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I am studying the effect of player characteristics on their team win rate (< 1). Because players are grouped in teams of 10, they share the same win rate. The goal is to predict team win rate from characteristics of its players and get insights on which combinations of these characteristics are optimal. How can I model this?

Things I've considered:

  1. Regressing on non-grouped player characteristics does not account for how a team performs, given characteristics.
  2. Regressing on the averages of player characteristics in each team does not account for team heterogeneity
  3. Multi-level and ME models tend to have levels of explanatory, not explained variables.
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As @Stefan alluded to, your best bet is to utilize the multilevel structural equation modeling paradigm. Software for this can be found both in existing general purpose programs/packages (lavaan and xxM in R, gsem in Stata) and standalone programs such as Mplus. See also these CV threads.

The challenge you have is that multilevel or mixed effects models require the outcome to be measured at the lowest level of the hierarchy (players within teams). But your outcome only resides at the team level. There is no equivalent of a player win.

In multilevel structural equation models, the outcome can exist at any level of the hierarchy. However, you are still limited in which predictors can be used to explain variance in that outcome. So in your case, the player level variables can only influence team wins via their aggregate characteristics. E.g., teams with higher percentages of X types of players tend to win more often. Note that to address your second point, you can introduce team-level measures of variability of player characteristics as predictors, in addition to means. If teams were organized into leagues, then league level variables could influence variance in wins at the league level.

In principle, it is not out of the question that individual player characteristics could influence team outcomes. However, there is no software implementation that I am aware of that can estimate such a model.

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  • $\begingroup$ I thought Dan Bauer had a paper on this, but I can't find it now. $\endgroup$
    – Jeremy Miles
    Commented Jun 27 at 17:59
  • $\begingroup$ Thank you for your response. It seems that MSEM is the way to go, although I am not sure what you mean "the player level variables can only influence team wins via their aggregate characteristics". If goals scored is one of the player characteristics, does it make sense to have it as a predictor since its aggregate determines win rate? $\endgroup$
    – Heiko
    Commented Jun 28 at 16:06
  • $\begingroup$ @Heiko, I do not think that goals scored is a good predictor for the reasons you mentioned. Maybe a rescaled version of it. Something like percent of shots on goal that were successful? $\endgroup$
    – Erik Ruzek
    Commented Jun 28 at 16:47
  • $\begingroup$ @ErikRuzek yep sorry I meant something like goals scored per match or something not absolute. Any reason this should not capture the individual effects? $\endgroup$
    – Heiko
    Commented Jun 28 at 18:17
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    $\begingroup$ I think that makes sense, @Heiko. You want a way to capture whether a player is good at goal scoring b/c presumably a team with more players of that sort will win more games. $\endgroup$
    – Erik Ruzek
    Commented Jun 28 at 18:18

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