Off-season: Explore the unlocked site! Projections reflect re-calculations of 2022, based on end-of-season knowledge.

Survivor Pool Strategy

New this year, I am using my weekly game score forecasting models for a new purpose: generating advice for Survivor Pools.

What’s different about the Subvertadown Strategy?

Main features:

  • The main input is from my own forecasting models for game scores

  • My algorithm optimizes the expectancy value of #weeks survival (“expected longevity”).

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

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

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

I do not optimize the sum of weekly probabilities.

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.

Suppose you make it to the last 3 games, and you have two path options: games with win probabilities of {71%, 71%, 71%} or {60%, 70%, 80%}. The first set has a higher sum, but the first option yields a higher product— i.e. the chance of winning them all. (When more than 3 games are remaining, the distinction between sum vs. product becomes even more pronounced.)

But I also reject chasing the this multiplicative probability. The odds of winning all is astonishingly low: less than 0.01%. This is contrary to many people’s expectations about the likelihood of wins: those 80% games usually feel like a sure thing. It doesn’t make 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.

Sequence matters for survival

In the above, I rejected the set {60%, 70%, 80%}. In fact, this example should be rejected even more strongly if it were meant as ordered (60%, 70%, 80%). A first game with lower probability (60%) decreases the expectancy value of #weeks survived. You can read about how to actually calculate that number in this article. The option (70%, 70%, 70%) makes this expectancy value 1.2 weeks; but the option (60%, 70%, 80%) gives 1.0 week.

This effect of good-ordering even overrides the effect discussed in the last section (preferring to multiply instead of sum). You can easily see how strong the effect of ordering is if you look at the reversed-order option (80%, 70%, 60%): expected longevity becomes 1.35 weeks, which is higher than 1.0 weeks and 1.2 weeks. I.e. we prefer (80%, 70%, 60%) above (60%, 70%, 80%). This reversal demonstrates that it can be logical to reduce your probability of “winning all weeks” (as seen from the start) in favor of increasing expected longevity.

Optimizing Expected Longevity

The Subvertadown approach is focused on optimizing this “expected longevity” (the expectancy value of # weeks survival) and re-computing it each week. By optimizing this parameter, earlier weeks naturally a higher weighting— but we prioritize an early win only if the early “good pick” does not prevent a later “great pick”. In fact, with a bit of analysis, it seems clear that the strategic difference between small pools and large pools is… somewhat minor. This is because the typical longevity expectation is 4 weeks— optimally starting the week at 5 and decreasing to 3 by end of season. So it might be fair to consider “winning the long run” equal to “winning a series of short-runs”.

Weeks further in the future are less certain

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.

Increasing the number of different pathways

To counteract the probability of losing each week, a theoretical “cheat” is 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. But "maintaining 2” really means you will require many more, because you should expect 8 total losses along the way. You’d need one path to diverge every 3 weeks, which 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 require 140 paths from the start.

Regardless of your diversification strategy, I take a practical approach for displaying advice on the website. The goals are:

  1. to display 3 picks each week

  2. to make sure they correspond to 3 distinct pathways, and

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

You can read more how this work here. Practically, I will highlight 1 principle pathway that gets priority picks, 1 alternate pathway that will be nearly as good, and 1 back-up. Each of these 3 pathways will come with 2 recommended picks for the current week: one best pick, and one alternative pick. 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 by now you may realize that it is no guarantee! There is still some small chance of failing before the end of season.