from this pattern of decay (more decay faster as we accelerate in difficulty) or we are going to see a lengthy period of hopping.

*1759 is our current count of entrants. Due to some technical glitches we actually added contestants since the contest started and I ran my first set of numbers in this blog: Xpovos' blog post - 1758 Men Enter; 373 Don't Even Try. That's why the numbers don't match up perfectly. But all of the math in this blog is based on 1759 initial starters.

As of this writing, we have 17 days of Leap Frog done. That has allowed us to watch the traditional exponential decay patterns establish themselves and to see in two different periods how the increased difficulty of adding a bonus achievement each week is changing the dynamic. The simple answer is pretty substantially. The first day of each new week, the first day that there is another achievement added has a dramatically larger impact on the number of croakers than just increasing the ratio. Day 8's drop was 91, compared with a total of 227 for the rest of the week. Day 15's drop was 61, ~50% higher than either of the days that has come since.

But these spikes are becoming less dramatic. 91 is a much bigger spike from 53 (Day9's drop) in terms of percentage than Day 16's drop. The exponential decays are becoming less spiky and likely converging.

I plugged the data into Excel, per usual and got our first graph using the built-in linear regression functionality. Here's what it spits out.

For those looking for some refreshers on what some of this means, check out my posts from Leap Frog 1: Xpovos' blog post - mTAhlete and Xpovos' blog post - LeapFrog: Croaked. So, our R^2 is looking pretty solid at 98%, so let's evaluate for 1. That is, how many days (x) do we need to get a value of 1 (y) for the sole survivor.

~86.8. Huuh. So basically we'd expect if the progression holds up that Leap Frog will end with a single survivor on day 87. The poor sucker who wins this will have earned on the day before 13 different achievements each with a ratio of 18.2 or higher. That seems improbable. I think in fact that our linear regression is inadequate. Excel is a good tool, but this is not the program's strong suit. Let's try a better regression analysis tool and see if we can't get a more accurate formula to evaluate.

Another way of trying to calculate exponential decay is to look at the half-life. That is, how long does it take 50% of what is remaining to turn into something else. In this case, how many days does it take for 50% of our frogs to croak? With 1759* frogs at the start, we hit our first day with less than 50% (<880) on Day 7 (half-life of 6-7 days). We're down to under a quarter now, so we get to check our math. Our first day with less than 25% of our original group (<440) was Day 16. So one half-life was 6-7 days and two half-lifes was 15-16 days. Therefore, we can estimate that our half-life is probably pretty close to 7 days, perhaps a touch over.

Next, how many half-lives do you need for Valve to release Half-Life 3? Wait, no. How many half-lives do you need for 1759 to croak down to 1?

Step one: Decay constant

ln(Nt/N0)=-kt

ln(1/2)=-k(7d)

-0.693=-k(7d)

k=0.099d

Step two: Back to the beginning with the decay constantln(1/2)=-k(7d)

-0.693=-k(7d)

k=0.099d

ln(Nt/N0)=-kt

ln(1/1759)=-0.099d(t)

-7.4725=-0.099d(t)

t=75.48d

So, with this half-life estimation path we get a contest that ends after 76 days. Despite being "only" 10 or 11 days shorter than the previous estimate, it becomes a lot simpler to hypothesize. Now the winner wins on only 10 achievements each at 16.0 ratio each. Still brutal, but nowhere near as bad.ln(1/1759)=-0.099d(t)

-7.4725=-0.099d(t)

t=75.48d

But isn't that still implausbile? There are only about 200 achievements total that could be unlocked for 16.0 or better, and likely some of them will have been used even to get to that point?

Certainly. But this has always just been about random speculation. I make no assertions that the math is genuinely predicting anything. I just point out that the exponential decay model fits pretty well and predicts a much longer contest than we are currently expecting. This outpaces even my hearty 40-60 day prediction from a while back. And the fact is that math never lies. We're going to have to see a change from this pattern of decay (more decay faster as we accelerate in difficulty) or we are going to see a lengthy period of hopping.

*1759 is our current count of entrants. Due to some technical glitches we actually added contestants since the contest started and I ran my first set of numbers in this blog: Xpovos' blog post - 1758 Men Enter; 373 Don't Even Try. That's why the numbers don't match up perfectly. But all of the math in this blog is based on 1759 initial starters.

Posted by Xpovos on 18 August 17 at 18:45
| Last edited on 18 August 17 at 23:11 | There are 4 comments on this blog post - Please log in to comment on this blog.

Aug

15

15

###### Fool's Gold; Fable Fortune

The news these days is coming fast and furious. Free-to-Play Collectible Card games are the wave of the future. The most recent contribution seems to be coming from F2P MOBA, Smite:

But that's just the latest announcement. Already in existence, we have the king of the hill, Hearthstone, though that it is not on console, and the very near to release

While there is certainly plenty of room for complaining about the oversaturation of the market with this type of game, as the genre is more interesting to me than most of the others that have gone this route (bald space marine on brown, anthropomorphic 3D platformer, MOBA, etc.) I will happily be the one to fall on the sword of checking them all out.

So, how does Fable Fortune hold up? It's in Game Preview, but I was still able to stream about an hour's worth of gameplay last night with Des.

We covered the pitfalls of this kind of "me too" game design, the inherent perils of a purely online digital collection game backed by real money, and even a little bit of the mechanics of the game. Along the way we had some interesting conversation diversions into game bugginess, how that can and should affect ratings, and of course, Isaac Newton, because nerds talking about nerdy subjects is our brand.

Further reading on the F2P CCG genre explosion:

Frankly, this list could go on a whole lot longer. There are so many and most of them will fail, even most on this list will fail. Magic Duels support is ending. If God is good, Lies of Astaroth will fail soon enough too. While a diverse marketplace is good for games, at the end, there can only be so many top-level brands that can survive, even if the genre is popular. Look at all of the shooters that were made trying to emulate the successes of Halo, Gears, and CoD. While there are some iconic games, mostly it'll result in just a handful of successful brands and a lot of trash. Hearthstone has established itself as the premier digital-only brand for CCG. Magic will always have a place in this ecosystem, even if they continue to hamstring their digital efforts. With a genre that is going to be less popular than shooters, how much room could there be left for new brands?

Finally, just a personal note that today will be my last day in attempting to Leap Frog. I've been contemplating letting it go for a few days now, but today will be my last effort for sure, if I even make it. I wanted to get to today because I felt 3+ and 3.8 was a fine challenge for me; one I can certainly do. Mostly today is just about proving to myself that I

__Hand of the Gods: SMITE Tactics Announced for Consoles__.But that's just the latest announcement. Already in existence, we have the king of the hill, Hearthstone, though that it is not on console, and the very near to release

**Gwent: The Witcher Card Game**. And not to be forgotten in the heap is last night's stream target:**Fable Fortune**While there is certainly plenty of room for complaining about the oversaturation of the market with this type of game, as the genre is more interesting to me than most of the others that have gone this route (bald space marine on brown, anthropomorphic 3D platformer, MOBA, etc.) I will happily be the one to fall on the sword of checking them all out.

So, how does Fable Fortune hold up? It's in Game Preview, but I was still able to stream about an hour's worth of gameplay last night with Des.

We covered the pitfalls of this kind of "me too" game design, the inherent perils of a purely online digital collection game backed by real money, and even a little bit of the mechanics of the game. Along the way we had some interesting conversation diversions into game bugginess, how that can and should affect ratings, and of course, Isaac Newton, because nerds talking about nerdy subjects is our brand.

Further reading on the F2P CCG genre explosion:

**Magic Duels****Lies of Astaroth**__Duelyst____Faeria____Shadowverse____Scrolls__This Mojang F2P CCG got them a lawsuit from Bethesda for daring to use the word "Scrolls" in their name. When that failed, Bethesda made their own F2P CCG:__Elder Scrolls: Legends__Frankly, this list could go on a whole lot longer. There are so many and most of them will fail, even most on this list will fail. Magic Duels support is ending. If God is good, Lies of Astaroth will fail soon enough too. While a diverse marketplace is good for games, at the end, there can only be so many top-level brands that can survive, even if the genre is popular. Look at all of the shooters that were made trying to emulate the successes of Halo, Gears, and CoD. While there are some iconic games, mostly it'll result in just a handful of successful brands and a lot of trash. Hearthstone has established itself as the premier digital-only brand for CCG. Magic will always have a place in this ecosystem, even if they continue to hamstring their digital efforts. With a genre that is going to be less popular than shooters, how much room could there be left for new brands?

Finally, just a personal note that today will be my last day in attempting to Leap Frog. I've been contemplating letting it go for a few days now, but today will be my last effort for sure, if I even make it. I wanted to get to today because I felt 3+ and 3.8 was a fine challenge for me; one I can certainly do. Mostly today is just about proving to myself that I

*could*go on for another week if I really wanted to... but I genuinely don't. Leap Frog is a fine contest and it has gotten me to do some things I have put off for too long, but it doesn't motivate me the way some other contests do. Besides, my "vacation" ends today so it's back to work for me which means far less time to earn these high ratio achievements. Good luck to everyone left leaping. I hope you find a pot of gold at the end of your parabolic hops.
Aug

11

11

###### Game Theory

It likely surprises no one that I am quite the fan of game theory. For those who need a quick refresher, game theory is a study of a specific set of games. The most common example is the classic "Prisoner's Dilemma" and it's many variants. A quick aside, I recently had the experience of coming at the etymology of the word dilemma through an odd back channel. It was amazing. If you like words, I recommend you look it up yourself.

Back to the theory. The Prisoner's Dilemma is a well-known problem and it is "solved" in that the optimal strategies are known. But that does not mean that everyone knows the problem, or the optimal solutions, and the problem of the dilemma is that if you are playing with uneducated, untrustworthy, unreasonable, or chaotic players, the optimal solutions can get you killed. Particularly if you only get to play once.

Political Science, one of my passions, spends what is probably far too much time looking at the Prisoner's Dilemma. When trying to understand rational actions by political actors, the dilemma is often used as a stand-in. Economics, another passion, does as well. So I end up coming at the dilemma from a lot of different perspectives in my pursuit of education.

But treating the dilemma as a political quandary is the case with a web-game I recently came across.

I recommend clicking through on the link. It says it takes half an hour to play, but I was done in ten minutes. I did then go on to spend another ten minutes playing around in the sandbox mode.

Someone less familiar with the material could easily spend a ton of time here, and gain a lot of insights, it is a well-programmed time-waster. The game mechanics are solid and fun to play with and it does a good job of teaching the basics.

Ultimately, though, it does fall a little short. I think the point that the author is trying to make about "life in general" is perhaps a little lost. Political scientists do love to think they have the solutions to all of life's problems; or at least the correct outline and definition of the problems.

However, life is not as simple as the Prisoner's Dilemma. And even this web game shows that.

But for a game without achievements, it's a good way to spend some time.

Back to the theory. The Prisoner's Dilemma is a well-known problem and it is "solved" in that the optimal strategies are known. But that does not mean that everyone knows the problem, or the optimal solutions, and the problem of the dilemma is that if you are playing with uneducated, untrustworthy, unreasonable, or chaotic players, the optimal solutions can get you killed. Particularly if you only get to play once.

Political Science, one of my passions, spends what is probably far too much time looking at the Prisoner's Dilemma. When trying to understand rational actions by political actors, the dilemma is often used as a stand-in. Economics, another passion, does as well. So I end up coming at the dilemma from a lot of different perspectives in my pursuit of education.

But treating the dilemma as a political quandary is the case with a web-game I recently came across.

I recommend clicking through on the link. It says it takes half an hour to play, but I was done in ten minutes. I did then go on to spend another ten minutes playing around in the sandbox mode.

Someone less familiar with the material could easily spend a ton of time here, and gain a lot of insights, it is a well-programmed time-waster. The game mechanics are solid and fun to play with and it does a good job of teaching the basics.

Ultimately, though, it does fall a little short. I think the point that the author is trying to make about "life in general" is perhaps a little lost. Political scientists do love to think they have the solutions to all of life's problems; or at least the correct outline and definition of the problems.

However, life is not as simple as the Prisoner's Dilemma. And even this web game shows that.

But for a game without achievements, it's a good way to spend some time.

Aug

09

09

###### Gin Rummy and Sexy Shelob

Things have been a little busy here of late, but not so busy that I couldn't take some time to stream with my friend Des again. Last night we cracked open

In large part because Des and I got into some heated discussion over the issues of the day, the entire hour was spent playing a single game of "Oklahoma" Gin Rummy, which was different (but not too different) from the game I remembered playing with my grandparents. As always, the game itself is just the background noise as Des and I discuss the issues of the day. Today we talked about:

Google's termination of a man for a misogynistic memorandum.

Shadow of Mordor's sequel, sexy Shelob and micro-transactions.

Disney and Netflix

and the usual suspects.

I also did a better job of keeping it at an hour this week.

**Gin Rummy**. With a name like that you know pretty much what you're getting. Sierra pushed out a quick and easy card game and was charging a full Arcade title price. That's why I hadn't bought it before. With the Backward Compatability Sale of a while back, though, the price reduction was sufficient to entice me.In large part because Des and I got into some heated discussion over the issues of the day, the entire hour was spent playing a single game of "Oklahoma" Gin Rummy, which was different (but not too different) from the game I remembered playing with my grandparents. As always, the game itself is just the background noise as Des and I discuss the issues of the day. Today we talked about:

Google's termination of a man for a misogynistic memorandum.

Shadow of Mordor's sequel, sexy Shelob and micro-transactions.

Disney and Netflix

and the usual suspects.

I also did a better job of keeping it at an hour this week.

Posted by Xpovos on 09 August 17 at 16:45
| There are no comments on this blog - Please log in to comment on this blog.

Aug

02

02

###### 1758 Men Enter; 373 Don't Even Try

It is Leap Frog time again. Every time the contest gets run, the rules get zanier in an effort to try to actually find a winner. For those unfamiliar with the history, the first version was just a run of achievements. 1 achievement on Day 1, 10 achievements on Day 10, etc. I projected that the contest would go an insane 74 days, with the winning contestant having earned a ridiculous 2775 (minimum) achievements over the contest period of about two and a half months. In fact, the contest ran even longer and the top two battled out to 100 days which required IrishWarrior022 to earn a minimum of 5050 achievements in a shade over three months. Let that sink in for a moment. For reference, Irish would go on to score roughly that number again in the entirety of 2016. So in three months of fevered achievement-hunting, he matched his next year, by that measure.

The good folks running the competition had not expected it to last that long, nor to be as draining a resource on the folks actually competing. Both Irish and his runner up, Emerald Axer admitted to being pushed to a kind of breaking point. The competitions here are intense, but they are supposed to be fun. We have some very competitive people, though, so it was clear that a better answer was necessary. One that was tougher, to end it faster--before it became a drain on people's health and well-being.

So Leap Frog 2 changed the goal to ratios. Since ratios are not a real indication of difficulty, this would let people play to very high points without necessarily spending 20 hours of the day grinding achievements. Instead, sometimes they just spent 20 hours of the day grinding a single achievement. And in fact the proposed solution worked even less well in terms of ending the contest faster, as new content keeps being released and new content is always at a stupidly high ratio point for the first day or two--people could stay in as long as they kept getting the newest content. Eventually, a gentleman's agreement came about and this contest fizzled out after something in the 115-120 day range, depending on how you figure the agreement played out. Either way, for all the efforts to make the contest harder and end sooner, the contest actually ran 15% longer!

This brings us to Leap Frog 3, and what is sure to be a longer contest result than any of us expects. In incorporates elements of both previous elimination schemes to make it seemingly impossible to achieve after a certain point. But I have long since learned to never doubt the dedication of the truly intense members of this community. Using some of the same mathematical approaches to the length of this contest, I came up with an answer of 32 days. I suspect we will actually run longer than that. The reason lies in my title. Right now my only way to predict the future eliminations is based on current eliminations. After one day, that's hardly going to produce accurate results.

1758 individuals registered for Leap Frog 3. First, I'll note that is a significant decrease from Leap Frog 1's 2000+ or even Leap Frog 2's 1800+. Second, just as in the previous years, there are a significant number of people who didn't earn even a single achievement. That is all that has been required each time through. 1 achievement for Day 1. 1 achievement at 1.0 ratio for Day one. It doesn't get any lower a bar. Apparently, the only lower bar than finishing Day 1 is registering for the contest.

I am being a little unfair. Of the 373 who entered and then sat down to watch other people play, there are some with valid reasons. Even, "I joined to increase my site participating badge" may be a reason for some of them. For others, the start was far enough removed from the registration that they forgot they needed an achievement "today". Still more had something come up in their real life. Maybe they'd have gotten to Day 3 or 4 otherwise, but stuff happens.

These people being eliminated now have nothing in common with the ultra-fit achievement competitors who will emerge and be in the running to take the final prize. But they are still the ones who I have data on to do the math and make any kind of prediction as to how far we will go.

If my first prediction is right at 32 days, the winner will need 5 different achievements each at 7.2 or higher to win. Yeah... that seems pretty hard. But I think we'll see at least 3 or 4 still at that point. As long as games like

The good folks running the competition had not expected it to last that long, nor to be as draining a resource on the folks actually competing. Both Irish and his runner up, Emerald Axer admitted to being pushed to a kind of breaking point. The competitions here are intense, but they are supposed to be fun. We have some very competitive people, though, so it was clear that a better answer was necessary. One that was tougher, to end it faster--before it became a drain on people's health and well-being.

So Leap Frog 2 changed the goal to ratios. Since ratios are not a real indication of difficulty, this would let people play to very high points without necessarily spending 20 hours of the day grinding achievements. Instead, sometimes they just spent 20 hours of the day grinding a single achievement. And in fact the proposed solution worked even less well in terms of ending the contest faster, as new content keeps being released and new content is always at a stupidly high ratio point for the first day or two--people could stay in as long as they kept getting the newest content. Eventually, a gentleman's agreement came about and this contest fizzled out after something in the 115-120 day range, depending on how you figure the agreement played out. Either way, for all the efforts to make the contest harder and end sooner, the contest actually ran 15% longer!

This brings us to Leap Frog 3, and what is sure to be a longer contest result than any of us expects. In incorporates elements of both previous elimination schemes to make it seemingly impossible to achieve after a certain point. But I have long since learned to never doubt the dedication of the truly intense members of this community. Using some of the same mathematical approaches to the length of this contest, I came up with an answer of 32 days. I suspect we will actually run longer than that. The reason lies in my title. Right now my only way to predict the future eliminations is based on current eliminations. After one day, that's hardly going to produce accurate results.

1758 individuals registered for Leap Frog 3. First, I'll note that is a significant decrease from Leap Frog 1's 2000+ or even Leap Frog 2's 1800+. Second, just as in the previous years, there are a significant number of people who didn't earn even a single achievement. That is all that has been required each time through. 1 achievement for Day 1. 1 achievement at 1.0 ratio for Day one. It doesn't get any lower a bar. Apparently, the only lower bar than finishing Day 1 is registering for the contest.

I am being a little unfair. Of the 373 who entered and then sat down to watch other people play, there are some with valid reasons. Even, "I joined to increase my site participating badge" may be a reason for some of them. For others, the start was far enough removed from the registration that they forgot they needed an achievement "today". Still more had something come up in their real life. Maybe they'd have gotten to Day 3 or 4 otherwise, but stuff happens.

These people being eliminated now have nothing in common with the ultra-fit achievement competitors who will emerge and be in the running to take the final prize. But they are still the ones who I have data on to do the math and make any kind of prediction as to how far we will go.

If my first prediction is right at 32 days, the winner will need 5 different achievements each at 7.2 or higher to win. Yeah... that seems pretty hard. But I think we'll see at least 3 or 4 still at that point. As long as games like

**Rare Replay**exist--with plenty of pretty easy high ratio achievements--or even worse games like**Killer Instinct**, and**SMITE**, which continue to drop new and readily obtainable for deep content players high ratio achievements, this contest has the potential to run long. It seems impossible to go 100 days yet again (Day 100 requirements: 15 achievements at 20.8 ratio each) and I am not going to predict a contest that long (I think 40-60 days is the actual end point, on a gut level) but I have never been disappointed by counting on some intense competitive streaks to push these contests beyond all reasonable limits.
Posted by Xpovos on 02 August 17 at 19:34
| There are 22 comments on this blog post - Please log in to comment on this blog.