Schaeffer's Outside the Box Blog
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Say you're a fund manager and you've had a nice year. Call it a very nice year. Not only have you beaten your benchmark, you've risen to near the top of your peer group. If the last month breaks right, you may actually top your group.

So what do you do the last month? Leverage up and/or completely change your mix of stocks so as to generate both some potential beta and variance? Probably not. Well, unless you're Screech [Powers'] cousin Jim Harbaugh and you coach the 49ers.

I was thinking about Harbaugh's recent QB change from Alex Smith to Colin Kaepernick. Setting aside the very small sample size of the data, Harbaugh is truly the NFL equivalent of a winning portfolio manager making a rather questionable swing for the fences.

NFL coaches are notorious for their misplaced risk-aversion. It statistically pays off to go for fourth downs aggressively, pass more often than the typical team chooses, and try more onside kicks. But it doesn't pay to just blindly become more aggressive. For example, onside kicks are successful something like 30% of the time -- if you catch the other team by surprise -- but 5% if they're expecting it. So clearly, if you tried an onside kick every time, your opponents would put their "hands" players to defend against it, and you'd drop your success rate. It's a version of Game Theory in action, in fact.

Harbaugh is one of the better coaches in the league regarding his risk/reward management (well, other than agreeing to the Saved By the Bell cameo). That being said, I believe he underestimated the downside of variance in a situation where you already have a winning hand.

How can we estimate variance in a QB? It's tough when there's a tiny pool of data to work with. Kaepernick's career has spanned three games as a starter. Anecdotally, though, they've spanned the entire performance spectrum. He was terrific in his first start versus the Bears, one the NFL's best defenses. He was then ehh versus the Saints, one of the weakest defenses. Then he was pretty poor against the Rams.

Even with the small sample size, though, I think we can get a sense what they've gained and lost with the added variance. Here's AdvancedNFLStats listing all the 2012 QBs. If you sort by AYPA on the far right, you can rank them by Adjusted Yards Per Attempt (this is yards per attempt, adjusted for sacks and a 45-yard penalty for interceptions). Lo and behold, Kaepernick currently leads the league. It's a pretty good proxy for quality of play, as the next three guys on the list are Tom Brady, Peyton Manning and Robert Griffin (RGIII). Alex Smith ranks 11th here.

But alas, it's not the only proxy. Every NFL play starts and ends at a distinct state, defined by down and distance and time on the clock. Thanks to the AdvancedNFLStats database, we can easily convert every "state" to an expected points total (defined as the average points of the next score in the game; it can be negative if the opponent is expected to score next). We can add these expected points (from before to after the play) and then divide by the number of plays and determine the expected points added per play for each QB. Sort here (EPA/P) and we find Kaepernick ranks 15th at 0.14, with Smith 17th at a virtually identical 0.13.

Finally, let's look at Success Rate (SSR%). A play is defined as "successful" if the expected points are greater after the play. Smith ranks 7th -- with a 51.3% success rate -- while Kaepernick sits at 15th, with 48.4%.

What's it all mean?

The numbers certainly bear out everyone's anecdotal observation that Kaepernick gives you high reward with high risk. His AYPA looks great, but it's very likely to regress with time. And in the small sample size, he's not using those extra yards to produce any extra points over Smith (or added Win Probability, for that matter). That all comes at the cost of fewer positive plays, as measured by success rate.

Think of the Niners as a stock that carries a similar price with the two QBs, but Niner options carry higher implied vol. with Kaepernick. That increases the value and delta of out-of-the-money (OTM) calls, implying a higher probability of winning a given game as an underdog, but also the value and delta of at-the-money (ATM) puts, implying a higher probability of losing as a favorite. But if you're already the better team in most instances and the new QB isn't appreciably adding to the price of the stock itself, where's the payoff?

A high variance strategy has its benefits, of course. If you have a team of middling talent, it makes perfect sense to try it. There's little downside turning an 8-8 team into an 8-11 team, but if you turn it into an 11-8 one, you're in the playoffs. The 2011 Tebow Broncos are a decent example of a weak team riding the crest of variance to an unlikely division title.

Look, Kaepernick's ultimately the more talented QB and I hope it works for them in at least the next three weeks -- I have him in Fantasy football and it's playoff time. But in the real world, it's a really high stakes gamble that he gets there in the next month, and it's very debatable the Niners gain enough to make it worth the risk.

Disclaimer: The views represented on this blog are those of the individual authors only, and do not necessarily represent the views of Schaeffer's Investment Research.

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