To start (a sub), or not to start (a sub), that is the question.
Some of you might remember a tweet by the wonderful @TheFFChaps from a week or two ago about whether managers should start their stars off the bench in any given week:
https://twitter.com/TheFFChaps/status/1340299325113561089?s=20
While I could have, like a normal person, just engaged in the ensuing Twitter thread, I instead decided to take a (not so) deep dive into the issue instead. Specifically, I looked at some of the fantasy studs in fantrax standard scoring to see if it makes sense (beyond the reasonable psychological rationale) to start one of your fantasy players when they find themselves on the substitutes’ bench. Before looking at the data, my gut reaction is no, for the following two reasons:
Points are very strongly correlated with minutes. If you don’t play much, you don’t score!
There are no guarantees a player will even get in the game. There are perhaps arguments to be made for starting a benched player if you were certain they would get subbed in eventually, but you’re really left to the whims of the manager.
There are two components that need to be examined. First, what is the probability that a player will get subbed in, and secondly, when they are subbed in, how many points are they likely to score? Because I didn’t have unused substitute data readily available, I limited my analysis to eight players who can conceivably be viewed as high-upside enough to warrant a sub-start and who have been substitutes at least twice over the last two seasons. For example, guys like Harry Kane or Jack Grealish are never subs, so it didn’t make sense to include them. On that note, a disclaimer: substitute sample sizes for most of these players are very small, even smaller than we already usually have to work with so this analysis is significantly underpowered. You could imagine pooling data together, including all players, or using data from pre-2019, but since it's the holiday season and I didn't want to spend a lot of time scraping data or manually sifting through FBref, this is what I'm left with. Let’s get into it.
Question 1 – When these players begin on the substitute bench, how often do they get subbed in?

In order to get you points, these guys need to actually get some minutes on the field. Some players are pretty reliably getting time, such as Adama Traore (94% substitution rate), Kevin De Bruyne (80%), and Sadio Mane (83%). Others, like Salah (40%) and Raheem Sterling (57%), get subbed on less frequently. When they play, however, they all average at least 20 minutes of game time (besides Aguero – 16 mins).
Question 2 – When this player gets substitute minutes, how well do they perform?

As in regular games, these players have demonstrated the ability for major point outbursts in limited time. All players except for Son (2 sub appearances; 7 fpt max performance) and, curiously enough, KdB (4 sub appearances; 7 fpts), have managed at least one game in the double digits coming off the bench. Only Salah manages to average in the double digits, buoyed by his 30-point outburst last weekend. No one else in this group, even averages 6 points per substitute appearance. For reference, this would place them below the likes of Steven Alzate (6.2 fpts/start), Ruben Neves (6.1 fpts/start), and Eric Dier (5.87 fpts/start) this season. Not the most illustrious group!
This calculation, however, presumes they are in fact guaranteed to get some minutes when they are subbed in. If we adjust the average points they score by the probability that they actually get subbed in (P(subbed in) * avg points), this yields the true average for all games where they begin on the bench.

Even Mo Salah drops precipitously here because of his inconsistent playing time when not starting (40% sub rate). While his average is still respectable, it’s pretty skewed by his recent insane performance. It’s unlikely this is a consistent outcome. For the remainder, they all drop to below 5 fpts/sub appearance.
So, is this *ever* a worthwhile play? If you are terrified of your league mates making fun of you when your benched star has that once-in-a-lifetime substitute performance, perhaps. But if you are trying to make the “correct” decision, based on this limited data, the answer is unsurprisingly, no, unless you are very desperate. Maybe if you need to overcome a major deficit, it could be worth throwing your fantasy superstar into your starting lineup even though he is riding the proverbial “pine” (AKA race car seat in the Prem). Yet ultimately, whenever it is possible, its best to find a player who is actually starting.
Note: This calculation definitely shifts when in leagues with autosubs. For those leagues, table 3 taking into account the probability of being subbed in can be ignored.