We're All Living in a Fantasy Simulation!
It’s game day!
Hopefully, you’re enjoying your Sunday. Whether you’re back from brunch, folding your laundry, cleaning up around the house, lamenting Mason Crosby’s ability to competently kick a field goal or marveling at Graham Gano’s impossible 63-yarder, it’s a great day to be alive.
And we are… alive, right? I ask because there’s a popular idea known as Simulation Theory, which hypothesizes that we are all just living in a simulated version of reality. Kinda like The Matrix. Even Elon Musk thinks it’s more likely than that not we’re living in a simulation, suggesting that there’s just a “one in billions” chance that we’re not living in a simulation right now. And he’s one of those smart guys.
So if our own lives can be simulated, then why not fantasy football? Luckily, I had some time to kill today (given that all time is worth killing since I’m living in a simulation) and thought why not simulate the rest of the season and see what happens. In fact, it might be able to tell us a little bit about… the playoffs.
Yes, the playoffs! (Playoffs?!) As we enter Week 5, we are now nearly one third of the way through the season. That means it’s finally time for us to turn our attention to the playoffs. First, let’s take a look at the standings.
Currently, Jess and Josh lead their respective divisions, which is important as the division winners take home the top two seeds and a first round bye into the playoffs. Joining them at 3-1 are Nick and Erik. Next up is a group of four 2-2 team owners including Alex, Brandon, Gray and Trevor. Were the season to end today, Alex and Brandon would claim the final wildcard spots based on the points tiebreaker. Finally, we have four 1-3 teams, again split between the two divisions.
You might recall that last week we took a look at the effect of playoff expansion, noting that a six-team playoffs significantly boosts the playoff odds of teams in the middle of the pack. For example, 1-3 teams (JT, Samantha, Geoff and Greco) used to have just a 17% chance of making the playoffs. Now their odds stand at 44%. Which is actually even better than the historical performance of 2-2 teams, which have gone on to make a six-team playoff just 43% of the time. That means we have a big group of eight teams, all with around a 40% chance. Or put another way, we might expect 3-4 of the teams from this group to make the playoffs. By comparison, 3-1 teams have a 67% chance of making the playoffs, which means 2-3 of the four team owners at the stop of the standings are likely to make the playoffs.
But of course, those odds are treating each team like they’re the same. And we know from our Power Rankings that not all 3-1 or 2-2 or 1-3 teams are alike. For example, two of our 2-2 teams (Alex, Brandon) actually find themselves above three of the 3-1 teams (Erik, Jess, Nick) in our rankings. And one of our 2-2 teams (Gray) is actually ranked below a 1-3 team (JT).
Luckily, TW% allows us to make a more informed projection for each team owner. All we need is the win probability function (pushes glasses further up bridge of nose). You might recall we discussed it a bit in Alex’s season preview as it relates to luck. But it’s primarily useful as a tool for calculating your probability of winning a game against any other team owner. This is what it looks like:
Brandon (29.9%) vs. Josh (70.1%)
Geoff (57.9%) vs. Greco (42.1%)
Gray (24.6%) vs. Jess (75.4%)
Nick (52.3%) vs. JT (47.7%)
Samantha (12.3%) vs. Alex (87.7%)
Trevor (28.1%) vs. Erik (71.9%)
This week, Alex (2nd in the Power Rankings) rates as the biggest favorite going against Samantha (10th) with a probability of 87.7%. Meanwhile, Nick’s matchup with JT rates as the biggest toss-up with Nick being favored by just 52.3%. The fact that a game between a 3-1 and a 1-3 team is a virtual toss-up while a 2-2 (not a 3-1) team is the biggest favorite of the week just goes to show how revealing TW% can be of team quality.
Now that we’ve shown we can calculate the win probability of an individual game, let’s go ahead and repeat the process for a given owner for the rest of the season. Let’s stick with Nick. Here is Nick’s remaining schedule with his chances of winning each matchup based on the win probability function.
As you can see, Nick is technically favored in six of his remaining nine games, though three of those contests are essentially toss-ups (his game this week plus two match-ups with Trevor). He is significantly favored in two games against Geoff and one against Greco. Then he has a three-game stretch midway through the season in which he is the underdog in games against Erik, Josh and Brandon.
Now that we know Nick’s chances of winning each game this season, we can project his wins for the season by doing a simulation. What’s a simulation? It’s kinda like the Matrix where tiny make-believe versions of Nick play fantasy football against tiny make-believe versions of the rest of you. See if you can visualize it in the lines of code below.
Okay, not really. That’s just a GIF from the movie.
What it really looks like is this:
That’s a screenshot of from my spreadsheet of a recent simulation from Weeks 5-7. So, no there are no tiny versions of you (at least that I’m aware of). To simulate a season, I simply have my spreadsheet create a random number between 0 and 1 for each remaining match-up. If a team owner (in the away column) has a probability of winning the game that is greater than that random number, they win. If it’s less, they lose. For example, in the screenshot above, you can see that in Week 5, the random number generated for Nick’s game was 0.156. Since Nick’s probability of winning is .455, he wins.
Then I do that 10,000 times. Well, not me. But the computer does it. It takes about 3 minutes and 38 seconds. Usually, I imagine tiny versions of Nick during that time crawling across my laptop like the Lilliputians from Gulliver’s Travels.
Then a little less than four minutes later, I’ve got a record of all 10,000 simulations, how many games Nick won in each “season” and whether he made the playoffs or even won the division. This is what Nick’s 10,000 simulations look like, organized by number of wins:
In the chart above, I’ve diagrammed the number of times Nick won a certain amount of games. For example, in 2,699 of 10,000 simulations, Nick won 7 games, finishing 7-6. As you can see from the chart, it’s the most common outcome. Just below that was 8 wins, which happened 2,692 times. Given that, we know that Nick has a 54% chance of winning between 7 and 8 games. And in fact, the average number of wins he finished with was 7.4.
But it’s not all roses, sometimes things did not go well for tiny Nick. In 10 of the simulations, Nick went on to lose 9 straight games, finishing with just 3 wins, which was twice as common as his tendency to win out, which happened just 5 times. Remember, in the first table above, we calculated that theoretically his chances of winning out were 0.06%. The fact that it happened in 5 out of 10,000 simulations or 0.05% shows how close we get to the theoretical mean when we simulate a season over and over and over again.
Finally, beyond wins, the most important thing we want to know here is how often Nick made the playoffs. After all, that’s the real knowledge we’re after. As you can see by the portion of the chart that’s been colored orange, Nick made the playoffs 7,637 times out of 10,000 or 76%. And he didn’t always need a lot of wins to do that. We can even see from the chart that he made the playoffs 527 times when he finished with a losing record of 6-7.
Now let’s place that information into our familiar Playoff Picture table.
As you can see, Nick’s numbers are consistent with what we saw in the chart above. He’s projected for 7.4 wins with a 76% chance of making the playoffs. Furthermore, he has a 12% chance of winning the Legends Divison, which is currently being led by Jess.
Okay, enough about Nick, what about the rest of you?
Unsurprisingly, three 3-1 teams lead the Playoff Picture and are heavy favorites to make the playoffs with odds of 96% and above. They are Josh, Erik and Jess. Not only do they currently have more wins than any other team, but they also are ranked highly in the Power Rankings, so the computer tends to see them as legit. Josh in particular has an 80% chance of winning the Leaders Division. (Though, this week’s game against Brandon will have big implications for that.)
But then we have two interlopers—Alex and Brandon. Though they are both 2-2, the computer likes them also to make the playoffs with between an 87-89% chance. Alex, in particular (as the 2nd ranked team in the Power Rankings) has a 34% chance of unseating Jess as the division winner. After Brandon, Nick has the aforementioned 76% chance of making the playoffs. That would be six teams.
Of the team’s currently on the outside looking in, the computer likes Trevor and Gray. Both are 2-2 teams with between a 21-29% chance of making the playoffs. Finally, JT, Geoff, Samantha and Greco (all 1-3) have a 3% or less chance of making the playoffs according to the model.
But… it needs to be said that these numbers drastically overestimate the playoff chances of the teams at the top and underestimate the chances of the teams at the bottom. After all, those probabilities seem exceedingly small for teams that are currently only one game out of a playoff spot, especially given the fact that historical trends dictate that 1-3 teams have a 44% chance of making the playoffs.
That’s because of TWO ENORMOUS CAVEATS.
Caveat #1: These numbers assume your team will continue playing at its current level.
We’re still only four weeks in and that means a fairly small sample size for your TW%, which will get more robust as the weeks pass along. But since that’s the number we have to go on, your current TW% is being used to calculate your win probability for games all the way down in Week 13.
And the truth is you’re team may be a lot better in Week 13. You might have previously underperforming players like Odell Beckham Jr. or an injured stud like Leonard Fournette or maybe you’ve got an All-Pro and first-round draft pick who has yet to show up (cough, cough… Le’Veon Bell). If that’s the case, then you can almost certainly expect your team will be performing better in the weeks ahead, and if so, your TW% will go up. And when it does, so do your odds to make the playoffs.
Also, the model also assumes the good teams will continue being this good. That’s why Josh has a better than 99% chance of making the playoffs right now. But even with a six-team playoff, that’s kinda silly. Because if he were to maintain his current pace, his team would easily rank as the best team of all-time—even better than Gray’s 11-2 team from 2016 that had a TW% of .808. So we can expect Game of Mahomes to cool off a little bit even if he continues to be a very good team. After all, winter is coming. The same can be said for Alex’s team whose stud RB James Conner probably has his days numbered in Pittsburgh. And that means good news for all the team’s further down in the rankings.
However, given all of that, if you believe your team to be truly as crappy as it has currently performed, then maybe it’s the time to start making some moves. Make a trade. Look for options on the waiver wire. Do something! Because if you don’t, you’re not going to make the playoffs without a lot of luck.
Caveat #2: Tiebreakers assume current point leaders hold.
We know there’s likely a good chance that at least a couple team owners with 7-6 or 6-7 records are tied at the end of the season for those final wildcard spots. And those spots will be divvied up based on total points scored. So in those 10,000 simulations, I used current point totals to break the ties that inevitably occurred.
As a result, players with high point totals have playoff chances that are probably overestimated. This applies to pretty much every owner near the top of the standings. Even Nick, Gray and Trevor benefitted as they currently have 349, 346 and 346 points, which ranks ahead of those below them in the standings. For Gray, specifically I added a point as a tiebreaker to the normal tiebreaker in the event that he and Trevor tied in both wins and points. Consider it a benefit of historical performance.
But the reality is that any of the team owners below them in the standings could easily catch up. When we run these numbers again next week, it’s not unlikely that Samantha (who has 317 points) could easily catch up and over the course of the season pass the other owners in total points scored. If that were the case, suddenly she or other owners like her would take away playoff shares from the owners above them in the standings.
So, given those caveats, I’m not sure at all how useful this Playoff Picture is beyond a look at the basic methodology behind the predictions. It’s early, but I do think it’s helpful to see where these numbers come from. And if you believe your team’s performance reflects its actual ability, then these odds should either give you comfort or reason to panic. Either way, it’s better to know now than later.
Unless of course we are just living in a simulation. In which case none of this matters. In fact, you might as well just “do your superman thing” all the way to the championship.
If only fantasy football were that easy.
