One of the biggest issues I have had with Mikel Arteta as Arsenal's coach is his in game management and particularly his use of the subs available to him.
The effect of fatigue on player performance is well known, with players who are substituted and the substitutes scoring at higher rates than players who play a full 90 minutes. This is something that clubs should probably even have better information on (given that they have more biometric data about their players) and something that can be planned out further in advance to maximize how players exert themselves during matches.
Since he has taken over as Arsenal manager/head coach, Arteta's first sub (non-injury forced or red card) has come in the 63rd minute. The second sub is on average in the 73rd minute and the last sub in the 82nd minute. Arteta does typically use all of the subs available with 95% of the matches that he has coached using all of his subs. However, he does show a pattern that he is risk adverse, especially with the third sub of potentially facing an injury and not having a substitute available to him.
Looking at overall sub patterns of other coaches Arteta isn't a big departure from orthodoxy:
Only 26% of his first substitutes played 40 minutes or more (including injury subs and subs after a red card). That grows to 46% playing 30 minutes or more, 80% playing at least 20 minutes and 98% playing at least 10 minutes.
The pattern for the second and third sub matches the curve almost perfectly as well. The second sub playes 40+ minutes 1% of the time, 30+ minutes 10%, 20+ 42%, 10+ minutes 70% and 5+ minutes 93% of the time. For the third sub these numbers are 40+ minutes 0% of the time, 30+ minutes 1%, 20+ 10%, 10+ minutes 33% and 5+ minutes 63% of the time.
What is interesting (and maybe a bit concerning) is that Arteta's sub patterns match almost exactly with the patterns of a time when there was only 3 substitutions allowed. In more than a third of the matches that Arteta has been in charge of he has had 5 subs to use and that has had almost no effect on his timing, with subs 4 and 5 playing nominal minutes in most situations.
There also doesn't seem to much difference based on the score. When the match is tied or Arsenal are losing at 60 minutes the sub pattern is roughly the same, especially for subs 2 and 3. The first sub is still on average at 58 minutes, the second sub comes at the 73rd minute (they are slightly more likely to play 20 or minutes going from 42% to 47%) and really no change at all for the third substitute.
This probably isn't a massive difference but maximizng the substitution patterns is something that would drive marginal gains for a team like Arsenal that while stocked with good players, is a team that doesn't enjoy overwhelming talent advantages in every matcht that they play.
The match against Villarreal was a great example where hesitency to make changes hurt Arsenal. In this match Arsenal had 5 subs to use, they were trying a tactical wrinkle with a false nine and incredibly high stakes. The team fell behind early and Arteta was very slow to utilize subs, even if he wasn't able to save the team from the Dani Ceballos red card, it is head scratching that he didn't use his second sub until the 85th minute and his finals subs as a way to waste time to see the match out in the 95th minute.
I am not sure if this is something that Arteta will change on but it is something that I strongly believe could be worth 3-5 additional net goals over the course of the season just through more agressive uses of substitutes that would like adding 2-4 free points to the team just by getting more out of the players that are already with the team.