A reader messaged me last week with a dilemma. He had the Houston Texans and Jacksonville Jaguars defenses. This seems like a coup—according to the league dominator, they were the #1 and #2 units in his league going forward—and it would be... if it weren't for those pesky bye weeks. He needed to make room for replacement starters, and his spare defense was next up on the chopping block.
His hangup wasn't the possibility of losing out on points (presumably the replacement starters would add more points, in expectation, than the defense he was cutting, or else he wouldn't cut the defense to make room). It was the idea that he was handing a top defense to one of his rivals for free, a defense which they would presumably use against him down the line.
And so he asked: surely there's some value to be placed on denying points to your opponents by keeping productive players away from them, right? If so, how much?
And so I answered: production on your bench (and therefore denied to your opponents) is worth approximately 9% as much as production in your lineup.
That's an Oddly Specific Value
Perhaps 9% seems a bit arbitrary. Why not 10%? Or 15%? How did I arrive at 9%?
Well, one could arrive at a value by running simulations. I know several sites that will, for instance, look at all remaining matchups in a league, estimate probable scores based on projections plus some random variance, simulate the rest of the season some arbitrarily large number of times, and produce an estimate of one's chances of making the playoffs, earning a bye, and winning a title.
With something like that already built, one could try to estimate the impact of adding a top defense to the free agent pool. Of course, one would also have to estimate the likelihood of the defense landing with each team, simulate the impact on each team, and weight each set of simulations by the estimated likelihood.
I didn't do that. It's a very complex approach, and around here, we don't believe in complex approaches to complicated problems. Instead, we attack them with simple rules of thumb. (That's right, we're doing that heuristics thing again.)
So here are two quick statements of fact.
- Fantasy football is a game of relative performance. The goal is only to score more points than your opponent. As a result, adding X points to your lineup and subtracting X points from your opponent's lineup are equally valuable.
- In a league with N teams, your odds of facing a specific team in any given week are 1 / (N - 1). (Why N - 1? Because you never play your own team.)
Combine these two, and the value of adding X points to your team is X, while the value of denying those points to someone else's team is X / (N - 1). In a 12-team league (such as the one the original reader played in), denying points is 1/11th as effective as scoring points, which works out to 9% (give or take a few decimal places).
The "But What If..." Section
But what if your league runs double-headers (where your team faces two opponents every week)? Simple: you face each opponent every 5.5 weeks (on average), but on any week you face them, they only represent half of the games you play, so that's 1/11th of your total matchups.
What about in all-play leagues, where every team plays every other team every week? In that case, points added help you in 11 out of 11 matchups, while points denied only help you in 1 out of 11 matchups.
What if you're in a league where you have "divisional foes" you face more often than usual? If the points you're keeping off the market land on one of your divisional rivals, you'll face them more than 1/11th of the time. But if they land on a non-divisional foe, you'll face them less than 1/11th of the time. Weight the number of matchups per year by the percentage of teams that are divisional foes, and the math works out to... a 1-in-11 shot that any given matchup is impacted.
What if you're in a total points league, where the team with the most points at the end of the season takes home the title? Once again, you'll find that the value is... wait, hold up, scratch that—this is a genuinely different problem: there are no individual matchups for you to win or lose.
The "But What If..." Section (Total Points Edition)
I had never given thought to how denying points would work in a total points league until I set out to write this. Let's try to reason our way through from first principles, shall we?
Let's imagine that at the end of the season, you finish in first place, but three other teams finish within 20 points of you. If we now imagine a counterfactual where you cut a player that would have added 20 points to whatever team signed him, there are three out of eleven possible landing spots where putting this player into the pool would have materially changed outcomes for you.
Thinking about it analytically, I would say making points available to your opponents only matters when it increases the "score to beat" (or the highest point total among your 11 opponents). If you make X points available, there is a 1 in 11 shot it lands on each team, and the "cost" of landing on each team would be (X - Y), where Y is how many points this team trailed the highest-scoring team by (provided X is greater than Y; otherwise, the cost is zero).
If you're making 20 points available in a league where the top scoring team will finish with 1,000 points, second place will finish with 990, third place will finish with 980, fourth with 970, and so on... there's a 9% chance it would increase the top score by 20 (if it lands on the highest-scoring team), a 9% chance it would increase the top score by 10 (if it lands on the second-best team), and an 82% chance it doesn't increase the top score at all. In this case, points held off the market were 13.6% as valuable as points in your lineup.
This places an upper bound (100%, assuming all eleven rivals tie with the exact same score) and a lower bound (9%, assuming the top-scoring competitor will finish more than X points ahead of everyone else). Note that the upper bound suggests that "denying" points can never be more valuable than adding points, which makes sense—it is impossible for your team to be worse off if you increase your score by X and also increase another random team in your league's score by X. Doing so ensures 10 teams are faring worse relative to you and the 11th team is faring no better than before.