January 19, 2015

Math Iz hard!

I almost posted this on my rant’s blog. But I’ve already posted there about people’s stupidity. More. Than. Once.  And this is baseball related anyways, so thought I’d just write about it here. 

Max Scherzer just signed a 7 year / $210 Million deal with the Washington Nationals. Congratulations to him, the organization and Mr. Boras on this signing. Right away I saw people on twitter and message boards talk about how $30 M per year was way more than Lester and he’s probably not worth that much more etc. A while later, started seeing posts saying since the money is deferred (he’s getting $15 Million per year over 14 years), the NPV of the contract is actually less than the 6/$144 he turned down from the Tigers last year, or Lester's money. And he’s signed for 7 years, not 6 so it’s actually more of a bargain.
Well, unfortunately, you need to be consistent when you try to calculate the time value of money. You can’t say that Scherzer’s deal is “only” worth $130 Million (or $150 or $170 depending on what discount rate you use in your projections), but Lester’s is worth $155. You know why? Because Lester isn’t getting all his money tomorrow. It’s not “deferred” with him getting some long after he’s retired, but he’s still getting it spread out over six years.  The Tigers also weren’t paying Scherzer a $144 M lump sum payment the day he signed either.

So… is the $210 Million really less than what it sounds? Yes, of course it is.  How much less depends on your discount rate assumptions.  But keep in mind that every multi-year deal (and for that matter single season deals too!) are always worth less in today’s dollars than the announced amount.

Here is a chart with some comparisons. Two sets of numbers, one assuming a conservative 3% discount rate, and one with a more aggressive 7%.

                                Discount = 3%                    Discount = 7%
Contract               NPV       Per Year               NPV       Per Year
Scherzer $210    $169       $24.2                     $131       $18.7
Scherzer 6/144     130        21.7                        114         19.1
Lester $155          140        23.3                        123         20.5

Some interesting observations: If the actual discount rate is 7% Scherzer would have made more per year taking last year’s rumoured 6/$144 offer. Also Lester’s deal is worth more per year and only $8 million less in total.  But at 3%, the offer he took pays him the most per year and in total. I'm not an economics expert, and I don't know what the right assumption is to discount future payments. That's left for people who are way smarter than me. And that's the point of this post:
Otherwise smart baseball people who are VERY good at math and statistics and calculating WAR, wOBA, xFIP etc., don't understand the basic economics behind the timevalue of money, but THEY STILL INSIST ON TALKING ABOUT IT! If you are a baseball analyst, stick to talking about baseball analysis. Don't start talking about related subjects you don't fully understand or you'll just add to the misinformation out there.  

Do I think Scherzer's deal is better/worse than other comparable pitchers or what he could have had last year?  I don't know. I only know enough that you can't just compare the raw numbers and come up with a conclusion. 

No comments:

Post a Comment