What is a goon? In 2005 John Cheney, then the coach of the Temple University basketball team,  sent in “seldom used” forward Nehemiah Ingram in order to give hard fouls and send a message. While Ingram is long gone, are there still players like him? What players pick up quick fouls in bunches, and what if they actually played starter minutes?

To investigate, I took all players in the “Big 6” basketball conferences (ACC, Big East, Big 10, Big 12, Pac 12, and SEC), and found a small group of players that may qualify as “goons”.

That being said, I don’t mean to say that these people are bad guys. I am just saying that when on the court, they pick up a large amount of fouls in little time and are big guys. We took their current fouls per minute rate and looked at what would happen if they played 33 minutes, which in college basketball was what the 90^th percentile of players played. So, without further ado, the “goon squad”:

Interestingly enough, 6 of the 9 players are from the Big East, known to be the most physical conference in College Basketball. Robertson Jr. is actually the only one of these players who has fouled out of games, fouling out twice in 10 and 11 minutes. Giplaye has a lot of fouls as well, reaching 4 fouls twice in 10 and 16 minutes. Geramipoor fouled out once in 12 minutes and twice reached 4 fouls in 10 minutes of game action. So, while they may not be “goons”, they seem to be very slow for the college game, or always ready to give a foul.

The reasoning behind WAR begins with the insight that creating or preventing runs adds to the number of wins a team should expect. In any given situation (inning, score, base runners, etc.), there is a historical number of runs that one should expect. Athletes can either increase or decease their team’s expected runs by playing well or poorly. Given baseball’s formula for Pythagorean expectation, 10 runs prevented or created equal one win. Football has a slightly different formula, as derived by Jim Glass:

Win Percentage = Points Scored^2.67 /(Points Scored^2.67 + Points Allowed^2.67)

Multiplying by 16, we can easily convert this formula into wins. To find how many points added equals one win, I plugged the league average number of points scored and allowed for each season into the formula above. I then began adding one to points scored until one could expect an additional win. Below is a table for the past seven seasons demonstrating how many points a win is worth.

There is a clear pattern here: one win is worth 10% of the average points scored in a given season. For the past few years, that number has centered around 35.

Like baseball has the number of expected runs in a given situation, football has a number of expected points given a certain down, distance, score, and time remaining. www.advancednflstats.com calculates expected points added (EPA) for offensive skill players, which makes finding their wins added much easier: we can simply divide their EPA by 10% of the average points scored to get the number of wins they contributed to their team. EPA is a flawed statistic, but we’ll critique later.

Finding EPA for offensive linemen and defensive players is much trickier. There’s no true equivalent to EPA for either group. For defenders, Advanced NFL stats uses a statistic +Expected Points Added, which only includes plays where the defense lowered the offense’s expected points added. This method, however, is far from ideal, as it cannot credit individual defenders for their mistakes. There is also no way to give linemen credit looking only at EPA. We need to find another way to value these players.

To remedy this problem, I collected data on Approximate Value (AV) for every offensive player who had a listed EPA in the past five seasons. AV is not designed to be precise, but it does allow us to cut across positions and seasons. EPA and AV share a strong, positive correlation with each other, 0.723, implying that there is some relationship between the two. With this data, I modeled EPA based on a player’s AV.

Expected EPA = -37.98 + 15.24(AV) -1.87(AV²) + 0.12(AV³) – 0.002(AV⁴)

This model comes with an R² of 0.59 and a standard error of 24. Those are ugly. Really ugly. But the critique comes later.

This model allows us to convert AV for defenders and offensive linemen into EPA, which we can then simply divide by 35 (or 10% of points scored that season) for the number of wins that player contributed to their team. Voila! We have determined how to find the number of wins added by an offensive or defensive player on the field! Hooray!

So why is this only a step in the right direction?

There are numerous problems with the above analysis. Most importantly, EPA and AV do not describe a player’s contribution on the field accurately enough. A 99 yard screen pass gives a quarterback the same amount of EPA as the receiver that made the run, but those are not equal contributions. Furthermore, it does not credit anyone who blocked for the play or any of the defenders responsible for allowing the play to happen. AV does not even purport to be precise: it’s even titled “approximate”. It is impossible to draw precise conclusions with imprecise data. However, until game-charting data becomes more advanced (and public), we have to make do with EPA and AV.

Another problem stems from the model of EPA using AV. The R² (0.59) is high enough to be significant, but not high enough to have a lot of confidence. We can say that the variation in AV, AV², AV³, and AV⁴ explains 59% of the variance in EPA: the majority of the variance in EPA, but just barely. More importantly, the standard error is enormous (24). If the data were normally distributed around the model, we could use the standard error to create a confidence interval for the average of players with a given AV.

Let’s use J.J. Watt’s season this year as an example. Watt had an AV = 10, so the model predicts an EPA of 28 with a 95% confidence interval of (25.5, 30.5). Not bad! However, that interval is for the average of players with an AV of 10. The prediction interval for an individual player is much larger: (-19.2, 75.2). So for any individual player with an AV of 10, we can be 95% confident that they contributed somewhere between -0.5 and 2 wins. To be confident that a player was better than Watt, the lower bound of that player’s prediction interval would have to be greater than 75 EPA. The next value of AV with such a high lower bound is 18. Only 12 players in the past 5 seasons have had AVs greater than or equal to 18. The seasons those players had are the only ones that we can be 95% confident were better than J.J. Watt’s season this year. So after all of this work, we can say with 95% confidence that J.J. Watt was somewhere between a mildly negative factor on the Texans defense to the 13^th best player in the past five years. Ugh.

However, the data is not normally distributed around the model, so the above confidence and prediction intervals are not even accurate. Running a test for heteroskedasticity returns a P value of 0.0000, meaning we can be 99.99% confident that there is not constant variance in the standard error of the model. Since there are negative values for EPA, using a log or square root transformation leaves a significant amount of data out of the model. This result makes it impossible to accurately create a confidence or prediction interval.

These critiques are all valid, and I would not be surprised if there are more that I did not think of. That said, there is at least one important thing to take away from this study: a win is worth 10% of the average points scored by a team each season. From there on in, everything becomes much less accurate because the statistics we are working with, EPA and AV, are inherently imprecise. While there are fatal flaws here, let’s take a step back: we now have a model that can predict the expected wins added of any player on offense or defense. It is not accurate whatsoever, but creating it is itself an accomplishment. The methodology presented here is not the way NFL analysts will compute wins added for football in the future. It is, however, a start.

With the new collective bargaining agreement came the rookie wage scale and a lengthy discussion of how the rookie wage scale would change draft strategy. Using salary data from www.spotrac.com, this analysis presents two models for rookie contract value based on overall pick drafted before and after the new CBA. Combining these models with my previous analysis of Career Approximate Value (a metric from www.profootballreference.com), I present a model for CAVOA/dollar both before and after the 2011 CBA to see how the rookie wage scale affected draft efficiency. (Note that throughout this post, salaries are in tens of thousands of dollars.)

Let’s start by modeling rookie salaries before the 2011 CBA. Salaries peak at the first overall pick, and rapidly decline until pick 34, after which salaries stay fairly constant. This sharp change makes a corner in the salary curve, so we need two equations to accurately model rookie salaries:

If pick ≤ 34, salary = -2197 * ln(pick)+8211.7 (R²: 0.92)

If pick > 34,  salary = -127.1 * ln(pick) + 843.74 (R²: 0.68)

Combining these equations, we get the model below (“eDollars” is expected salary):

Having accurately modeled rookie salaries, we can get CAVOA/dollar at each pick simply by dividing the expected CAVOA by the expected salary of each pick, which results in this graph:

CAVOA/dollar starts at 0.060 at the first overall pick and rises to 0.499 at pick 56 where it begins to fall until the end of the draft. The first 21 overall picks are the most inefficient of any in the draft, but the expected value of those picks is so large that teams accepted the relative inefficiency of those picks. However, it is clear that early first round picks are extremely inefficient compared to the rest of the draft. This inefficiency was one of the reasons that the league instituted the rookie wage scale. But how successful was this policy in making early draft picks more efficient?

The 2011 draft provides some answers. Like in 2010, there is a kink in the salary curve, but significantly later in the draft at pick 68. After this point, salaries become almost constant. Because of this corner, there are two equations to model salaries before and after pick 60:

If pick ≤ 62, salary = -529.2 * ln(pick) + 2451 (R²: 0.97)

If pick > 62, salary = -68.67 * ln(pick) + 574.29 (R²: 0.80)

Combined, these equations form the model below.

Rookie salaries under the rookie wage scale have a very similar shape to salaries before the 2011 CBA. However, the first overall pick’s expected salary is over $55,000,000 less under the 2011 CBA. Because of that shift, rookie salaries are significantly lower at every pick than in previous years.

Having created this model, all that is left to do to get Career Approximate Value Over Average/dollar is divide expected CAVOA by the expected salary of each pick to get CAVOA/dollar. The result is below:

CAVOA/dollar begins at 0.203, and steadily rises until the 61^st pick, where it peaks at 0.497. From pick 62 on, CAVOA/dollar falls to 0.112 at pick 252 (the final pick of last year’s draft). So picks become more and more efficient until the 61^stoverall pick, where efficiency begins falling. The average CAVOA/dollar is 0.294 and the median is 0.288, which makes most of the first round relatively inefficient. Picks 25-147, on the other hand, are all relatively efficient. Given their inefficiency and low expected value, picks after 147 have severely limited value. It is not the case that no individual picked after 147 can be valuable. Rather, those picks have a low CAVOA and are financially inefficient. In terms of trading draft picks, trading out of the first round and into the second definitely increases the efficiency of a team’s draft. However, trading back after the 61^st pick sacrifices both overall value and efficiency, which is the opposite of what teams, in general, want to do.

There are some significant differences between these two CAVOA/dollar models. Earlier draft picks are much more efficient under the 2011 CBA than in previous years. Efficiency starts higher and peaks later in the draft. However, the new CBA makes late round draft picks much less efficient. This change is great for teams, as they are better able to invest significant money in top draft picks without sacrificing as much efficiency as they had to before. While teams should love this change, future early round draft picks lost a lot of money because of the rookie wage scale. All in all, the league accomplished its goal of making rookie contracts more efficient.

You can also read this post on the Boston Globe’s website here

Bill Belichick and the postgame podium are notorious for being a lethally boring tandem. Week after week, he stymies reporters with concise non-answers, vague summaries, and robotic praise of players, giving them nothing of substance to write about his team.

Belichick’s public persona may be as inscrutable as his gameplans, but that doesn’t mean we can’t try to break it down, as he would do to an opposing offense. To get a more in-depth look at the man, we analyzed Belichick’s speaking patterns from the transcripts of his post-game press conferences this season and, for purposes of comparison, gave the same treatment to the more media-friendly Tom Brady.

We started by looking at how long each of them is willing to stand in front of the podium. There’s actually not much variation between the two; Belichick answers questions with an average of 72 words, whereas Brady’s answers average 60 words. However, the difference in the two personalities becomes apparent when we split these averages up by wins and losses. Brady’s answer length barely changes; after a win, his average response length is 59 words, as compared to 62 words following a loss. Belichick is quite a bit less eager to talk to the media after a defeat. Though he averages 82-word answers following a win, he cuts his responses to an average of 25 words after a loss, less than one-third of his post-victory average.

We also examined the word frequencies for each speaker. Of course, the most commonly used words were ordinary ones like ‘a’, ‘the’, and ‘it’. It is more interesting to look at which words had the largest difference in frequency between the two (i.e. which words had the greatest ratio difference between two). Below are the top ten words used most commonly by Belichick and Brady in proportion to one another. (Note: words used less than three times by any one of the speakers were not counted.)

Unsurprisingly, the results for Belichick include a list of profoundly uninteresting words, matching his style at the podium. And Brady, though his list includes a few more syllables, isn’t conveying much more meaning; “We gave them another chance” tells me just as much (or little) as “We didn’t take advantage of our opportunities.”

We also wondered if it was possible to determine the speaker at each press conference just by the style of their speech, examining the frequency of the various words used. Statistician Frederick Mostellar famously used this method to ascertain if Alexander Hamilton, James Madison, or John Jay was the author of the articles of the anonymously published Federalist Papers. At HSAC, we also used it last year to determine the authorship of sports articles, based on individual writing styles. Using these same probabilistic methods, we randomly selected four post-game press conferences (Brady’s and Belichick’s post-game press conferences from last season’s victory over the Packers and loss to the Browns) and tested the question: can a set of equations detect the true speaker?

The answer is a solid affirmative. The model works by producing a probability that a given set of words belongs to either Brady or Belichick, given the speaking patterns analyzed above. In all four cases, the generated probabilities were lopsided (more than 99.9 percent in favor of one speaker), and in all four cases the model was correct in identifying the true speaker.

All in all, this underscores just how little can actually be learned from sports interviews, given the short, recycled nature of their content. Personally, we appreciate Belichick’s approach. The Hoodie has no intention of giving comprehensive answers to anyone’s questions, but at least he doesn’t pretend to by dragging out the same timeworn clichés heard all over the sporting world. His concern is winning football games, and the less other people know about how he does it, the better.

(Huge thanks to TeamRankings for providing the data used in this post)

Last November, I wrote a post on how the lockout did not significantly affect injuries in the NFL this season. Now that the regular season is over, I wanted to take another look. The much discussed lock out could have exacerbated or limited the mounting “wear and tear” and “buildup of cuts and bruises” that develop throughout the season. In reality it did neither. There was almost no difference in injuries this season when compared to the past two years. For various reasons, there has been a lot more attention paid to the injuries that did happen. That increased attention has made it appear that there were a lot more injuries this season, despite efforts by the NFL to limit concussions and hits on defenseless players. If the league is serious about reducing injuries, that attention needs to focus on prevention going into next season.

As the graph below clearly shows, injuries this season are almost exactly the same as the past two years. This constant level of injuries suggests that neither the lockout nor the recent rule changes have had any significant effect on the number of injuries in the NFL.

While it appears that the past two seasons have had a lot fewer injuries than the 2009-2010 season, that difference stems from an extremely high injury rate in the first two weeks of the preseason that year. Removing the preseason, it is clear how little the number of injuries has changed over the past three years.

To accompany this consistent injury rate, injury severity has not changed either – despite the NFL’s recent efforts to penalize and fine players for dangerous hits. Those policies are good for the health of the players, but more should be done if the NFL wants to protect the men on the playing field. To calculate severity, I created a system where a player listed as “probable” had a severity of 0, “questionable” equaled 1, “doubtful” was 2, “out” equaled 3, and “injured reserve” was 4. A metric like “weeks missed” would be better than this system, but those data, unfortunately, are hard to come by. Below is a graph of average severity in each week of the season. As you can see, severity is well within the normal range of the past couple of seasons.

Furthermore, through the end of the regular season, 308 players have been placed on I-R, compared to 259 in the 2009-2010 season and 338 in 2010-2011. Even the most serious injuries have not fallen significantly.

With so many big name players seriously injured this season and recent studies on the effects of concussions on players’ long term health, talk about injuries has become commonplace this season. It may simply be that football as it is played requires this level of injuries. It is up to people who know much more about football than I do how much, if at all,  the NFL should change the game to ensure the safety of its players. What I am putting forward here is simple: neither the lockout nor recent rule changes has significantly changed the injury rate or the severity of those injuries. For that to change, the NFL must continue to change its rules.

Using my previous analysis of career approximate value (CAV) on how to value draft picks, this study analyzes how the results apply to the quarterback position. As the five-month debate on what the Colts should do viz. Peyton Manning and Andrew Luck is just beginning, these findings can help inform the Colts’ decision. As with the entire draft, quarterbacks selected first among quarterbacks and earlier in the draft have more expected upside and more expected value. The following analysis looks at the quarterback position in terms of both order drafted and overall pick.

Let’s first look at quarterbacks by order drafted. Both the upside and expected value of the first overall pick stand out here. The upside of drafting the first overall quarterback taken is two and a half times greater than the downside; these both fall very rapidly as more quarterbacks are drafted. Here’s the graph:

The median is a much better metric to use here because there are so many outliers that skew the mean up. For the first overall quarterback taken, however, the mean and median are both 59, just a little worse than David Garrard at 61. The upside, however, is unparalleled. The upper bound is 152, just three below Brett Favre at 155. This upside drops immediately, falling to 116 and 96 at the second and third overall quarterbacks selected respectively. Those are still great picks: Tom Brady has a CAV of 115 and Mark Brunell has a CAV of 96; however, this is the absolute best-case scenario for these picks. They are much more likely to be closer to the median quarterbacks selected second and third overall: second quarterback should be right below Tim Couch at 31 CAV; the third should be right above Patrick Ramsey at 14 CAV.

These findings also imply that, in general, NFL teams are good at identifying players who will become good quarterbacks. If they did not, the above graphs would have trendlines sloping up.  Given the strong negative slope of the median curve above, it is clear that CAV falls continuously as the draft continues. There are obvious exceptions to this trend: Alex Smith going over Aaron Rodgers; Tom Brady drafted after Chad Pennington, Giovanni Carmazzi, Chris Redman, Tee Martin, Marc Bulger, and Spergon Wynn. However, perspective is important. These are the exceptions; the rule is that teams are good at identifying talent at the quarterback position.

Order drafted is not the only important way to analyze the quarterback position. Overall draft pick is also important. Looking at the data from draft pick instead of order selected requires grouping picks into 16-pick (half round) buckets; without this grouping the sample sizes are way too small. Even with these groups, the models are very noisy. The graph and analysis follow below.

The large groupings hide the drop in value from early to late round picks in the mean and median graphs. That said, there is still a clear downward trend from early rounds to later ones. The upper bound line is the most important line here. The extreme drop after the 33-48 bucket is the really significant point to take from this chart. Before the 48^th overall pick, any quarterback has the potential to be the next Jim Kelly or Drew Bledsoe. After that pick, the upside vanishes. For the rest of the draft, the maximum upside of every quarterback is right around the David Garrard range. Mark Brunell solely causes the peak at the 113-128 bucket, which demonstrates that it is possible to find a talented quarterback late; it’s simply highly unlikely.

Tom Brady

The conclusion here is simple: if you need a quarterback, draft a one as early as possible. If you draft a quarterback after the 48^th overall pick, temper expectations. There’s a reason Tom Brady’s story stands out: he’s the only quarterback of 262 drafted after pick 100 since 1980 to have a CAV over 100. Only Mark Brunell and Trent Green are close, but Brady’s CAV/year is a full 4 points higher than theirs, putting him in a class apart. If teams want a good quarterback, they must draft one early.

Conventional wisdom and anecdotal evidence holds that these breaks, and the distractions around this time of year, can lead to letdowns, especially for favored teams. In fact, just last week Pittsburgh lost to Wagner, #4 Louisville trailed at home to both College of Charleston and Western Kentucky, Michigan struggled with Bradley, and Kansas lost to Davidson. All of these teams were heavily favored at home. Jeff Goodman summed up this view succinctly, tweeting that “Louisville’s players look as though they have already left for Christmas. Down early to WKU but Cards should come back.”

But do BCS home teams really perform worse than usual during this exam break? Do they schedule easier competition to account for poorer play? Looking at my database of 35,000 college basketball betting lines and results from 1996-2011, this does not appear to be the case. As I have explained before, the Vegas line, while imperfect, is still the best predictor of game results. It also is a great way for us to judge performance: if teams really do play worse over this break, we should either see them doing significantly worse relative to the lines. In my dataset, that worse performance simply is not there.

I defined my timeframe as games played between December 19th and December 28th. These specific dates could have been moved a day one way or the other, but the range covers the first game back for most teams after exams, and any games played around the Christmas break. Most teams let players go home for Christmas itself before having them back to campus for the next game. If there is a “Christmas/exams” letdown, it would appear in these games.

I compared performance in these games to performance in non-conference games prior to  exams (November-December) because other non-conference games are a fair peer group  at a similar level of competition–conference play can differ dramatically. The first issue to look at is whether teams schedule easier games during this period. The raw data is summarized in a table below:

BCS Non-conference home game spreads

Unsurprisingly, BCS teams are usually big favorites in non-conference home games. They are, on average, a point bigger favorites (-9.3 vs. -8.3) in Christmastime/ exam period games, but this difference is not statistically significant (using both t-tests and a Kolmogorov-Smirnov test of equivalence of distributions). While the level of competition during the exams/Christmas period is on average a bit easier, it does not appear that teams are scheduling down significantly during this period.

What about performance against that expectation? Again, there does not appear to be a significant divergence in results over exams/Christmastime. At home, BCS teams outperformed the line by an average of 0.5 points in the rest of non-conference play. Over the exam/Christmas period, they outperformed the line by an average of 0.8 points, a small and insignificant difference. The two samples also have almost identical standard deviations, meaning results are not spread out more from the line over the Christmas period.

One might argue that looking at simply the average and standard deviation is not enough. Maybe on average teams do well, but a portion of the BCS favorites simply collapse and lose big at home, missing the line substantially. Let’s look the two distributions of results  compared to the Vegas line (positive numbers indicate that the home team outperformed the line, negative that they underperformed):

Visually, it does not appear that the two distributions differ much at all. This is confirmed by the Kolmogorov-Smirnov test. What this means is that, relative to the Vegas line, the distribution of a BCS home team’s performance is the same in the rest of the non-conference as it is over the exams/Christmas period. There does not appear to be any evidence for a Christmas letdown or worse performance.

While this analysis focused on the home teams, it also tells us about the converse: road performance over the period in question. The teams that travel to play BCS opponents over Christmas do not do significantly better than their counterparts over the rest of the non-conference. This lack of significance extends across the country: including non-BCS home games over the break does not change the finding.

The numbers are convincing, but do not tell the whole story. One caveat may be that Vegas prices in some poorer performance, and thus the spreads for exams/Christmas games are artificially suppressed. More qualitatively, it does seem that teams do perform more sloppily after long breaks. What is clear, however, is that this sloppiness is not somehow only limited to favored home teams.

Your favorite team may lose a shocker over this Christmas and exams period, but if they do, please buck the conventional wisdom and do not blame it on the season.

Big news hit the baseball world yesterday as the Los Angeles Angels announced a $254 million, 10-year contract for 31-year-old Albert Pujols, a strikingly large contract for such an old player, even if Pujols is still a perennial all star and MVP-candidate. It’s pretty clear that the contract is long and a lot of money for a player so late in his career, but just how much is he getting overpaid? Let’s take a look.

To get a sense of what the rest of Pujols’ career will look like we can examine how other top players’ performance typically drops off at the end of their career. Looking at other top first basemen from the past, we can map out a typical trajectory for a player in Pujols’ position, and then make a reasonable estimate of what will happen for him. We use Wins Above Replacement as a proxy for overall production (not a perfect proxy, but a good estimation of each player’s value to the team – FYI, we use Baseball Reference‘s version of WAR). On average, top first basemen start to decline precipitously after age 32. Using this trajectory, we can expect Pujols to contribute approximately 47 WAR over the rest of his 10-year contract. (Here we are generous in assuming that he won’t have any wrist, or other, issues and will be able to bounce back to a high level this year like his counterparts from the past instead of continuing his decline from the past few years. There is a bit of sample bias here in Pujols’ favor because we have used as comparables other Hall of Fame / MVP / All Star caliber players who played out their career and did not see it cut short by injury. We also assume he’s actually 31-years-old… unlike some people)

(Note: it’s strikingly difficult to find a large sample of first basemen who ended their career recently, performed at a near-MVP level and haven’t been suspected of steroid use. I used the group consisting of Jeff Bagwell, Frank Thomas, Mark Grace, John Olerud, Jim Thome, and Will Clark – not all perfect comparables to Pujols, but they still should provide a good sample of how performance degrades over time, including some players that transitioned to DH to extend their productivity)

So how much is 47 WAR worth? Many writers cite a value of $5 million for a marginal win on the free agent market today, implying that Pujols’ remaining years should be worth approximately $235 million to over $254 million depending on salary inflation – right around his contract with the Angels. However, looking at the 2011 salaries and performance of all non-pitchers in the league (excluding those who did not play), teams will pay, on average, $600,000 for a replacement level player (WAR = 0) and $3 million for each incremental win above replacement (including players on pre-arbitration salaries). Given these market values and annual salary increases of about 2.7%, the Angels should theoretically be able to find the performance that Pujols is bringing to the team over the next 10 years with $159 million – overpaying by a whopping $95 million. [Additional note: this does not include the fact that having Pujols would free up talent coming up through their farm system to be traded, so the net overpayment would be somewhat lower.]

This has also just looked at the baseball side of things. It’s also possible that the Angels expect to garner significantly more ticket sales or merchandise revenue from Pujols’ arrival besides just what he is adding on the field. To look at Pujols like the Angels’ front office, additional revenue would need to be considered, not just WAR. But a gap of up to $95 million is a large gap to fill, especially if you only expect another 3-4 quality years from him. (Additionally, the market rates we’ve used to calculate the market value of a WAR should already take into account teams “overpaying” to get additional off-the-field revenues).

Albert Pujols is an extraordinary player, and it’s certainly possible that he could extend his career and play at a high level longer than others have in the past, but if using history as a guide and being a little less rosy about how his career will progress, the Angels could end up being stuck with a $100 million mistake.

A couple weeks ago we did some analysis on Tim Tebow, attempting to explain how he’s been winning games despite his poor statistical performance. Simply put, he has been performing poorly overall but has saved his best for the most crucial game situations. After a couple more wins from Tebow, we thought it deserved another look.

A word on the methods used: each potential game situation (down, distance, and yard line) carries with it a certain number of expected points –– the amount of points, on average, a team scores (or allows) from that position, based on NFL play-by-play data. Similarly, every play in a football game adds (or subtracts) these expected points by altering the game situation. For example, a 1^st and 10 on one’s own 20 yard line is worth 0.4 Expected Points, and a 1^st and 10 on the 20 yard line of the opposition is worth 4.0 Expected Points. A 60-yard bomb on first down following a touchback, then, would be worth 3.6 Expected Points Added, the change in Expected Points generated by the play’s outcome. This last statistic, EPA, is what we used to evaluate Tebow’s raw numbers, free of the context of timing within the game.

But that context can also provide meaningful information about how players affected a game’s outcome, so we also examined Tebow’s Win Probability Added, or how much his plays contributed to the Broncos’ chances of victory. WPA works a lot like EPA –– it calculates the change in a team’s probability of victory following each play –– except that it also factors in time remaining in the game. A 20 yard touchdown pass to take the lead as time expires will be worth much more WPA than a 20 yard touchdown pass to take the lead in the 1st quarter because, in the second scenario, there is still a sizable chance that the opponent comes back to win. (Note: credit for both EPA and WPA goes to advancednflstats.com, which compiles both figures on its website)

Our findings from a couple weeks ago revealed that Tebow’s EPA to that point in the season (-13.4) was worse than Kyle Orton’s (-0.3) during his tenure as the Broncos’ starter, meaning that he objectively produced worse results over all of his plays. However, Tebow recorded a significantly better, though still negative, WPA (-0.06) than Orton (-0.45) –– his plays contributed more to the chances of the Broncos winning. The majority of his positive plays occurred at crucial points in the game, when they had a much larger impact on the outcome: his 20 yard TD run for the lead with 58 seconds left against the Jets, for instance. Likewise, Tebow’s negative plays have come at points where their effect was less harmful, like his entire first half against the Jets.

As one might expect, EPA and WPA for individual players are highly correlated; they measure very similar things, with the only difference being WPA’s allowance for the mystical “clutch” factor. With regard to Tebow this season, his WPA is above and beyond

what you would expect, given the raw results of the plays he has executed on the field. In fact, the difference between his performance and expectation is statistically significant at the 90% level. Other players, like Tom Brady and Aaron Rodgers for example, have had similar discrepancies in their first years, but over time the differences have regressed toward the mean, ultimately coming more in line with expectations.

Yet, in the interim, Tebow apparently chose to ignore our column and win two more games. Did anything about his performance change?

In Week 12, the Broncos beat San Diego with a game-winning field goal in overtime. Tebow’s WPA (still negative at -0.23) was actually slightly lower than expected, given his EPA (-0.2). This means that, as before, Tebow’s plays negatively affected the Broncos’ chances of winning. In previous weeks, Tebow was able to come through with a big play at a crucial moment, thereby disproportionately raising his WPA, but that was not the case here –– Denver tied the game on a field goal with 1:34 left and won with another field goal in overtime (after the Chargers bungled a field goal chance of their own). Though he deserves credit for the game-tying drive he engineered at the end of regulation, the plays that had the greatest effect on the Broncos’ win probability –– San Diego’s missed 53-yard field goal in overtime (which also swung field position dramatically), Willis McGahee’s 24-yard run to set up the winning field goal –– occurred with little to no help from Tebow.

In Week 13, Tebow played arguably the best game in his short career, throwing for 202 yards with a completion percentage of 67%. This resulted in an EPA of +2.0, a positive contribution to his team’s success. Using our regression from last week, however, his WPA of +0.24 was still higher than expected (by 0.31), given his raw on-field performance. Again, this was a product of a pattern Tebow has followed quite often: playing poorly early in the game and coming through late. After throwing for no touchdowns in the first half, he tossed two in the 3rd quarter and rhino-charged in a two point conversion to tie the game in the 4th. And, once more, Tebow was the beneficiary of a healthy dose of late game fairy dust: Vikings quarterback Christian Ponder’s interception, returned to the 15-yard line with 1:33 remaining, which set up a chip-shot, game-winning field goal by Matt Prater.

So, broadly, Tebow has indeed exhibited “clutch” performance –– performing pretty ordinarily overall, but at a higher level when it matters most. Given our previous analysis of other quarterbacks who did this in their first year (including Tom Brady, Aaron Rodgers and Drew Brees), it’s unlikely that this is a sustainable course in the long run. However, it

should be encouraging for Tebow fans that his performance has been improving in absolute terms. Whether he exceeds the expectations of our model or not, you can expect him to win more games if he keeps playing at a higher level.

As an addendum, we’d like to clarify some things about our analysis that may have caused some confusion. First EPA and WPA take into account both turnovers and time of possession. Turning the ball over has a negative expected point value and a negative impact on the player’s team’s win probability, accounted for in the individual player’s accumulated EPA and WPA stats. Additionally, WPA takes into account the timing of plays in the game, so if a team possesses the ball for a longer period of time, it will inherently be represented in WPA. Secondly, it is true that the two stats we use, EPA and WPA, don’t take into account read option plays where Tebow may actually have an impact on the play’s outcome despite not accumulating stats (this not being represented in traditional stats, either). However, this also doesn’t help explain the Broncos’ recent winning ways because the running backs to whom Tebow is handing off have actually performed worse during Tebow’s starts, have a negative WPA, and, like Tebow, are exceeding EPA-based expectations. 

Last week we debuted our BCS prediction model, using it to predict what would happen in the BCS rankings under certain scenarios for the week’s games. Turns out there wasn’t too much chaos as all the favorites at the top of the rankings won, but that doesn’t mean we won’t see some interesting scenarios play out this weekend. Below we let you know how the race for the BCS championship will likely play out depending on the results of the SEC Championship between LSU and Georgia and the Bedlam between Oklahoma and Oklahoma State. For each scenario we show the probability that it will occur, according to TeamRankings predictions, in parentheses.

Scenario 1: LSU and Oklahoma State win (49%)