I was pointed to a recent Salon arti­cle about the “fresh­ness” of can­di­dates for Pres­i­dent. It made for an inter­est­ing read, indeed. Here’s the basic gist: since 1900, if you got elected to your first major office over 14 years ago, you won’t be elected Pres­i­dent unless you’re already Pres­i­dent. Years as Vice Pres­i­dent don’t count toward the 14 years.

The one excep­tion, Lyn­don John­son, became Pres­i­dent with­out being elected Pres­i­dent, which per­haps had some­thing to do with him being an excep­tion. Every other gen­eral elec­tion can­di­date with more than 14 years lost. We haven’t had an elec­tion since 1844 in which both can­di­dates would count as “stale”.

The idea behind the the­o­rem makes sense if you think about it. Fresh means excit­ing, and excite­ment is a valu­able tool to get peo­ple into the polling booths. It’s hard to see what’s mag­i­cal about 14 years, though, so I fig­ured I’d do a lit­tle sta­tis­ti­cal analy­sis on the the­o­rem to see if, in fact, there’s a cor­re­la­tion between length of time in major office and vote margins.

The first thing I noticed about the the­o­rem is the lack of sig­nif­i­cant data points. We’re talk­ing about 27 elec­tions in total, so a max­i­mum of 54 gen­eral elec­tion can­di­dates. With the incum­bents seek­ing reëlec­tion, though, the real num­ber of can­di­dates is a mere 38. How many of those can­di­dates count as “stale”, accord­ing to the 14 year rule? Ten of the 28 losers, and only one of the win­ners. At least the the­o­rem stands up to the ruda­men­tary analysis.

I started off with a sim­ple regres­sion, fol­low­ing the rule to the let­ter. The inde­pen­dent vari­able was a dummy vari­able of exceed­ing the 14 year rule, and the depen­dent vari­able was a dummy vari­able of win­ning the elec­tion. Here are the results:

R2=0.096

Coef­fi­cients P-​​value Lower 95% Upper 95%
Inter­cept 0.568182 2.5E-10 0.421735 0.714628
Stale? –0.38636 0.021643 –0.71383 –0.0589

This looks pretty good. There’s a 98% chance of cor­re­la­tion (the P-​​value is 1 minus the like­li­hood of cor­re­la­tion). Now, granted, this is a case of start­ing with a par­tic­u­lar obser­va­tion, and build­ing a the­o­rem around the obser­va­tion. So it shouldn’t be all that sur­pris­ing to find that the rule holds up.

How does the rule do when we add ear­lier elec­tions? Pretty poorly. Look­ing at the prior 20 elec­tions (going back to John Quincy Adams), nine of the win­ners were stale, accord­ing to the rule. Eight of those nine won against fresh can­di­dates. Only six of the losers were stale, one of whom was beaten by another stale can­di­date. A regres­sion using the same rules, but applied to these 20 elec­tions, shows no sta­tis­ti­cal significance.

OK, so maybe it’s the mod­ern media that is to blame here. Peo­ple in the faster mod­ern soci­ety tire of can­di­dates more quickly. If this is true, one would expect the mar­gin of vic­tory to be greater for fresher can­di­dates. Does this hold up? To find the answer, I used the “age” of the can­di­date as the inde­pen­dent vari­able, and the mar­gin of vic­tory as the depen­dent vari­able, and got this:

R2=0.013

Coef­fi­cients P-​​value Lower 95% Upper 95%
Inter­cept 10.59259 4.75E-14 8.514366 12.67082
Mar­gin –6.16972 0.403246 –20.8608 8.521369

A P-​​value of 0.4 is as bad as we got apply­ing the ear­lier rule to the 19th cen­tury. Not sta­tis­ti­cally sig­nif­i­cant at all. But, then again, it could be that the rel­a­tive fresh­ness mat­ters. That is, going against a less fresh can­di­date gives a big­ger mar­gin of vic­tory than going against a fresher can­di­date. So I took the “age” of the win­ner, sub­tracted the “age” of the loser, used that dif­fer­ence as the inde­pen­dent vari­able, and got a P-​​value of 0.97, nearly the max­i­mum value of 1, mean­ing essen­tially that there is no cor­re­la­tion at all that can be discerned.

How does it look if we go back to the 19th cen­tury? The answer might sur­prise you:

R2=0.27

Coef­fi­cients P-​​value Lower 95% Upper 95%
Inter­cept 0.000618 0.959679 –0.02398 0.025215
Year Diff 0.00265 0.000624 0.001214 0.004086

27% of the vari­a­tion in the pop­u­lar vote mar­gin can be attrib­uted to the rel­a­tive fresh­ness, with 99.9% cer­tainty of a cor­re­la­tion. But the big sur­prise here is that the coef­fi­cient is pos­i­tive. That is, in the 19th cen­tury, the less fresh the can­di­date, the more votes he got, albeit a mere 0.2% greater mar­gin per year.

The argu­ment I’d make here is that expe­ri­ence was con­sid­ered much more of a pos­i­tive back then. In most pro­fes­sional fields, this is the norm; the more expe­ri­enced you are, the eas­ier it is to rise to a higher level. Per­haps the “out­side the belt­way” sales pitch didn’t carry any weight until more recent years.

So what does this all mean for 2012? It seems that the expe­ri­ence fac­tor, which was some­what impor­tant in years past, has more recently become nearly irrel­e­vant. The rapid rise of Obama, Palin, and Bach­mann would cer­tainly sup­port this notion. But has it become a net neg­a­tive? The evi­dence doesn’t sup­port that at all. The 14 year rule looks more like a case of coin­ci­den­tal over­fit than any­thing else, like the rule we “dis­cov­ered” here a while back that showed all sit­ting Pres­i­dents whose last names ended in “N” were re-​​elected.

If this is true, then what can we con­clude? In short, there’s no such thing as a stale can­di­date, at least by the def­i­n­i­tion described above. And this is great news!!!! for Rick Santorum!!!!