By Subvertadown

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How to Use , Understanding Statistics , Survivor PoolsIn 2022, I started using my weekly game score forecasting models for a new purpose: generating advice for **Survivor Pools**.

Main features:

The main input is from my

**own forecasting models**for game scoresMy algorithm optimizes the

*expectancy value of #weeks survival*(“**expected longevity**”).Reasons elaborated below.

I give 3 picks, weekly, to assist decision making.

Each pick is attached to one of

**3 distinct pathway options**.There will always be an alternative pick.

FYI week 18 is not factored until we come to it.

The rest of this article explains why I chose the above key features.

If you are familiar with algorithms which optimize the season’s sum of weekly game probabilities, be aware I am not advocating that approach. One main reason is that the overall chance of “winning all” depends on the product (not sum) of probabilities.

It can be confusing, but let’s look at an example. Suppose you make it to the last 3 games, and you have two path options: games with win probabilities of {70%,70%,70%} or {60%, 70%, 80%}. The probability to “win it all”, for set {70%,70%,70%}, is the *product*, which is 34.3%. Meanwhile, the set {60%, 70%, 80%} has the same sum, but the product is only 33.6%. The drawback of summing gets even clearer if we consider more than 3 games.

But this simple idea of multiplying probabilities also something I reject. To begin with, the odds of winning all is astonishingly low: close to 0.01%. But more importantly, many of the candidate survivor paths have very close win-it-all probabilities. And it doesn’t make really much sense to obsess about the difference between an 0.005% and 0.006% path.

Other things matter more, as you will see outlined below.

The set I rejected above {60%, 70%, 80%} is even worse as an *ordered sequence *(60%, 70%, 80%). For Survivor strategy, (80%, 70%, 60%) would be much more favorable. That might even be intuitive to you: choosing the lower probability game first (60%) decreases the expectancy value of #weeks survived.

And it is this “# weeks survived” that we want to optimize at each present time. You can read about how to actually calculate that number in this article. As an example, a pathway option with (70%, 70%, 70%) makes this expectancy value 1.2 weeks; but the option (60%, 70%, 80%) gives 1.0 week. The reversed-order option (80%, 70%, 60%) is naturally even better: expected longevity becomes 1.35 weeks

This effect of good-ordering (to optimize longevity) even overrides a high mathematical product of probabilities. (And it definitely overrides summing.) In other words, it can be logical to reduce your probability of “winning all weeks” in favor of increasing **expected longevity**.

The Subvertadown approach is focused on optimizing this “expected longevity” (the expectancy value of # weeks survival). It must be re-computed each week to make the best series of future picks. By optimizing this parameter, earlier weeks naturally a higher weighting. Of course, we don’t prioritize getting an early win if it prevent a later “great pick”.

Note that others have suggested that the size of the Survivor pool should influence whether you take a great pick early. In fact, with a bit of analysis, it seems clear that there should not be much strategic difference between small pools and large pools. This is because the** typical longevity expectation is only 4 weeks**. When you expect your Survivor run to last only 3-5 weeks on average, it does not help to view the competition in large pools as lasting any differently. It might be fair to consider “winning the long run” equal to “winning a series of short-runs”.

There is another reason for weighting nearer-term weeks: future week outlooks are less certain. Especially as seen from the outset of pre-season. A future high probability game could end up missing key players when the time comes. Conversely, a new good option can suddenly appear in a future week, e.g. if there are injuries to the opposing team. This effect is not considered in the Subvertadown approach, but by optimizing for expected longevity, the later weeks are already less influential on the optimization.

To counteract the probability of losing each week, a theoretical “cheat” would be to **diversify**— to run parallel “do-over” pathways.

How many paths would be optimal? Mathematically, it turns out that, to promote a *50% chance of one path surviving to the end*, you should always maintain 2 active paths. However, maintaining “2” pathways would actually require beginning the season with many more. That’s because you should expect 8 total losses along the way (losses combined from the “2” paths). To counteract the effect of losses, you would need to prepare for a loss every 3 weeks by doubling each pathway (into a primary pathway and an alternative backup). Adding up all these pathways splittings would means **starting with about 70 bets** in week 1. If you would choose to maintain 3 paths instead of just 2, the survival probability would increase to 87%, and it would require 140 paths from the start.

Regardless of your diversification strategy, I take a practical approach for displaying advice on the website, based on the above logic.

The structure of the Survivor feature is to:

to display 3 picks each week

to make sure they correspond to 3 distinct pathways, and

always point out which alternative pick could be used for each path.

You can read more how this work here. Practically, I will highlight 3 primary pathways. The first pathway gets priority picks each week, but the other 2 will often be nearly as good (sometimes better depending on how the teams evolve). Each of these 3 pathways will additionally provide an alternative, making a total of 6 that get displayed. Should one of the main 3 paths get eliminated, I will substitute it with the alternative.

The purpose of doing this is to be able to continue advising a path for the season duration. However, from the above analysis, it should be clear there is no guarantee! There can still be some small chance of all pathways failing, before the end of season.

/Subvertadown

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