For the last decade or so, various versions of payroll efficiency estimators have popped up to measure which teams are getting the most bang for their buck in terms of spending. The late Doug Pappas pioneered this research in MLB, using a formula he called Marginal Dollars, Marginal Wins. That is basically the ancestor of the present $/WAR calculation we often cite, looking at the cost a team paid to add wins to their side of the ledger. These kinds of calculations have helped identify which teams have invested their resources wisely, and which teams are simply squandering their wealth while getting little in return.
However, there’s always been a bit of a problem with $/WAR calculations, because we know that the value of each win added is not linear. The value of a win is better described as a curve, with a sharp inflection in the mid-80s when each additional win significantly increases a team’s chance of making the postseason and going on to compete for a World Series title. A team should not be incentivized to pay as much as for their 78th win as they are for their 88th win, and a rational GM would indeed pay more to make a marginal upgrade on a contender than he would if his team was expected to finish out of the running.
$/WAR calculations ignore the marginal differences in the value of a win, and end up putting too much emphasis on teams that manage to be good and cheap while penalizing teams that are great and expensive, even though the wins added that pushed the great team into that next tier are the ones that make the most sense to overpay for. So, today, I thought I’d try a new spin on the team efficiency calculations, using our expected playoff odds instead of a team’s projected WAR to measure the value of team spending.
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