The Fantasy Football Philosopher: Thinking About Tilting
Tilting is – for better or worse – a core part of fantasy football.
You have almost certainly tilted at some point in your career, be it at the draft, on Sunday, or even when the waiver wire results come out. You might not have heard the specific word before, but everyone has ‘gotten unreasonably angry when something in the fantasy football world didn’t go their way and possibly ended up making questionable fantasy decisions down the line’.
Sound familiar? You might be hoping a certain RB comes back to you in the second round and, when they get sniped right before your pick, become flustered and mess up your next couple of selections. You might narrowly lose a game because of an unlucky bounce (two years ago I went to bed thinking I was a sure winner only to lose by a fraction of a point to a Josh Allen / Stefon Diggs stack in a monstrous Week 15 performance) and spend it all on a dubious FAAB pick-up the next day.
While it might be a tall task to eliminate tilting entirely, that doesn’t mean we can’t strive to understand the phenomenon of tilting and, in some cases, even take steps to mitigate it. What better time to face tilting head-on than the start of the fantasy season? Let’s dive right in; all data, unless otherwise specified, comes from nflfastr.
May The Best Team Win
Possibly the most common tilt-inducer in fantasy is losing when you felt you deserved to win. Of course, this happens all the time: fantasy football is a challenging game with a ton of randomness.
First, we have to think about how ‘roster skill’ is distributed. Here’s a situation with an ‘extreme’ distribution; the x-axis represents team skill, and the y-axis represents density, or how often these types of teams occur. In this plot, there is basically an equal number of teams with all skill levels, ranking from absolutely terrible to insanely awesome.
The extreme distribution probably doesn’t represent real life: while there are very good and very bad fantasy teams, there’s generally more density around the middle, or average fantasy team. Therefore, we’re going to use a mound-shaped distribution like this to represent skill.
This shape more closely matches the weekly scoring distribution we saw in a previous entry about consistency in fantasy, so that bodes well for our model!
Now, we want to find the relationship between team skill and team success, which we will define here as making the playoffs. This will be for a 12-team Half PPR league, where the top-4 teams make the playoffs after a 13-week regular season (and a 4-week playoff).
With this setup, we can easily simulate an entire league season with this algorithm:
- Sample 12 ‘skill levels’ from the mound-shaped distribution above; this will represent the strengths of the 12 teams in the league.
- Generate the matchups and have each team play a 13-game season; use the team strengths to simulate which team wins (i.e., stronger teams have a higher win probability*).
- Mark the top-4 teams as playoff teams, using a random draw with team strengths as the weights for breaking ties.
- Do steps 1-3 a total of 10,000 times.
Once all is said and done, we can plot the relationship between team skill (x-axis) and probability of making the playoffs (y-axis). Note that this line isn’t strictly increasing – there is some noise – because this is a simulation; the general trend is more important:
- A horizontal line is drawn at 33%, which, intuitively, intersects the dots at about a team skill of 50%. This makes sense: a perfectly average team has a one in three chance of making the playoffs since 4-of-12 (or, one in three) teams make the playoffs!
- Unsurprisingly, there is a positive relationship: stronger teams have a higher probability of making the playoffs. Still, the relationship is not as strong as you might expect: a 60th percentile team has a 38% chance, while a 70th percentile team has a 42% chance of making the postseason. Even the best teams max out at around 70%, although things get a bit funky when we consider edge cases like this.
I find this…a bit disappointing. We see that a quite good team – 70th percentile – has just a 9% better chance of making the playoffs than an average team (42% vs. 33%).
This is especially surprising given that we now have a longer NFL season than in previous years (teams will play 17 games instead of 16, so the fantasy regular season will be extended one week). In general, the longer a regular season, the more likely that the best teams will come out on top: playing more often helps to ‘ride out the noise’ of upsets, wacky wins, and so forth.
We can repeat the same algorithm above but for the old-school, 16-week NFL schedule (12-week fantasy regular season). I just included 10 dots so things wouldn’t be too cluttered; the black dots are from the original chart, while the red dots are for the shorter season:
There is a slight trend here: good teams (>50th percentile) have a slightly higher win playoff chance in the longer season (black dots) than a shorter season (red dots), and vice versa for bad teams (<50th percentile). However, this effect is quite small (1% or less) and isn’t even consistent across all of the dots. Unfortunately, the effect of one extra game doesn’t move the needle that much in terms of the ‘cream rising to the top’. In a 100-game regular season, for instance, you can be almost certain that the best teams would make the playoffs; going from 12 games to 13 games, though, won’t shake things up that much. You can read more about ways to ‘reduce the element of luck’ in this recent Fantasy Architect entry; tilting, though, is a more nuanced beast.
How Not To Tilt
So far, this hasn’t been a very fun article. While we’ve seen that better teams win more often, the increase in playoff chances just isn’t as large as we thought for quality teams. As mentioned, fantasy football is a game filled with randomness: the best we can do is manage the probabilities in our favor and hope for the best in any given week.
However, there are steps – two specific steps – that can be taken to reduce the amount of ’tiltage’ in your fantasy football career. The first is simple: manage more teams.
I don’t have the stats on this, but most of you reading this likely play in a number of different fantasy leagues. As you would expect, the more teams that you manage, the more likely it is that at least one makes the playoffs. Specifically, this ‘larger sample size’ effect of more teams is very strong, unlike the larger sample size of a longer season (which we saw is not very strong).
Here is the probability of making the playoffs in at least one league based on the number of teams you manage; this is assuming good teams in the 60th percentile, which is likely if you are playing in multiple leagues!
As you can see, adding teams greatly increases the probability of at least one getting into the playoffs. You’ll exceed 80% at four teams and 90% at four teams. Now, this isn’t quite right, since your teams will be correlated: you will tend to prefer picking certain players over others (your ‘My Guys’), and thus will likely have lots of exposure to certain players across teams. This yields a sort of ‘boom/bust’ profile: if one roster does well, it’s more likely the others do well (since they will share players). Still, the above trend is certainly accurate on average and in general.
The second ‘anti-tilting tip’ is to check less. This is a big time ‘do as I say not as I do’ moment, since I’m glued to the screen for basically all of Sunday. However, there’s a reason why checking the scores/games less can improve your tilting experience. This has to do with ‘loss aversion’, which, simply put, means that humans often dislike losses more than they like wins. We can construct a simple model to illustrate this point.
Say that there is a 60-minute NFL game happening, in which you and your fantasy opponent have multiple players involved in. Each minute of the game, you have a 55% chance of gaining a fantasy point on your opponent, and they have a 45% chance of gaining a fantasy point on you. Note that your probability is over 50% since your players in this game are better!
Now let’s imagine that you check the scores every minute. When you see that you have gained a point on your opponent, you experience +1.0 ‘happiness’. When you see that you’ve lost a point, you experience -1.5 ‘happiness’, or a 50% larger move (in magnitude) than when you gained a point; this is that loss aversion in action.
Let’s plot this specific game. The green dots represent when you check and see you gained a point, and the red dots when you check and see you lost a point. The black line represents your cumulative happiness over time: it goes up 1.0 units for every green dot and down 1.5 units for every red dot:
Sadly, your happiness ended negative. Here’s the crazy thing: in this scenario, you ended up with +2.0 overall. This might mean that you’re happy at the end of the game, but you can see how during the game your happiness drifted negative with all of those red dots.
One approach to fix this is aggregating data, or, simply put, checking less. Imagine that you only check once per quarter, and again get +1.0 happiness if you’ve gained points and -1.5 happiness if you lose points. You’ll see this simpler picture:
Same outcome, different tilt! The outcomes in every minute were identical, and you are still up +2.0 on the game, but when we look at this on a by quarter basis vs. a by minute basis, we are less exposed to the smaller ups and downs. In this case, at a quarter level, you won the 1st, 2nd and 4th quarters and thus were happy for the entire game!**
Tilting stinks. As we’ve seen, fantasy football is a game with lots of inherent randomness, and even very good teams still have a significant of not performing well over the season.
There are steps that you can take, though, to guard against the tilt. Join more leagues to increase your chances of at least one roster breaking through, and avoid the constant refreshing of your fantasy app to ensure that you don’t fall prey to the constant swings of fantasy (although I can’t promise that I will take my own advice here!). Of course, my hope for you is that your team does so well that you never even need to tilt.
Good luck this season!
Tilting? Message me on Twitter.
*Specifically, if Team X has strength x and Team Y has strength Y, then Team X has a win probability of x / (x + y) in a head-to-head matchup and Team Y has a win probability of y / (x + y).
**This is an approach fleshed out in Fooled By Randomness (Taleb), specifically in the context of checking investments with a generally upward drift (i.e., your 401k).