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Wins and losses are all that matter. Margin of victory isn’t important.

Hm. Hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm.

Context

Emeryville Public Market. Lunch. Football. The San Francisco 49ers. It started when I expressed a nagging concern about losing to the Raiders in Week 14. Because you know, $*!% happens.

Why are you worried about the Raiders? They’ve lost 16 games in a row!

I know. That is a lot of games to lose. The Raiders are bad at football. I expect the 49ers to beat them; and given the respective current states of each team, I would expect these 49ers to beat these Raiders…90% of the time, or something. But half of the Raiders losses have been by 7 points or fewer; that means they are 0-5 in games decided by a touchdown (/one possession) or less. They lost 14-19 on the road to the Jets, 9-16 on the road to the Patriots, 28-31 at home to the Chargers, 24-30 on the road to Seattle, and 6-13 on the road to the Chargers this past weekend.

Does that matter?

Yes. Look at this Bill Barnwell piece from 2012:

In last year’s primer, I highlighted five teams that had particularly good records in close games in 2011: the Raiders (7-2 in close games in 2011), Packers (5-1), Saints (4-1), 49ers (6-2), and Steelers (5-2). In 2012, despite the presence of several star quarterbacks on their respective rosters, those same five teams went a combined 16-16-1 in games decided by one touchdown or less.

A team’s record in close games looks an awful lot like a random variable, and winning or losing a high percentage of close games in the past does not suggest that a team will continue that clip in the future. Rather, in close games teams tend to balance out around a .500 winning percentage. #regressiontothemean

Think about this conceptually. All else equal, would you rather play a team that had lost 10 games by 20 points each, or a team that had lost 10 games by 1 point each? Presumably the second team, with the much narrower margin of defeat, is a tougher opponent. Next, would you rather play a team that had lost 9 games by 20 points each and won 1 game by 1 point, or a team that had lost 10 games by 1 point each? The second team has the worse record; the first team has the worst point differential. All else equal, despite their worse record, the second team is still presumably a tougher opponent than the first team. This is because wins and losses are an imperfect measure of pure performance. Think about how these imaginary teams “performed”. The first team was dominated 9 times out of 10. The second team has been rather competitive with every opponent, only losing by one point. Context matters!

I think this is about where we came in.1

Wins and losses are all that matters. Margin of victory isn’t important.

Obviously, in a sense that is true. The teams with the most wins make the playoffs. But purely in terms of predicting how well a team will play (say, against the 49ers in Week 14), margin of victory matters a great deal. In fact, margin of victory is a better predictor of a team’s future chances than victory itself.

How can that be? Reducing a game purely to a win, a loss, or a tie for each team is not very useful. Not all wins are created equal.2 If Team A beats Team C by 1 point, and Team B beats Team C by 20 points, while Teams A and B are equal in wins, B certainly seems stronger than A. Turns out, there is a way to quantify such measures, aggregating across many games and years.

Pythagorean wins is an estimate of what a team’s expected record should be, based on their point differential. The formula is as follows:

Pythagorean Wins = [(Points Scored ^ 2.37) / {(Points Scored ^ 2.37) + (Points Allowed ^ 2.37)}] * 16 games per season

I have gathered the wins, losses, ties, points for, and points against for all teams for each year from 2002-2013.3 The 2008 Detroit Lions went a historic 0-16. Yet their point differential (268 for, 517 against) maps to 2.8 Pythagorean wins. They may not have counted in the score book, but perhaps it is some comfort to Lions fans that their winless season was only the 8th worst in the sample, by Pythagorean standards. The 2007 New England Patriots, meanwhile, went an equally historic 16-0. Their point differential (589 for, 274 against) is in fact the very best of any team since 2002. Yet in 2007 they totaled 13.8 Pythagorean wins. To be sure, that is a lot4, but short of the 16 actual wins they achieved.

So what?

The whole point here is gauge a team’s likely future performance. What do you think is the better indicator of a team’s record next season: their actual record from the year before, or their Pythagorean record from the year before? (Hint: It’s the Pythagorean record. I didn’t write this for no reason.)

Oversimplifying5, a win in a given season amounts to .28 more wins in the next season; there is a positive correlation of 28%.6 And similarly, a loss in a given season amounts to .28 more losses in the next season. However, a Pythagorean win in a given season amounts to .38 more (actual) wins in the next season; there is a positive correlation of 38%. All else equal, Pythagorean wins say more about a team’s future than actual wins. Margins–of victory, and defeat–matter.

Graphs

WinsPythagorean_Wins


  1. I spent roughly 35 minutes looking for a clip of that quote from the end of Fight Club on YouTube. It’s not there. F@%^ you, YouTube. F@$% you. 
  2. In addition to margin of victory, think location (home vs road vs neutral), strength of opponent, weather, etc. The others are important too, but they are not included here because #toomuchwork. 
  3. Why 2002? That is the first year under the NFL’s current number of teams (32) and divisional alignment (8 divisions of 4 teams each). 
  4. I believe the official term is “f^&*ton”. 
  5. Ie, without explaining what a regression is. Please Google if you’re curious. Regressions were simple and limited to one independent variable, but coefficients were found to be significant. 
  6. Again, simplifying. 

Yesterday I detailed how Colin Kaepernick’s extension seems to be a pretty great deal for both sides. Kaepernick will be among the top paid handful of players in the league so long as he or the team performs at a truly elite level. The 49ers will recoup several million dollars should that fail to happen. This contract ought to anchor the 49ers talented roster for years to come, possibly into the next decade. But will Kaepernick’s contract create a dynasty on par with that of Joe Montana’s four Super Bowl championships? Probably not.

Whether Kaepernick’s yearly cap hits end up being closer to $16, $18, or $20 million remains to be seen, but no matter what that money cannot go to anyone else on the team. Under Jim Harbaugh, who has coached in three NFC championship games in his three years with the team, the 49ers have yet to pay a premium for their quarterback services.

Season Starting QB Cap Hit % of Cap League Average % of Cap
2011 Alex Smith $4,900,000 4.08% $6,478,783 5.40%
2012 Alex Smith $9,250,000 7.67% $8,257,642 6.85%
2012 Colin Kaepernick $1,164,613 0.97% $8,257,642 6.85%
2013 Colin Kaepernick $1,397,535 1.14% $10,293,699 8.37%

Under Harbaugh the 49ers had one season when Alex Smith cost the same as a league-average starter1, and the other two years the 49ers’ starting quarterback cost them very little relative to the rest of the league. Getting quality quarterback play for such low cap hits gave the 49ers that much more money to add and retain talent elsewhere. And in 2014, Kaepernick’s cap hit remains a scant $3.767 million. But after that?

Year Cap Hit
2014 $3,767,444
2015 $17,265,753
2016 $18,765,753
2017 $21,365,753
2018 $21,865,753
2019 $21,200,000
2020 $23,400,000

Over the six-year extension (2015-2020), Kaepernick’s average cap hit is $20.644 million. Again, that could fall a few million in some seasons, depending on his and the team’s performance, but it will be at least $16-$18 million every year, if not more. It is not known what the salary cap will be in those years,2 but since 19993 the cap has, on average, increased each year by 7.15 percent. This is not, by any means, a perfect predictor of what the cap increases will look like going forward, but it may be close.4 If the cap increases roughly as it has in the past,5 what will Kaepernick’s contract amount to as a percentage of team spending?

Season Kaepernick’s Cap Hit (Overly Simplistic) Projected Salary Cap Percent of Salary Cap
2015 $17,265,753 $142,509,500 12.12%
2016 $18,765,753 $152,698,929 12.29%
2017 $21,365,753 $163,616,903 13.06%
2018 $21,865,753 $175,315,511 12.47%
2019 $21,200,000 $187,850,570 11.29%
2020 $23,400,000 $201,281,886 11.63%

Jim Harbaugh is a terrific football coach, but he has never had his team spend such a high share of its budget on the starting quarterback. General manager Trent Baalke and Paraag Marathe and Co. have never had less money to spend on the other 45 players who will suit up on game day. Quarterback is the most important position, but there are 10 other guys on offense, and 11 other guys on defense, and three unique guys on special teams, too, and some backups, and they all matter to some degree. Even if Kaepernick’s contract diminishes some, and the cap increases more than the 7.15 percent average annual rate of the past, the 49ers will still likely spend 10 percent of their available funds on Kaepernick every season.

Teams spending so much on their quarterbacks can win the Super Bowl. But it is not easy.

Year Super Bowl Winning QB % of Team’s Salary Cap Super Bowl Losing QB % of Team’s Salary Cap
1999 Kurt Warner 1.31% Steve McNair 10.60%
2000 Trent Dilfer N/A Kerry Collins N/A
2001 Tom Brady 0.46% Kurt Warner 3.46%
2002 Brad Johnson 9.56% Rich Gannon 5.22%
2003 Tom Brady 4.42% Jake Delhomme 2.37%
2004 Tom Brady 6.28% Donovan McNabb 9.69%
2005 Ben Roethlisberger 4.94% Matt Hasselbeck 7.72%
2006 Peyton Manning 8.38% Rex Grossman 1.50%
2007 Eli Manning 10.75% Tom Brady 6.73%
2008 Ben Roethlisberger 7.11% Kurt Warner 5.17%
2009 Drew Brees 8.42% Peyton Manning 18.88%
2010 Aaron Rodgers N/A Ben Roethlisberger N/A
2011 Eli Manning 11.75% Tom Brady 10.79%
2012 Joe Flacco 6.63% Colin Kaepernick 0.97%
2013 Russell Wilson 0.55% Peyton Manning 14.23%

Reliable data for the salaries of Dilfer and Collins back in 2000 was not available, and in 2010 there was no salary cap.6 But in the other 13 seasons since 1999, 26 unique teams made the super bowl. Only six of those 26 teams paid their quarterback more than 10 percent of the salary cap: the 1999 Titans (McNair), the 2007 Giants (E. Manning), the 2009 Colts (P. Manning), the 2011 Giants (E. Manning), the 2011 Patriots (Brady), and the 2013 Broncos (P. Manning). (Whole lotta’ Mannings comin’ at ya.) Only a small minority of recent Super Bowl teams had crossed the 10 percent threshold with their starting quarterbacks. What does it all mean? Are the 49ers’ Super Bowl dreams dashed?

Perhaps not, at least not completely. Five of those six teams come from 2007 or later, with four coming from the last eight teams to play in the Super Bowl. Fans keep hearing it, and not without reason: the game really has changed significantly, even since I started watching football 15 years ago. More than ever, it is a passing league. Quarterback salaries are, literally and figuratively, on the rise, not only in absolute terms but relative to other positions. That the 49ers will spend more than 10 percent of their budget on their starting quarterback every year may not be ideal, but it makes a lot more sense now than it would have 15 or even 10 years ago. And this is not just any starting quarterback we have been talking about; it’s Colin Kaepernick.

Nonetheless, with two more years on his contract, Russell Wilson remains the envy of every general manager in the league. Not to overreact, but at what point do we start discussing rather Wilson is the greatest draft pick of all time?7 If the Seahawks win the Super Bowl again next year? Peyton Manning is still probably better than Wilson, but his share of the Broncos’ cap when they met in the Super Bowl last season was nearly 30 times larger than Wilson’s. The Seahawks had a lot more money to spend elsewhere. We all saw what happened.

The 49ers, meanwhile, have a powerful opportunity this year, with Kaepernick only taking up 2.8 percent of their funds. After that, the road gets tougher, with every draft pick, every low-budget signing becoming that much more important. Hopefully the 49ers can pull out a Super Bowl win in the next seven years, maybe two with a bit of luck. But do not expect an NFC championship game appearance every year, Harbaugh or no. It’s just too darned expensive to keep getting there.


  1. The average cap hits of the top 25 paid quarterbacks in each year, according to OvertheCap.com. I use the top 25 because though there are 32 teams and therefore, technically, at least 32 starters, the dregs of the league tend to see high turnover rates and are not really “true” starters, due to poor play, repeated injuries, or what have you. 
  2. Kaepernick’s cap hits escalate every season, as the salary cap is expected to, so Kaepernick’s percent of the whole cap will hopefully change little year to year, even as the 49ers pay him millions more. 
  3. 1999 is something of an arbitrary end point; the modern salary cap really began in 1994. For some other findings in this piece I didn’t find much data before 1999, but most of the data after 1999 is available, so I am keeping it consistent. Something of a nice coincidence, as the Titans-Rams Super Bowl following the 1999 season (played in 2000) is the first one I remember watching in its entirety. 
  4. Most increases were five to six percent, with a couple outliers wherein the league drastically increased the amount of money teams can spend. Since the new collective bargaining agreement, the 2012 salary cap was 0.5 percent more than 2011’s, 2013 was 2 percent more than 2012’s, and now 2014’s is 8.13 percent more than 2013’s, so who really knows what the hell the league will do. 
  5. Again, this is not guaranteed to happen. It is a very, very, very simplified estimate, not a concrete prediction. 
  6. Salary data from Spotrac.com 
  7. Yes, Tom Brady went in the 6th round. But Brady was not drafted to be who he is today; he was clearly a backup coming out of camp and fell into the Patriots’ lap as a great player when Bledsoe was injured. The Seahawks took Wilson in the third round with the intention of him competing to start from day one, and that is exactly what happened. Goodness, how they have reaped the rewards. 

Kaepernick Signs Extension

Last Wednesday the San Francisco 49ers signed quarterback Colin Kaepernick to a six-year extension. On top of the one year remaining on his rookie deal, the 49ers now own his rights through the 2020 NFL season. Needless to say, Mr. Kaepernick was pretty excited about the prospect of earning $126 million to play football.

Kaepernick Deal

The Six Million Dollar Man…times twenty-one.

And, needless to say, 49ers fans were pretty excited as well.

See Kaepernick Make Money

Yet, even in the moment, there were some doubts. Averaging $21 million a year over the extension would currently make Kaepernick the second-highest paid player in the NFL, after Aaron Rodgers. And $61 million guaranteed is the most any player has ever received, eclipsing the $58 million the Denver Broncos guaranteed Peyton Manning in 2012. Despite some struggles, Kaepernick has clearly been a keeper since emerging as the starter, especially since his electric, dynamic, record-breaking, many adjective performance against the Green Bay Packers in the 2012 NFC Playoffs.

See Kaepernick Run

But, even for the above, even in the NFL, $21 million a year with $61 million guaranteed is A Lot of money. Or so it seemed in the moment. In the aftermath some key details emerged.

The Deal Is in the Details

Kaepernick’s cap hit for the coming season remains very low, with only $3 million of his prorated $12 million extension signing bonus adding on to a base salary of $645 thousand. (That is, $3,000,000 onto a base salary of $645,000 for a cap hit less than $4,000,000.)

And of the $61 million guaranteed, only $13 million is fully guaranteed. His 2015 salary (amounting to nearly $15 million all told) only guarantees if he is on the roster on April 1st, 2015. His 2016 and 2017 salaries also guarantee only if he is on the roster in April of those years. Roughly $5 million of his 2018 salary guarantees for being on the roster in April of 2018, and after 2018 nothing is guaranteed. Throughout the extension, the 49ers can evaluate Kaepernick’s contract at the end of each season and decide whether to continue or release him at minimal cost.

And it gets better. For every year that the 49ers do not appear in the Super Bowl and Kaepernick is not selected a 1st or 2nd Team All-Pro, Kaepernick loses $2 million a season. But as soon as the 49ers do appear in the Super Bowl or Kaepernick is selected as an All-Pro, that $2 million kicks in for every year left on the deal. The 49ers or Kaepernick must be in the top two league-wide for one season, or Kaepernick will lose $2 million each year until that happens.

Kaepernick also loses some money if, for whatever reason, he does not play. From 2015-2020, $12 million comes via $125,000 per-game roster bonuses. Throughout the extension, for each game Kaepernick is not on the active roster the 49ers keep $125,000. And, in after-tax dollars, he must purchase a $20 million disability policy to be paid to the 49ers should his career end in injury.

 

A Win-Win, Unless They Lose…

All of these details make the deal pretty terrific, for both sides. If the worst should happen, the 49ers really only lose the $12-plus million signing bonus and some change. Until both Kaepernick and the 49ers play at a truly elite level (as indicated by Kaepernick being a 1st or 2nd Team All-Pro or the 49ers reaching the Super Bowl), the 49ers retain $2 million of the deal per season. The deal’s dead money drops to a manageable $5 million by the 2017 season, and disappears completely by 2019.

Most likely, the 49ers will pay Kaepernick lots and lots of money, but it is about as risk-free as a deal for a starting NFL quarterback can be. 49ers beat writer Matt Maiocco remarked that Kaepernick had bet on himself, and so too has the 49ers front office bet on themselves. It is an expensive deal, but a low-risk deal, a fair deal, a great deal, a many adjective deal.

But…

As a fan, I could not be happier for Colin Kaepernick, and I could not ask for more from 49ers chief contract negotiator and salary cap architect Paraag Marathe. This contract may cement the 49ers as a team to be reckoned with into the next decade, and 49ers fans will get to enjoy one of the league’s most exciting players every game. Will they win the Super Bowl during Kaepernick’s six-year extension? Maybe…but history indicates it may be a bit tougher going forward. Check back tomorrow for more.

First, here are the numbers on Bethea. Player performance grades come from Pro Football Focus; salary information from Spotrac.com; all averages and rankings are position specific; and a player’s contract quality is the number of standard deviations his performance is above/below the average minus the number of standard deviations his average annual salary is above/below the average.

Age: 29 (30 on July 27th)
Old Team: Indianapolis Colts
Old Contract: 4 years/$26 million, $6.5 million average (9th highest of 85 safeties)
2013 PFF Grade: -2.9 (52nd)
2013 Contract Quality: -2.08 (81st)
New Team: San Francisco 49ers
New Contract: 4 years/$23 million, $5.75 million average (projected 12th highest)

Last season, Bethea’s below-average on-field contributions were worth about two million. It is worth mentioning that his performance was not just below the league average, but below his personal career average. In 2007 (his second year in the NFL) he was PFF’s seventh highest graded safety (6.4 grade) of the 80 who played 25% or more of their teams’ snaps; in 2008 he was 17th (5.7) of 83; in 2009 25th (3.5) of 88; in 2010 16th (7.2) of 85; in 2011 21st (3.7) of 87; and in 2012 69th (-4.2) of 88. These numbers suggest his play has fallen off, but they do not say why.

Perhaps Bethea lost a step as he neared 30; perhaps he did not fit as well in Coach Pagano’s system. Regardless, his decline in play does not necessarily mean he has lost a lot of his value. Through his previous contract Bethea’s on-field worth averaged roughly $4 million. The Colts paid him $6.5 million, and the 49ers just decided to pay him $5.75 million on the other side of 30. Why would they do that?

A recent article by 49ers beat writer Matt Maiocco hints at the answer. Maiocco’s post, “Bethea provides ‘smart, steady’ leadership in 49ers secondary“, notes that in addition to eight years of NFL experience:

“Bethea is viewed as a ‘good locker room guy’ and great in the community.”

General manager Trent Baalke has demonstrated a reluctance to chase the high-priced free agent who may disrupt team chemistry. Baalke’s signing of Bethea not only underscores Baalke’s philosophy, but indicates just how much the 49ers value teamwork, isolated from talent. Bethea’s professional demeanor and strong character are seemingly worth $2-4 million or so, at least to some NFL front offices.

As always, it is likely other considerations play into his value. With two prior Pro Bowl appearances Bethea may emerge as a fan favorite, or at least a recognizable presence in the defensive backfield. And, though his talent may be slipping, Bethea has not had injury problems. Nor has he stooped to committing penalties; Maiocco reports that he was not called for a single infraction last season. That, at least, would be a welcome change from Whitner, who was whistled eight times.

The bottom line for Whitner ended up being the $7 million a year the Cleveland Browns were willing to give him. The 49ers, meanwhile, will be paying his replacement more than $1 million fewer each season. Perhaps best of all, 49ers games will finally be rid of out-of-date stories discussing a potential name change to Donte Hitner. Oh, and we have another million and change for a few years to maybe work out a deal with Colin Kaepernick. And if the intangibles of an NFL safety cost into the millions, surely a team needs every cent for a quarterback’s.

On April 28th, 2011, the Jacksonville Jaguars traded two draft picks–the 16th and 49th overall–to the Washington D.C. Football Team and moved up six spots in the first round to select quarterback Blaine Gabbert tenth overall. Using Kevin Meers’ (president of the Harvard Sports Analysis Collective) draft pick approximate value, did this look like a good trade at the time? No.

Meers’ chart, pictured below, uses the career approximate value statistic from Pro Football Reference going back through the last 20-plus drafts to estimate relative pick worth, and answer the question: what is a fair deal when trading draft picks for draft picks?

 

Using Meer’s valuation, you can see this never looked like a good deal for the Jaguars. On average the tenth overall pick is 39.9 (units1) more than the 16th pick, or 15 percent better. In giving up their second round, 49th overall pick worth 148.4, the Jaguars seemingly overpaid substantially. The difference between how much moving up was worth and what Jacksonville actually gave up–110 units–is worth the 82nd overall pick, in the middle of the third round. The trade would have been reasonable for a top-three pick; but, even just seven spots later down at tenth, the numbers indicate it was a bad idea.

The numbers do not tell everything. Meers’ valuation does not reveal that Gabbert was rushed into starting prematurely after presumed starting quarterback David Gerrard bizarrely left football, or that he played behind a below-average offensive line in each of his three seasons, including the third-worst league-wide his second year (per Pro Football Focus). These factors cannot be forgot. But after three years of awful play from Gabbert, yesterday the Jaguars traded him to the San Francisco 49ers, for the current fourth-to-last pick of the sixth round, worth about 45 points in Meers’ system.2 Ironic how that is the sort of pick the Jaguars should have traded to move up in the first place.

The good news for Jaguars fans is that it is over. Well, almost, as Gabbert will still count $1.807 million against Jacksonville’s salary cap this season in dead money. The good news for 49ers fans is that we have obtained a 24-year-old backup quarterback, whom our organization once thought highly of (and still somewhat does, apparently), for a very late draft pick unlikely to contribute to our current roster, and the well-documented quarterback whisperer Jim Harbaugh is still our head coach. (Yup, gotta’ save the best for last.)


  1. These particular numbers do not mean anything outside the chart; they are used to rank picks in a simple way. They are derived from real numbers, the career approximate value figures of Pro Football Reference. 
  2. The 49ers gave up the current fourth-to-last pick of the sixth round for Gabbert. That pick will not be 189th overall, as the league has a handful of compensatory selections to award between some of the rounds, but it should be close. 
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