Expected Value: What It Is & Why It Matters For Survivor Pool Picks
Expected Value is the measure by which we determine how valuable each survivor pick is, looking at just that week's info.
Eddie Vanderdoes leads the NFL in being positively EV (Photo by Daniel Dunn/Icon Sportswire)
Expected Value is one of the measures by which we evaluate each potential survivor pick. It compares the value of picking each team against all other potential options for that week. Expected value combines both win odds and pick popularity into one measure to compare the interplay of both.
The concept of expected value (also referred to as “EV”) considers all the potential outcomes of making a particular survivor pick. It goes beyond just taking the team with the best win odds. Avoiding popular picks is an important aspect of survivor strategy, but how do you know if the most popular choice in a given week has such high win odds that it is still the best choice or not? That’s where expected value comes in.
Every week is different, and the interplay of every potential result, and the amount of entries picking each team, along with the overall size of the pool, impacts the expected value of a selection.
Calculating Expected Value
Expected Value represents the average pot share expectation when considering all the possible outcomes of making a particular choice. Let’s walk through a really simple, one-game, example to start and then build from there to illustrate Expected Value.
A Simple Expected Value Exercise
Imagine a one-week contest where you must pick the outcome of just one game. The winner of the prize is then randomly drawn from all entries that pick the game result correctly. In this exercise you can pick either the Monstars or the Looney Tunes. The Monstars have win odds of 70%.
Let’s say that of every 100 entries, you know that 85% are picking the Monstars.
Conditional EV Explained
Before we go further into EV, we need to talk about conditional EV. Conditional EV is the expected value you get, IF a particular outcome (or set of outcomes) occurs.
For example, your expected value by picking the Monstars, IF the Monstars Win, is 1.18.
We get that from dividing the original number of total entries (100) by the number of remaining entries after a Monstars victory (85).
Conversely, IF the Monstars Lose, THEN your Conditional EV is 0.
Think of that Conditional EV this way. At the outset of the contest, your EV was 1.00. You had a 1% chance of winning in a pool with 100 entries. If you picked the Monstars, and IF the Monstars won, then your chances of winning would improve to 1.18%. 1.18% divided by 1% equals 1.18, meaning your chances of winning would be 1.18 times as high as they were before this game. That’s what Conditional EV represents — the impact that a certain pick and outcome would have in improving (or hurting) your chance of winning the pool.
Combining the Conditional EVs for the Overall Expected Value
So by picking the Monstars, you would have an expected share of 1.18 70% of the time, and 0.00 the other 30% of the time. That works out to an expected value of 0.82 on average.
By picking the Looney Tunes, on the other hand, you would have an expected share of 6.67 30% of the time, and 0.00 the other 70% of the time. That works out to an expected value of 2.00 on average.
The best choice here is pretty clear: you want the Looney Tunes if they are only being picked 15% of the time with 30% win odds. Yes, even though they are the underdog, the chances of success are higher by going to a random draw with far fewer entries.
To put it plainly, if you repeated this exact same contest many times, with the same teams, win odds, and pick rates, you would win more money over the long run if you picked the Looney Tunes every time.
Now Let’s Add Another Matchup
We walked through the previous example and how to determine EV step-by-step. But figuring out that the Looney Tunes were the better choice, despite having the worst win odds, was probably fairly evident to some of you by just comparing the differences between win odds and pick popularity.
But in survivor pools, you rarely see many true head-to-head situations — essentially just the Super Bowl. Figuring out the best EV becomes more difficult when you add more games and options.
Let’s add another matchup and look at a two-game, four-team example.
Gryffindor has 70% win odds against Ravenclaw. Slytherin has 60% win odds against Hufflepuff. You can pick just one of the four teams, and the same victory rules apply (your team must win, and you then must win a random draw against all other winners).
Let’s also say that the pick popularity of each is as follows:
- Gryffindor is being selected 50% of the time;
- Slytherin is being selected 30% of the time;
- Hufflepuff and Ravenclaw are each being selected 10% of the time.
Can you tell which selection has the highest EV?
Working Through the Conditional EVs in a Four-Team Combination
Instead of just one game result, we now have four potential combinations of results. The winners could be:
- Gryffindor and Slytherin (42% of the time)
- Gryffindor and Hufflepuff (28% of the time)
- Slytherin and Ravenclaw (18% of the time)
- Hufflepuff and Ravenclaw (12% of the time)
Let’s walk through just calculating Gryffindor’s EV with these outcomes. Here are the various odds of each outcome, number of surviving entries, and the Conditional EV for each possibility:
|Outcome||% Chance||Surviving Entry %||Conditional EV|
|Gryffindor Loss||30%||12% or 18%||0.00|
So, Gryffindor’s EV is 0.99. Meanwhile, using the same method, Hufflepuff comes in as the top EV at 1.07, with Ravenclaw just behind at 1.05, while Slytherin had the lowest EV, at 0.98. You might have also thought that Hufflepuff was a clearly better choice than Ravenclaw as they had identical pick percentages, while Hufflepuff had superior win odds. The EV’s are actually quite close, and that’s a result of the connected nature of some choices. Any Ravenclaw win automatically eliminates half the pool, thus increasing the pot share more and nearly making up the difference.
Slight Changes Have the Potential to Make a Big Difference
In the above example, the two underdogs (teams with less than 50% win odds) still have the highest EV. But changes to either the win probability or pick popularity percentage can alter that. Let’s now just consider the same hypothetical, with identical pick percentages, but with Gryffindor now having an 80% chance of winning against Ravenclaw.
Here’s what happens to the EVs for each option by just making that one change to the team that already had the highest win odds:
- Gryffindor: 1.13 EV
- Slytherin: 0.90 EV
- Hufflepuff: 0.93 EV
- Ravenclaw: 0.70 EV
Gryffindor was a near-average choice at 70% win odds with 50% popularity, but behind both Hufflepuff and Ravenclaw in EV. At 80% win odds, though, Gryffindor becomes the clear best choice based on EV, even with high popularity.
Meanwhile, Ravenclaw’s EV takes a nose dive as Gryffindor’s chance of elimination (and Ravenclaw’s chance of survival) drops. Ravenclaw becomes the clear worst choice by EV with a drop in win odds.
We did not change anything about Slytherin or Hufflepuff. Nevertheless, while both saw their EV’s drop, the relative gap between the two also closed down. Hufflepuff dropped more. The reason for this is Gryffindor’s improved win odds also meant that at least half the pool would survive at a greater rate, thus putting a relatively higher premium on safety, compared to the previous hypothetical.
Taking Into Account the Impact of Your Own Pick on EV
The above hypotheticals ignored the impact of your own selection on the pick popularity numbers, and thus the EV. We did that to focus on some other factors and keep the math simpler. You should, though, keep in mind that your selection does impact the EV in your particular pool. The amount of that impact depends on the number of other remaining entries and the number of surviving entries in the various potential scenarios.
Let’s quickly illustrate again using the Monstars/Looney Tunes example, where 85% of the public was on the Monstars. Now, we’ll use exactly 100 other opponent entries, and add in the impact of our own choice.
If you choose the Monstars
You become the 86th entry to select them out of 101. Your chances of winning the pool are 1 divided by 86. The EV is 0.82. That’s still the same EV — with such a large number of entries picking the same team, your choice had minimal impact on the EV calculation.
If you choose the Looney Tunes
You become just the 16th entry, out of 101, to select them. If they win, your chances are now 1 divided by 16 (6.25%). That changes the EV to 1.89 (previously, it was 2.00). In this case, with fewer other entries also surviving, the EV did go down when calculating the impact of your own entry. (Picking the Looney Tunes is still the best choice here).
Your Own Decision Has a Bigger EV Impact With Fewer Entries Remaining
Now, think back to the scenario involving Gryfinndor, Slytherin, Hufflepuff, and Ravenclaw. Hufflepuff and Ravenclaw, the two underdogs and unpopular picks, had slightly higher EVs. But let’s say you are down to just 10 entries remaining and the picks are distributed the same way (5 for Gryffindor, 3 for Slytherin, and 1 each for Hufflepuff and Ravenclaw). Your decision now has a huge impact on the EV.
In fact, becoming the second entry to pick Hufflepuff drops the EV of that pick to 0.88. It goes from being the best pick in our hypothetical to now the worst EV because you chose it!
We’ll delve into this more in a discussion of end-game strategy, but the point here is that your choice does have the potential to impact EV, and it’s why we also recommend that you pay attention to who your opponents can and cannot pick as the season continues. With larger pools and earlier in contests, our public pick estimates do a pretty good job predicting how your pool picks will look. But when the amount of entries gets much smaller, knowing the specific tendencies, available choices, and likely decisions of your opponents becomes more important.
If you knew that no one else could pick Hufflepuff, it is the best option in that hypothetical. If just one other entry selects them, though, it switches to the worst because of the impact of your own selection.
Doing the EV Math for Sixteen Games a Week is Complex
The previous examples show how EV is dependent on the interplay of pick popularity and win odds not only involving one team you might select, but also the other potential options. Now, imagine doing that for sixteen games, where the effects are all intertwined.
With only two games and four teams to choose from, we had four potential combinations of winners. Move up to three games and six teams, and the number of combinations increases to eight. By the time you get to sixteen games and 32 potential teams to choose from, there are over 65,000 combinations of outcomes.
Processing all that is virtually impossible without the use of a computer. The concepts used to calculate EV for a full NFL weekly schedule are the same as illustrated above, but once you get to a real-life, full NFL schedule, the number of possibilities and outcomes becomes very complex.
A Real-Life Example of Expected Value
Let’s take a look at one example of EV outcomes by going back to Week 1 of the 2018 season, which featured the New Orleans Saints as the most popular selection. Here is a summary of some of the data that TeamRankings takes into account when assessing survivor options.
This chart lists the spread, our projected win odds, the public pick percentage, and Current Week EV for the sixteen teams we projected with win odds above 50% for that week.
|Team||Opponent||Spread||TR Win Odds||Public Pick %||Current Week EV|
|New Orleans||Tampa Bay||-10||80%||31%||1.06|
|LA Chargers||Kansas City||-3.5||60%||1%||0.91|
Expected Value is reported as a number that can be above or below 1.00. The higher the number, the better the Expected Value of making that selection. You can see that there were six teams with a current week EV above 1.00.
This current week EV is not the final input in deciding which games are the best plays. Future value and schedule and likely pick popularity in future weeks also factors.
Taking the Saints in Week 1 would not have been a bad EV move despite their pick popularity. Selecting Detroit against the Jets, for example, had lower value despite fewer entries taking the Lions, because they were still relatively popular at 11% when compared to several other options with roughly similar win odds.
But taking the Saints also was not the best EV play. The Packers and Rams games had a higher EV, because even though the expected win odds for each were a little lower, that drop was offset enough by the large gap in public pick percentage.
While we aren’t focusing on Future Value here, those considerations also moved the Saints down relative to the other options. It also closed the gap between the Saints–who had one of the highest future values at the outset of the season–and the Ravens.
But this week illustrates how value includes both win odds and pick popularity. You don’t want to take games that are too risky just because few others are picking them. You do, however, want to consider teams that have nearly as good a chance at victory if the pick popularity is low enough.
As it turned out, nearly half of all survivor pool players were knocked out in Week 1 of 2018 with the Saints and Lions losing and the Steelers game ending in a tie. That outcome is an illustration of why being diversified from the crowd while still selecting another solid favorite can potentially pay huge dividends. If you imagine a counter-hypothetical world where you picked the Saints and followed the crowd, the Saints won, but the Rams lost, that set of outcomes would have had a smaller impact on your ultimate chances of winning the pool.