## Risk-Seeking Behavior?

Michael N. wrote me Sunday to suggest that coaches aren't so much risk-averse as they are simply operating without any sound knowledge of the odds. Maybe it's not risk-aversion as much as a lack of clear utility information. Maybe they're just as risk-seeking as they are risk-averse, erring on either side of the equation depending on the question asked.

Mike makes risk-seeking pretty clear with an example: "You'd think a person would pay \$1 for a 1% chance to win \$100. But they don't. They're willing to pay \$5.50! For a 10% chance of winning \$100, they're willing to pay \$18.60."

I've been looking for examples of risk-seeking behavior in the NFL for years, and although there are a few examples of coaches going for it on 4th down when they probably should kick or punt, these examples are extremely rare. In fact, coaches are so reliably risk-averse on 4th down, I use such counter-examples to identify bugs in the algorithm or errors in the NFL's data.

So I thought I'd throw it out to the smartest readership in football--you guys. Are there any examples of consistent risk-seeking behavior in football? What about in all of sports--soccer, cricket, rugby?...I know there are some diverse fans out there.

What about in finance?

### 48 Responses to “Risk-Seeking Behavior?”

1. Joshua Perry says:

Mike McCarthy throwing a pass with a punter instead of Aaron Rodgers on 4th and 8.

2. BIP says:

The first thing that came to mind was the hit-and-run in baseball, especially when managers put it on with a slow runner on first base.

3. Anonymous says:

I'm curious about the basis of the Mike's claim: "You'd think a person would pay \$1 for a 1% chance to win \$100. But they don't. They're willing to pay \$5.50! For a 10% chance of winning \$100, they're willing to pay \$18.60."

Where exactly does this data come from? Just interested.

-Allen

4. Anonymous says:

Allen, I'm guessing he is thinking about people playing the lottery or gambling in casinos.

Risk-seeking coaches: how about college coaches that run up the score? They may not be reducing their win percentage that much, but they may be reducing it a tiny bit in order to make the final score look a little bit better for the sake of getting ranked higher in the polls.

5. Kulko says:

I think I remember reading an artical somewhere showing that base stealing has a net negatice expected return, but its still is use i Baseball as far I am aware.

@ Anon The amounts sound very high, but I think the overall assumption is correct.

Of course it depends of the value 100\$ have for me, but in general I would say, my price is at least \$1.20. I think the assumption that the price should be \$1 is fundamentally incorrect and shows the shortcoing of current decision maing theories.

6. mattieshoes says:

Finance has unlimited upside. You can only get one win in one game.

7. Anonymous says:

I can explain this perplexity using principles I learned from http://www.cbsnews.com/8301-505123_162-57454375/the-link-between-stocks-and-lottery-tickets/.

"People can be risk-averse or risk-tolerant depending on the level of risk involved and on whether the gamble relates to becoming better off or worse off. This explains why the same people may buy both insurance policies and a lottery tickets."
...
"Investors have a preference for securities that exhibit positive skewness (values to the right of [more than] the mean are fewer but farther from the mean than are values to the left of the mean). Such investments offer a small chance of a huge payoff (winning the lottery). Investors find this small possibility attractive. The result is that positively skewed securities tend to be "overpriced" -- they earn negative average excess returns."

---
People (in any domain) are consistently risk-seeking in situations like Mike's example described -- where there is "positive skewness." I think situations that offer positive skewness are rare in football because I'm struggling to think one up. But if you can think of a situation in football does, I wouldn't be surprised to see consistent risk-seeking behavior there.

-Allen

8. Anonymous says:

Regarding my first comment about Mike's example-- I don't doubt it's veracity. I just love this stuff and wanted to know where he got those specific numbers from. Anyone know?

-Allen

9. Willy Hu says:

What about teams kicking away from Devin Hester? For example, I think the Bears' average starting field position against the Lions was somewhere around the 40 yard line. It seems like coaches are basically saying "I can afford to gamble and give the Bears good field position, thereby giving up the points later, as long as I don't give up the points now". According to your nifty calculator, the difference between starting at your own 40 yard line and your own 20 yard line is about 1.1 expected points. Now I have no way of knowing how to weight 'Devin Hester's punt returns' into this, but it seems like as the possessions accumulate, coaches end up leaving more and more points on the table. Hell, Detroit punted 8 times that game--that's basically the margin of victory!

10. williams_482 says:

In baseball, many of the "small ball" strategies (stealing bases and the hit and run, as mentioned earlier) would be considered high risk, and you could argue the same for an intentional walk (depending on the situation). I think these are good examples here, given that they are usually used too frequently. Alternately, the sacrifice bunt is perhaps the most frustratingly overused baseball maneuver but is definitely a "low risk" one (greater chance of one run, net reduction in total runs scored), so this is not just baseball managers being gamblers while football coaches are overly conservative.

11. SlackerInc says:

First, a semantic nitpick: isn't it in a sense risk-seeking any time a strategic or tactical decision is made which is less than probabilistically optimal? By that standard, we see such decisions all the time--as endlessly catalogued on this blog, but with the most recent example that comes to my mind being the decision by the Arizona Cardinals coach to kick a FG on 4th and 2 from the 12 yard line, down 24-0 at the end of the third quarter.

That nitpick aside, using a more colloquial definition of "risky", it seems to me there was a game Sunday in which a coach went for an early onside kick (maybe Detroit vs. Chicago?).

You asked about other sports. I would love to see some probabilistic analysis of tennis, my favourite sport. Many times I have heard commentary to the effect that when a player is already up a break of serve in a set, s/he will feel free, when returning serve, to "take a chance on going for a winner".

There is so much to unpack there. What is it that stops a player from "going for it" on a return when they are still on serve? Particularly if both players are strong servers, there is no pressure on the returner as the server is expected to hold anyway. And why is it not the player who is *down* a break of serve who should be "taking a risk" (increasing variance at the cost of a decrease in the average likelihood of breaking serve), especially if against a strong server who is difficult to break given a conventional game plan?

A "risk" I always think tennis players *should* take but rarely see is to play the game score, more than the set score, particularly in a 40-0 situation. The server, especially if they have a strong first serve that rarely gets returned effectively but only a mediocre second serve, should resolve at that score to go for an overpowering first serve up to five consecutive times if necessary. If all five are missed (unlikely), or they are made but the returner manages to win two points in a row anyway (also unlikely), the server will still be up 40-30 and can then hit a more conventional second serve and play more conservatively from there. On the other side of the ball, being either down 40-0 or up 0-40 (triple break point) seems again like a good time to swing freely, going for high variance attempts at winners, especially against a strong server (or just a player who is overall significantly higher ranked).

I don't however see a lot of evidence that players "play the score" as they should, although maybe they are doing so in subtle ways that are hard to spot.

12. Anonymous says:

If you want to think of situations where there is a very tiny chance at a very high reward in football, just look at situations where a team's win probability is 0.01. For instance, a team is down by 10 with 1 minute left to play and no timeouts. The only way they can win is by scoring very quickly, recovering an onside kick, scoring again, and possibly going into overtime and scoring there as well.

The only thing is it's hard to say what exactly that team is risking by continuing to play instead of just letting the clock run out so the game ends. The only things that come to mind are injuries and playing time for the second stringers. I have seen situations where the starting players were pulled when a team was losing badly, but normally only when it's truly hopeless (down 3 scores or more near the end of the game, as in the Panthers' game against the Giants earlier this year). It's more common to see starters pulled on the winning side of a blowout.

13. MFLoGrasso says:

Brian,

I know it's not a common practice in football, but an earlier poster mentioned the surprise onside kick.

Another scenario in another sport is in hockey when teams pull their goalie for an extra attacker. Sure, they're already in a desperate situation (usually down a goal with 1-2 minutes left or down 2 goals with 2-3 minutes left), but I can't recall many situations where it actually succeeds in leading to a goal for the trailing team. More often, I would venture that it leads to a goal for the leading team (thus expanding their lead and making victory about as certain as can be).

In basketball, isn't the three-point shot effectively a risk-taking proposition, especially when it's the drawn-up play? You are intentionally taking a shot that is less likely to go in than one close to the basket with the hope of a 50% greater payoff (three points instead of two). From that perspective, any shot other than a layup or dunk is risk-taking, even moreso when it's not beyond the three-point line.

14. james says:

If risk seeking is favouring a high variance option with a low average return over a over a low variance option with a slightly better average return then I cant think of any in serious sports.

All of the high variance tactics used at the end of a game (Hail Mary, pulling the goalie, deliberate fouling, bringing the outfield in with a man on 3rd less than two outs bottom of the 9th in a tie game) are risk neutral in that they are presumably increase the chance of winning in the long run even if they will often lead to bigger losses when they backfire.

In soccer pulling the goalie is very rare and usually only happens in knock-out compeitions. I've nevcer seen it happen in a league competiion (other than on the last day of the season where a team knows it must win or draw) as goal difference is always the first tie-breaker.

In rugby I've never seen an analysis of whether a team should kick a penalty (low risk 3 point reward) or instead opt for a scrum 5 yards out or kick to touch for a line out near the tryline(high risk but 5 or 7 point reward). I suspect teams kick penalties too much in the same way that teams punt of kick a FG too much in Football.

15. Alex says:

http://en.wikipedia.org/wiki/Prospect_theory

16. dlr says:

Brian,

In finance there are many potential examples of risk-seeking but the evidence is never quite conclusive. Predictably low risk-adjusted returns to very highly indebted companies and very-low priced stocks show evidence of risk-seeking (lottery ticket type situations that are overpriced by the market). The momentum premium (short-term excess returns to stocks which have gone up) is very robust and can also be seen has having a risk-seeking component. There are also studies using stock options and real estate that show strong evidence confirming the false reference point idea -- i.e. that investors become risk-seeking after experiencing a loss.

I don't see many good examples of lottery ticket type risk seeking in Football coaching. This may be because conventional wisdom warps the perceived expected utility, or it could be because coaches motivations are more complex than gamblers or financial market participants: reputation is a part of job security. An interesting test might be isolating the play calling tendencies of teams who deep longshots but not statistically eliminated to make the playoffs, as opposed to teams merely down a lot in a single game. You could then control for warped expectations by comparing groups, but that would require additional adjustments to the extent that wins and losses had different expected utilities for the longshots versus non-longshots.

Team and GM based risk-seeking may be easier to unearth, perhaps in the false reference context. Are teams with a history of losses more likely to make risk-seeking moves than similarly situated teams without such a history? Risk seeking might be hard to define in this context, but maybe trading many-for-one like the Herschel Walker or RG3 trade could be a starting point. Another false-reference possibility is to look at the behavior of coaches within games who have either (1) blown leads within the game or (2) lost their previous game unexpectedly. This could be expected to create risk seeking from loss experience and again could be compared so as to control for absolute utility biases.

17. Steve Winkler says:

There are quite a few examples in finance. I'll leave out the many where someone is playing with other people's money as those aren't true risk seeking but rather principal-agent problems. The most common risk-seeking behavior occurs when people allow their personal portfolios to hold concentrated positions in individual stocks or single bond issuers. Generally the problem is a misunderstanding of the risk being taken and ignorance about the virtues of diversification. As this generally hinges on not understanding the risk rather than just accepting riskiness, this may not fully be an example except in the cases where investors are knowingly taking these chances.

18. Eric says:

In regards to the baseball strategies (bunt, steal, etc.)- is that consistently risk seeking behavior? Those strategies do not usually provide a positive payoff (increase in WP), however that's not what the managers think. They don't know the percentages the same way football coaches don't know the percentages. Or they've been told the percentages and choose to ignore the data. So baseball managers don't think they are utilizing high risk strategies.

19. Rob says:

I can think of one in basketball. A team is down by 2 points with very little time left on the clock, say 10 seconds. Some teams design a play to take a 3 point shot and go for the win instead of a 2 point shot.

Now, statisticaly, the 3 point shot is a more effecient shot in basketball than a long 2 point shot, but not than a close in 2 point shot. It seems a little risk seeking to me when coaches try for the 3 (and the win) instead of a close in 2 and the tie.

20. MFLoGrasso says:

Rob,

That seems like the perfect counter-example to when a football team down by 7 scores a late touchdown and has to choose between the (almost) certain tie or the much less likely immediate win (or, a team down by three late near the goal line either has a fourth down or is certainly at the last play of the game...FG attempt or go for the TD?). In football, it nearly never happens, whereas in basketball, it happens regularly enough to be considered. My thoughts on why this is more likely in basketball than in football:

1. If the three-pointer isn't available, a two-point shot may be a viable backup as the play develops. In football, you can't go for the win then change to shoot for a tie in the middle of the play.
2. The odds are different. Ball on the two-yard line, a kick has over a 99% success rate, but scoring a touchdown in one play has shown about a 40% success rate on average. In basketball, even a layup may be contested, making it a less-than certain proposition.
3. In both sports, if you go for the tie, you still need to then make it through overtime. Knowing nothing else, that's a 50-50 shot at winning. So, speaking to point 2, the attempt at a tie needs to be more than twice as likely to succeed as the attempt at an immediate win to be preferred. In football, this is so. In basketball, unless you have a dominant center in the prime of his career or absolutely nobody who can make a three-point shot, I can't imagine this to be the case.
4. The football season is 16 games long. The basketball season is 82 games long. Each football game on its own has over 5 times the impact that each basketball game has.
5. Also, in football, only 6 out of 16 teams in each conference make the playoffs, and outside of the division winners, only 2 of the remaining 12 in each conference make the playoffs. In basketball, 8 out of 15 teams in each conference make the playoffs, and outside of the division winners, 5 out of the remaining 12 in each conference make the playoffs. Combine this point with point 4, and each loss in football has a much more dramatic impact than a loss in basketball to a team's success during the season as measured by making the playoffs.

21. MFLoGrasso says:

By the way, to the fifth point in my previous post, if all teams are equally-skilled and equally-coached (please grant me this obviously over-simplifying assumption for the moment), a team's probability of making the playoffs is:

P(playoffs) = P(win division) + (1 - P(win division))*P(wild card|non-division winners)

For the four major North American sports (yes, I still consider hockey a major sport), in order from easiest to qualify for the playoffs to toughest to qualify for the playoffs:
NBA/NHL: P(playoffs) = 1/5 + (4/5)(5/12) = 1/5 + 1/3 = 8/15 = 0.533
MLB, AL West: P(playoffs) = 1/4 + (3/4)(2/11) = 1/4 + 3/22 = 17/44 = 0.386
NFL: P(playoffs) = 1/4 + (3/4)(2/12) = 1/4 + 1/8 = 3/8 = 0.375
MLB, AL East/AL Central: P(playoffs) = 1/5 + (4/5)(2/11) = 1/5 + 8/55 = 19/55 = 0.345
MLB, NL East/NL West: P(playoffs) = 1/5 + (4/5)(2/13) = 1/5 + 8/65 = 21/65 = 0.323
MLB, NL Central: P(playoffs) = 1/6 + (5/6)(2/13) = 1/6 + 5/39 = 23/78 = 0.295

22. norm says:

RG3 and Ricky Williams draft day trades come to mind.

That and pretty much any FA signing.

23. Trent says:

I have a finance-related situation that is similar to the question of risk seeking v.lack of knowledge that you posed for coaching.

Any investment in a mutual fund is actually risk-seeking behavior because buying ETF shares in the S&P 500 will produce the same, if not better, returns with less risk. From 1993 to 2003, only 0.03% of US mutual funds produced returns over the S&P 500, and there are probably even fewer today. In actuality, investors are really loosing money because they pay have to pay a management fee and those funds usually have to take on more risk to make the same returns.

I was shocked to learn this, and dismissed it at first. After all, there are hundreds of billions of dollars invested in equity mutual funds each year, and there's no way that many people could be that wrong, right?

Anyways, it turns out that its true and it begs the question, is this an example of a lack of knowledge or true risk-seeking behavior?

24. MFLoGrasso says:

Trent,

I think that is closer to a lack of knowledge in many cases. Consider that many investments in mutual funds are small amounts by many small investors through their banks/retirement accounts, who filter their clients to a small number of funds they have predesignated as the only ones they offer (often managed by the bank or administrator of the retirement account, a classic principal-agent dilemma).

25. Anonymous says:

I think we're forgetting about the defensive side of the ball with the risk seeking discussion. Blitzing is a risk seeking behavior. The risk averse counter example is playing a soft zone defense to keep the other team from scoring too early.

On offense, throwing the bomb is risk seeking.

For personel decisions, playing a rookie QB when you have a high priced veteran would be risk seeking (Tom Brady vs. Drew Bledsoe, Russell Wilson vs. Matt Flynn, the movie "Any Given Sunday")

26. Anonymous says:

Trent,

I think what you may mean by your .03% number is that .03% beat the S&P 500 every year or every quarter.

From 12/31/93 to 12/31/03, there were 655 open end mutual funds that could be considered "S&P 500 like". The Vanguard 500 Index fund was built to precisely track the S&P 500. Of those 655, 203 beat the Vanguard 500 and 451 did not. The numbers are not flattering to the industry, but with roughly 1/3 outperforming it is much better than .03%.

source: Morningstar

27. Chase Stuart says:

Three thoughts.

-- Regarding the examples in the OP, I disagree with the premise. Yes, some people will be willing to spend \$18.60 for a 10% chance at \$100, but lots of people wouldn't be willing to spend \$5 for a chance at \$100. You can't just look at the far right end of the curve.

-- The RG3 was the first thing that came to mind when discussing risk-seeking behavior, which was already pointed out.

-- Also agree that blitzing is risk-seeking behavior.

28. Andrew Meyer says:

I do think there's one sport where the player's rewarded for risk-seeking as opposed to risk-averse behavior. That sport is tennis. Actually, it's really only 1 shot in tennis where it's true, and that's on the serve.

Tennis, like most sports is about eliminating errors and giving randomness/luck/momentum or whatever you call it, the best opportunity to go in your favor. The one place that's not true is the serve, especially for big servers.

If you have a big serve, there is an immediate reward for hitting an ace. Some might say that people go after big serves, because you have a second serve, but there are two places this falls down.

There is the percentage of first serves in and there's the percentage of points won on first serve. It behooves a player to have both of those as high as possible. However, if you're going to let one of those drop, and you have a big serve, you're better off being taking the risk and going for the big serve.

This is true to a lesser extent on the second serve also. If you're more aggressive with your serve, your opponent can do less damage with their return.

I don't want to write a thesis on it, but I believe the way the service game is structured, if you have a good serve, you are better off being risk seeking than risk averse. It's the structure that drives that particular outcome.

29. Michael Beuoy says:

As a Colts fan, I remember Jeff Fisher trying mutliple onside kicks against the Colts in a 2004 game. In the first half. Some googling turned up this article, with some interesting quotes:

JEFF FISHER'S TITANS WERE ON THE VERGE OF BECOMING IRRELEVANT. THEN THE RISK-LOVING COACH MADE SOME RADICAL CHOICES- STARTING WITH LENDALE WHITE AND VINCE YOUNG

From the article:

Actually, the Titans' balls-to-the-walls mind-set comes from a time when they had nothing to lose. In December 2004, Fisher's team officially was a mess. Following two Straight playoff seasons, Tennessee had fallen to 4-7. With their defense decimated by injuries, the Titans faced a road game against the red-hot Colts offense. After two allnighters, Fisher and his staff came to a conclusion: We have no chance of winning unless we roll the dice. "We thought, Why not just onside kick it?" says Fisher. "So we did. And we did. And we did."

The article has a timestamp of July 2012, but it looks to date from around 2007.

30. Philip Kendall says:

Pulling your goalie in hockey has already been mentioned.

The one other example I can think of is in first class/Test match cricket, where matches are time-limited - you will not uncommonly see one team declare (voluntarily end their innings early) to give themselves a chance to bowl the opposition out, thus converting a virtually certain draw into a situation where both teams have a chance of winning.

I'm sure there are lots of board game examples of this; doubling in backgammon instantly springs to mind.

31. Martin says:

Exampels of high variance (risky) choices I can think of:
Soccor: pulling the keeper when down one goal on a conor.
Handball: basiclly the same as situation as hockey, except 31-30 games is very likely, so at least on the surface, it seams more likely to succed. the court is the same size as basket,and the ball is easy enough to throw into the goal from your own goal.
All endurance based sports: When forcing the tempo. You don't know of you hit halfway through. The difference between that and 4th down in NFL is that here, the reaction is: "no guts, no glory," while in the NFL, it's :"why did you do that, you have no confidence in your D, etc."

32. Anonymous says:

My guess is that the Broncos are doing so well exactly because they were playing from behind so much this season....so they had to take risks. Hard to quantify though.

JudoJohn

33. Marver says:

Philip - Doubling in backgammon is not a losing proposition unless you're doubling poorly. (The same applies for accepting the proposition of a double.) Surely poor doubles happen professionally, but nowhere near common enough to qualify for what Brian is talking about.

34. Anirban Mukhopadhyay says:

Philip Kendall already mentioned declarations in cricket -- ending your innings early to get more time to turn a draw into a win. There are also certain players who bat with minimal concern for defense (e.g., Shahid Afridi, nicknamed Boom-Boom), and bowlers who try to get wickets despite the possibility of conceding runs (Lasith Malinga).

Some colleagues of mine just published a paper showing that social exclusion leads to increased financial risk-taking ("Show me the honey!": https://www.jcr-admin.org/pressreleases.php?issue=54).

And speaking of board games, how about Risk itself? :-)

35. probable picks says:

It’s unfortunate that I’m only getting to comment on this now, because what I’m about to share with you will (hopefully) change your thinking about risk adversity. A year ago, Ole Peters pointed out a fundamental flaw in economics regarding the risk and reward trade-off.

Paper here: http://arxiv.org/pdf/1011.4404v2.pdf

Good summary here: http://rick.bookstaber.com/2011/10/crack-in-foundation-error-that-has.html

I highly recommend reading the paper, but I will do my best to summarize, and will do so in the context of gambling for ease of understanding. To further simplify, I will use a linear utility function with respect to wealth, because all of the analysis on this site seems to imply that a linear utility function is rational in football, in a sense that teams should be maximizing their chance to win.

Economics has long maintained that you should take the action with the highest expected utility; the action with the highest arithmetic mean. This is called the ensemble approach, because it supposes multiple parallel universes that could happen, of which we will experience one. So, in the context of gambling, you would choose the bet that maximizes your expected wealth (with a linear utility function). However, Peters shows why this is flawed reasoning (unless we expect to die just after the event). Instead of an ensemble approach, the correct approach is a time series one. This means choosing the option with the highest expected geometric mean. This will lead to different choices than the ensemble approach for any process that is not ergodic. In the context of gambling, this will look like risk aversion, because the rational gambler will avoid going broke at all costs, even if he has something that looks like it is nearly a sure-thing.

To give an example, suppose a gambler has \$10 total wealth and is offered a bet that he knows with certainty to have exactly a 70% chance of winning. The bet returns double the wager amount if it won. He also has no other uses/opportunities for his money at this moment, but may have opportunities again in the future with unknown probability. We’re still assuming a linear utility function, so using the ensemble approach the rational decision is to bet his full \$10 to maximize his expected wealth, but has a 30% chance of going broke. Using a time series approach, he would choose to bet \$4. To get this, you search for the optimal bet amount by maximizing the weighted geometric mean of the expected end states using the equation found here: http://en.wikipedia.org/wiki/Weighted_geometric_mean

Under the traditional economics philosophy, a gambler betting \$4 would be seen as irrational given his linear utility function. But regardless of the shape of the utility function, choosing the action with the highest geometric mean is the only strategy to maximize his wealth over the long run.

Here’s how it might apply to football: a coach believes that he will have to make multiple tough decisions with risky choices over the course of the game. Choosing risky options early and often can get his team into a deep hole quickly (the equivalent of going broke for the gambler). They should choose the option with the highest expected geometric mean, not the highest expected arithmetic mean. As a result, they will often appear to be less rational using the ensemble approach than they actually are using the time series approach.

The one wrinkle is that in a sense the head coach does “die”at the end of the game. So it would seem that the rational thing to do would be to take fewer risks earlier in the game when failures have a chance of compounding over the length of the game (don’t go broke too early), and then take more risks as the end is near (and score differential doesn’t matter, just win or lose, so don’t worry about high risk/high reward plays if you’re behind). So it seems that the rational thing to do is to move from a time series approach toward an ensemble approach as the game moves on. And in fact, that does come closer to what we actually see.

36. Ropke says:

In curling, the skip with the hammer will often choose to score 0 points rather than 1 point, depending on the situation, because it makes it far more likely that s/he will score multiple points (and far less likely that the opponent will score multiple points) in the following end.

37. Anonymous says:

I don't understand what is meant by "risk aversion" here. If we are talking about the context of a football game, strictly speaking, there should be no notion of risk aversion or risk seeking - for every decision, there is one that maximizes the probability of winning. The other decisions are suboptimal. Of course, determining which decision is best is not always easy (and may involve some subjective assessments).

This is unlike finance where the units are money and you can tradeoff expected money for downside risk. Football is zero sum.

So when we say "risk aversion" in the context of the decisions of coaches, what exactly is meant? Are we talking about their incentives and job security, as well as how they will be judged?

38. Jared Doom says:

I think specific individual players will often exhibit risk seeking behavior - consistently over their careers.

Specifically on defense more aggressive/risk-seekers get more statistical glory - for example a cornerback that keeps the QB from throwing his direction receives no credit for +EPA, interceptions, tackles, passes broken up, etc. See Nnamdi Asomugha. Nnamdi has had the highest ratio of (snaps in pass coverage) / (balls thrown at), by an impressive margin, for the 2011, 2010, 2009, and 2008 seasons.

- Defensive backs tending to try to jump a route & intercept may be risk-seeking, or a DE going for the strip+sack rather than only the strip. Guys going for the big hit instead of avoiding a missed tackle.

This is one possible problem I've thought of with your measuring individual defensive player performance by "+EPA" only. If a defensive player is a risk seeker then their EPA / play distribution would be a lot wider than a "risk-neutral" player, so if you're only showing the positive plays, they'll tend to be more positive, but it may be hiding that the negative plays are much more negative.

- Brett Favre - I would not be surprised if his ratio of throw-aways to interceptions is < 1.0. If you remember he would also often do ridiculous little shovel-pass things in very tight windows, or make extremely risky throws while being pulled down by a defender.

- Fast/Quick RBs: Chris Johnson, Jamaal Charles, Barry Sanders, etc. I know Barry was known for the amount of negative yardage runs he would rack up, and I've seen both CJ0.7K and JChars cut runs back all the way across the field (occasionally with success). Having said that I do remember you having an article noting the lack of variation b/w running back YPC distribution, but my instincts say, of backs with 4.0+ YPC, these guys are up there in % of runs losing yardage.

- Fast WRs / return guys running backwards, cutting all the way back across the field, and/or exhibiting poor ball security - Deion (ran palming the ball), Randy Moss, DeSean Jackson. Seems like a lot of the "divas" are risk seeking players. Moss would occasionally throw unecessary laterals when getting tackled, and perhaps caught some balls with one had where he could have used 2.

- Troy Polamalua (sp?) - On several occasions he has jumped over the line of scrimmage and latched onto the QB just as the ball is being snapped. Given I've never seen him screw that up, maybe it's not risk-seeking. But he doesn't seem to stand out in a particular game as an amazing guy every play. It seems like his value is concentrated on a few incredible (often high-risk) plays.

39. Jared Doom says:

Going back to your original "measuring defensive playmakers" post, I see you've already noted my concerns with +EPA/+WPA.

Ignore related statement in previous post, I suppose.

40. Unknown says:

i am by no means an expert in probabilities, i just wanted to say that people reading this page is extremly educated, i am really impressed with the comments, you people surely know your thing.i read you to see if something sticks with me.

41. Jared Doom says:

Expanding on the topic you're already aware of, some anecdotal evidence (I'm guessing I'll be able to find non-anecdotal when I have some time) - in 2009, of starting CBs, (then) Miami's Vontae Davis allowed a league-high 2.4 yards per snap in coverage (893 in total), BUT ranked 3rd in +WPA.

So, he was a playmaker alright, just at the expense of being the worse cover corner in the league. What's interesting is the handful of guys scoring very well.

It may interest you that DeAngelo Hall shows similar tendencies (great playmaker, horrible at covering people).

42. Unknown says:

i am by no means an expert in probabilities, i just wanted to say that people reading this page is extremly educated, i am really impressed with the comments, you people surely know your thing.i read you to see if something sticks with me.

43. Jared Doom says:

correction: What's interesting is the handful of guys scoring very well in both +EPA / +WPA and limited yards allowed per coverage snap.

Message board spam over.

44. Eric Moore says:

It seems like the draft could be an example of consistent risk-seeking behavior. Every year there are high draft picks and millions of dollars spent on combine warriors without the body of on-the-field work that would justify the expense.

45. tmk says:

@ Allen

I skipped ahead so sorry if this was answered already. The risk/reward study numbers for the lottery come from numerous psychology and economics experiments and studies. Not sure which he used.

As was mentioned, risking \$5 for a 1% chance at walking away with \$100 seems counter intuitive, except when you think about how much value \$100 has to you versus the value you place on \$5 and the thrill of a risk.

The risk of putting yourself out there to secure a win doesn't correlate because the loss is worth the same amount as the win (except in the post season) and as we have all seen, they way football is played in the final 2 minutes of a close game is far different then the average.

When it comes to risk, I thinknof Tony Romo. (Whom I affectionately refer to as The NFL's Premier Quarterback).

46. tmk says:

@ probable picks

YES, however while I agree that the game works much in the way you describe, I disagree that the coach dies at the end of the game. It drives me crazy when a middle of the road offense pulls out all the stops in a "unwinnable game" i.e. down 18 points w/ 6 minutes left and Tony Romo under center.

A geometric series thought process could argue that the focus of the game should be on running successful plays, building a positive history, and protecting your playbooks from video. Instead, the risk adverse coach only sees the impending loss and compounds the loss withe the psychological noise of throwing 5 interceptions...or 3.

Also, I have wired money to Louisiana, because a friend was holding the 9 of spades while the flop and turn showed10, J,Q,K. All in, with a marker he lost to a guy holding the Ace. His wife was not happy, and after the 4 hour drive home I'm sure he wished I'd sent enough for her to take a plane, lol.

47. Trent says:

On my original comment about 0.03% of mutual funds beating the S&P 500, it was measured over a 10 year period. So, if you invested \$100 dollars in the S&P 500 and \$100 dollars in every mutual fund in 1993, only 0.03% of the mutual fund investments will be worth more than the \$100 invested in the S&P 500.

Over the course of a quarter there will be tens of thousands of funds that beat the S&P. If we believe that returns are normally distributed (they aren't, but they are close enough for this example), then half of all funds will be the S&P 500. Less will beat it for four consecutive quarters, but there will sill be thousands. After 10 years, there will still be a couple that have beaten the S&P 500, but the vast majority (99.97% according to this study)will fall short of the index. Was this more clear?

48. Anonymous says:

A couple of possible examples of risk-taking that I have wondered about: intentional fouls in basketball that send an opponent to the free-throw line, and running a kickoff out of the end zone when protecting a lead late in a football game (or attempting a punt return vs. fair catch in similar circumstances). Also NHL shoot-outs where a coach saves his best shoot-out player as the third shooter.