Earlier this morn, after the author had cracked for himself some eggs and roasted up a homestyle country breakfast, the brazen alarum bells of domestic politics sounded. According to Pro Football Talk, the Browns have signed Joe Haden to an extension through the 2019 season, with $22M guaranteed and an additional $23M guaranteed in case of injury – in short, Joe Haden is guaranteed $45M.
In this offseason, the Browns have added substantial help to the secondary, adding, in the first round of the draft, Oklahoma State cornerback Justin Gilbert and, in free agency, Ohio State safety, known by no one as Margrave Whitner of Hits. At this point, the Browns have – to the shock and awe of all – assembled what is on paper one of the best secondaries in the league in the next several years. And while a great secondary on paper isn’t a guarantee of success, it’s also not the guarantee of mediocrity that the Browns have had for over a decade. Browns fans are allowed to feel #blessed for at least few minutes.
Yet while the move eclipses Richard Sherman’s deal as the most lucrative guaranteed deal for a defensive back thus far this offseason, other premier cornerbacks in the league have their eyes on even bigger amounts. In response to Haden’s extension, Arizona Cardinals’ cornerback Patrick Peterson puts forward his own contract demands – demands not only outrageous, but wholly unprecedented.
Peterson’s demands are shocking. At first glance, it appears that he’s expressing shock at Haden’s $45 million guarantee – a large number for any player, tremendously so for a non-quarterback. Such a response would only be reasonable, since it bodes extremely well for Peterson’s own upcoming contract talks.
Yet this interpretation (Tweet as Reaction) belies the true purpose of the post – Tweet as Negotiation Foray. In Patrick Peterson’s Tweet, we see a contract demand far outstripping any contract demand in the History of the Earth.
Patrick Peterson, in Tweeting out ’45!!!!!’ is not demanding $45 million – but rather, 45 quintuple factorial, a demand that, if met, would indebt the NFL to Patrick Peterson for centuries to come.
To put this demand into perspective, 45 factorial (presumably, in dollars) is a tremendously large number. According to the author’s trusty Excel 2000, 45! is equivalent to 1.1962E+56. 1.1962 times Ten to the Fifty-Sixth. The difference between 1 dollar and 1E+56 dollars is the difference between Planck’s constant – the smallest unit of energy that can exist – and the sum total of solar energy that reaches the surface of the Earth on a daily basis. That gulf is the difference between one Jr. Bacon Cheeseburger and the first possible understanding of Patrick Peterson’s request.
In reality, however, Peterson’s demands are not so ambitious. Normal Factorials follow the following method:
5! = 5*4*3*2*1 = 120
In contrast, double factorials take a different tact:
5!! = 5*3*1 = 15
The additional exclamation mark increases the gap between the numbers – whereas single factorials decreased by one, double factorials decreased by two – multifactorials increase the gap between numbers based on the order of the factorial (or number of exclamation marks). Therefore, the addition of an extra exclamation mark does not mean that we should interpret his contract demands as (((((45!)!)!)!)! – an unfathomably large number, a number so large that faithful Microsoft Clippy has instructed the author to seek psychological care. Rather, we should interpret Peterson’s contract demand as a quintuple factorial, wherein:
45!!!!! = 45*40*35*…*5*1
The last function, due to the rule of factorials, dictates that 0! is equal to 1 – hence, a multiplication by one rather than zero. Therefore:
45!!!!! = 708,750,000,000
Patrick Peterson is not asking to become Eternal God of the Multiverse. In demanding ’45!!!!!’ dollars, Patrick Peterson demands less than $709 Billion in exchange for his services. The difference between his requested figure and the crisp Washington that glares at you is no more than the difference between a One Dollar Bill and All Of Saudi Arabia’s 2013 GDP.
Of course, Peterson’s demand of $708 Billion is not a hard number, merely an opening salvo. The Cardinals are likely to fire back with their own contract number, and in the end, it’s likely the Cardinals and Peterson are likely to come to an agreement in the range of only $300 Billion guaranteed. Peterson will become the wealthiest human in the history of the universe, and the Cardinals will lock up one of the top ten cornerbacks in the league. A fair exchange, it seems, but one wonders whether Peterson was right to deflate the market by requesting a quintuple factorial as opposed to a single – or even double – factorial.
In light of this negotiation tactic, however, the Browns should feel extremely relieved they locked up Haden for only $45 Million guaranteed. In light of the move’s fall-out, locking up Joe Haden for $45M guaranteed through 2019 is an unequivocally good move for the Browns, both from a talent perspective, and from the perspective of understanding the future market for cornerbacks.