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In partnership with the Buffalo Bills, AFA is pleased to announce this once in a lifetime offer. For a limited time, you can now sign up for the Bills Visa card with no spending limit, and a special introductory interest rate of just 486%! That's right, the Bills believe this is a fair exchange of present and future value. Get $1 of value this year, and pay $4.86 next year. What's not to like?

How do I know the Bills believe this is a fair interest rate? Because this is the implicit discount rate they paid when they traded with the Browns last year for the pick that landed WR Sammy Watkins. The Bills got the Browns' 4th overall pick in 2014, and in exchange gave up their 9th pick in 2014 plus their 1st and 4th round picks in 2015. If we add up the expected value of those picks, the Browns obviously got the better end of the deal. Cleveland got 14.0 points of Approximate VAlue (AV), while Buffalo got 7.5 points of AV. But there was a catch. The Browns would have to wait a year to cash in on 7.8 points of their total 14.

For this trade to be fair in terms of total AV, the Bills must have discounted the value of those future picks. This is a good example trade because it's clear that the Bills believed that 7.8 worth of next-year's AV must have only been worth 1.3 AV in the current year. Add that 1.3 AV to the 6.2 AV of the 9th pick they gave up in 2014 and you get the 7.5 AV they received in the form of the 4th overall pick. To devalue 7.8 AV in to 1.3 AV in one year, you'd have to believe the going interest rate is 486%.

Approximate Value Model
Bills got Browns got
Pick Value Pick Value Disc. Val.
4 7.51 9 6.18 6.18
    12(+1y) 5.71 0.97
    108 (+1y) 2.10 0.36
Total 7.51   13.98 7.51

In the world of capital investment this is known as an Internal Rate of Return (IRR). If I borrow from the future to make an investment now, that investment should provide a return at least as costly as the premium I pay to borrow. Different capital investment options provide different streams of benefits and costs over a series of time periods. The IRR is the discount rate necessary for an investments stream of net costs and benefits to be zero. In the context of a trade that includes future draft choices, the IRR is the discount rate needed for the value on each side of the trade to net out to zero.

Is a 486% discount rate plausible? Sammy Watkins could turn out to be a great player, but even the most optimistic forecasts could not justify such an outrageous rate.
I'm actually being a bit unfair. Although teams should be using something similar to the AV draft values to evaluate potential trades, in practice teams very often rely on the conventional trade value chart, sometimes known as the Jimmy Johnson chart. According to the Johnson chart, the Watkins trade makes more sense, but not that much more. According to convention, the implied discount rate of the trade would have to be 184%, still outrageously high.

Jimmy Johnson Chart
Bills got Browns got
Pick Value Pick Value Disc. Val.
4 1800 9 1350 1350
    12(+1y) 1200 423
    108 (+1y) 78 27
Total 1800   2628 1800

What if went a step further and looked at Massey-Thaler surplus value? That’s the net value of each pick according to how much you’d have to pay a free-agent (FA) with an equivalent expected performance level. In the M-T model, the Bills got nearly $1.4M in surplus, and the Browns received a total of almost $2.8M in surplus of which $1.4M came one year in the future. That makes for a discount rate of over 20,700%. That’s kind of a silly number, because discount rates that high pretty much mean the borrower doesn’t value the future much at all. Essentially, the 4th and 9th overall picks are about equal in surplus value, so the 1st round and 4th round picks in the future year can be discounted to near zero and the trade would be fair.

M-T Surplus Value Model
Bills got Browns got
Pick Value Pick Value Disc. Val.
4 1,368,107 9 1,361,409 1,361,409
    12(+1y) 1,370,065 6,576
    108 (+1y) 25,452 122
Total 1,368,107   2,756,926 1,368,107

You’d much rather be on the Browns side of that trade than the Bills side, and it is generally shrewd over the intermediate-term and long-term for the team trading down to do so, given the super high premium that such trades command. But the Browns were nearly as guilty as the Bills, trading up in that same draft. Cleveland traded picks with Philadelphia, getting the Eagles’ 22nd pick in exchange for the 26th and 83rd picks in the same year. There’s no discount rate to compute, but in terms of AV the Browns got 5.5 points but gave up 8.3 points. The Johnson chart was far more kind to Cleveland, calling the trade marginally beneficial for Philadelphia. The Massey-Thaler surplus model says there is about twice as much value on the Philadelphia side of the bargain as on the Cleveland side, mostly because the M-T model loves mid round picks.

All that said, I don’t claim that every trade must be equal and that any discount rate other than zero is the correct way to do business. In some cases it would make sense to pay a premium to move up in the draft, either with picks this year or with future picks. Quarterbacks are particularly scarce, and they may be a special case. But unless a GM has special super-human powers of prediction about how well a pick will turn out, in general teams should be very, very reluctant to pay such heavy premiums to trade up. And on the flip side, it’s good to be on the other side of the equation, and trade down whenever the opportunity presents itself and the situation allows.

Speaking of quarterbacks, the RG3 trade is one of the most notorious in recent memory. To get the 2nd overall pick in 2012, Washington offered St. Louis the 6th and 39th picks in that same year plus two more 1st round picks, one in each of the subsequent seasons. According to the Jimmy Johnson chart, the trade represented (by NFL standards) a defensible bargain with a 211% annual discount rate. But in both the AV and M-T models the discount rate was incalculably infinite. The value that Washington offered in the present-year 6th and 39th picks alone exceeded the value of the 2nd overall pick. The future-year picks could not be discounted any further than zero. It’s as if Washington was paying St. Louis to take those 1st round picks off their hands.

I think the reason why teams overpay for picks is due to several factors. First, as Massey and Thaler demonstrated, team decision makers are overconfident in their ability to identify the players who will turn out well in the pros. Second, it’s very difficult for teams to intuitively judge the relative values of these picks and the result is a lot of uncertainty. Within that uncertainty, sellers need a large premium from buyers to make sure they aren’t losing a lot of value. But the biggest problem might have to do with the time-horizon of the decision making process. NFL teams appear to have the planning horizon of a starving crack addict given two weeks to live with a terminal disease, something I’ll get into in more detail in a separate article.

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