Washington Nationals' Bryce Harper stretches in the dugout last season. (Ross D. Franklin)

Just a day ago, Bryce Harper sat on the sidelines of free agency, a super star without a contract. Manny Machado already committed to a 10-year, $300 million contract with the San Diego Padres. The Colorado Rockies also decided to not take any chances with one of their future potential free agents and secured 27-year-old third baseman Nolan Arenado to an eight-year, $260 million extension. We were all wondering what was taking so long with Harper. Thursday afternoon things changed quickly.

Harper agreed to a new contract with the Philadelphia Phillies for $330 million over the next 13 years with no opt-out clauses, according to The Post’s Barry Svrluga. Earlier today I wrote why a $300 million contract over 10 years wasn’t a good investment for any major league club. Adding on three more years doesn’t change the calculus by much.

Figuring out the future worth of any player isn’t an exact science, but we can get a ballpark estimate that’s reasonable. The first step is using a modified version of Marcels, a simple forecasting system created by baseball analyst Tom Tango, called WARcels, which only uses a player’s wins above replacement as its gauge of performance. That, in turn, is regressed to the mean and adjusted for age, giving us a ballpark value for a player over any length of time in the future.

The second step is to assign a dollar value to each win above replacement. It was calculated in 2013 that one marginal win is worth $7 million, while FanGraphs assigns approximately $8 million per win above replacement in today’s environment. This is our starting point. Because nothing costs the same today as it did 10 years ago, we are going to increase the cost of a win in free agency by 3 percent each year, which is in line with the annual rise we saw from 2013 to 2018 (2.7 percent). I used a 5 percent inflation factor in the past but recent market conditions point to 3 percent as preferable.

By this method, Machado’s value in 2019 is expected to be worth 4.5 wins above replacement which, in turn, puts his 10-year value at 34.2 fWAR per WARcels. Using the cost and inflation method above pegs that at a $308 million price tag for the next 10 years. That’s pretty close to the 10-year, $300 million contract he signed with the Padres last week.

Arenado’s value in 2019 is pegged at 4.9 wins above replacement with an eight-year total of 31.5 fWAR from 2019 to 2026. That’s estimated to be worth $276.6 million, just a few million more than his new eight-year, $260 million extension.

Contracts signed by Manny Machado and Nolan Arenado (None/Neil Greenberg)

That brings us to Harper. His contribution in 2019 is estimated to be 3.6 fWAR which may sound low to some but consider that’s in line with his production over the past few years. Using that 2019 estimate as our starting point, Harper’s 13-year value is a total of 30.3 fWAR over the life of the deal, which should carry a price tag of $278.7 million after accounting for age effects and inflation. My initial valuation on a 10-year deal projected at $239.8 million.

Even if my numbers are off — and they very well might be — Harper’s chances of outperforming a $330 million contract over 13 years seems unlikely. For example, including his spectacular 2015 campaign, which earned him a unanimous NL MVP award, he was worth $235.6 million to the Nationals from 2012 to 2018, which is $33.7 million per year. Take away the MVP campaign and that average annual value drops to $26.8 million per season. But that’s during the early parts of his career, it’s unlikely he will be able to continue above-average production into his 30s, more or less his late 30s.

Sure, the Phillies would love to think they were getting the player Harper was in 2015 each year over the next decade but that’s just not realistic based on his performances to date — that season is a clear outlier compared to his other major league seasons.

Neil (Neil/Neil)

If this all sounds like a slight on Harper it isn’t, a four-win season is certainly worthy of praise, but to earn the richest contract in MLB history there simply should be a greater certainty of production, and that’s something Harper has yet to show at an elite level. There very well could be some great seasons posted along the way, but the Padres and Rockies should feel much better about the contracts handed to Machado and Arenado than the Phillies should feel about their new pact with Harper.

This story has been updated from a previous version.

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