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The Most-Valuable-Player Problem Remains Unsolved

My analysis of player-value in "Solving the MVP Problem" adopted parts of an earlier analysis of player-value put forth by Neil Feit and myself (2). On this account, player-value is concerned with what a player contributes to his team, rather than what he contributes to the average team or the league in general. More specifically, one player has more value than a second if and only if he contributes more to his team than other players do toward their teams. On this theory, winning is the central goal of competitive athletics and a player's value is a function of the degree to which he contributes to that goal via his on-the-field play. Another way to say this is to say that a player's value is the net benefit that his on-the-field play brings to his team's winning. On my earlier theory, the net benefit is the difference between a player's benefit and cost to his team. The net benefit is measured by comparing the team's performance with the player against some other state in which the player is not present. The latter state is called the "baseline state." At issue is the nature of the baseline state. There are three different states that might serve as the relevant baseline state. Consider the states we might compare with Joe Montana playing quarterback for the San Francisco 49ers. First, the state might be compared with one in which no one occupies that position. Second, the state might be compared with one in which a counterfactual player occupies that position. Third, the state might be compared with one in which the actual backup player occupies it.