Monday, February 6, 2012

Ring Probability Added

by Joe Harris
When arguing a QB's "greatness" people often quote the number of rings a player has as a definitive conclusion to a debate. For example, Dilfer is obviously greater than Marino because he has a ring. And there is nothing else to it. That statement takes the logic a bit further than most people would, but that is essentially how a lot of fans view the world. Whilst I am not a fan of this form of logic, I thought that it would be interesting to look at this concept through the lens of WPA or, more specically, RPA - Ring Probability Added.

Ring Probability Added
The basic idea is to take Brian's WPA stats and weight it depending on the magnitude of the game. For example, in 2004 when New England beat Carolina, Tom Brady essentially did enough to win the game single-handedly with +0.97 WPA. This corresponds to +0.49 RPA - he increased New England's chances of winning the Superbowl by 49%.

The game magnitudes I assigned were:

    Superbowl: 50%
    Conference Championship: 25%
    Divisional Round: 12.5%
    Wild Card Round: 6.25%
    Regular Season Game: 0.4%
The logic behind the Regular Season weighting was that I wanted to keep all the games equal. So I used a weighting of 1/256 (the number of games in a season). What this doesn't do is account for the fact that, when it comes to winning a Superbowl, 0 wins for the season is just as useful as 6 wins - either way your team misses the playoffs. But in the end the regular season had very little impact on the final results.
I thought it would also be fun to think about the Total Rings a player wins for himself and his teammates. Based on the assumption of 53 players on an NFL roster, I multiply the RPA by 53. Using this logic I conclude that in Brady's career he has won 73 rings for himself and his teammates.

It should go without saying that every QBs RPA is extremely dependent on the performance of the O-line and receivers in the same games.

The Results
The results are not hugely surprising. Brady leads the way with +1.38 RPA, followed by the Manning brothers, Roethlisberger and Brees - the winners of 5 of the last 6 Superbowls.

My favourite result is that Rex Grossman managed to total -0.38 RPA or -20 Total Rings in just one season. This is amazing but it is really a testament to that Bears defence; Not only did he play badly enough to lose each playoff game, the rest of the team bailed him out just enough that he had a chance to further hurt their chances in the next round.

RankNameRPATotal Rings
1T. Brady+1.3873

Some Final Thoughts
When I started this analysis I was hoping that the results would show Peyton in a more favourable light. Whilst I obviously wasn't expecting him to outperform Tom Brady, I did think that he would do slightly better vs Eli and Big Ben. However, if you account for the number of seasons each QB has played all three QBs have just over 3.5 RPA per season.

For good quarterbacks, having a good defence and running game is still very important when it comes to accumulating RPA. The chart below shows that Peyton has actual done more to get his teams to Superbowls than Tom Brady. Unfortunately for him this only translated to 2 Superbowls in real life vs Brady's 5.

(click on the chart for a larger, clearer version.)

Conversely, for bad quarterbacks, it can be better to have a bad defence - as highlighted by Rex Grossman who otherwise would never have been in a position to post such terrible stats in big games.


James said...

What years did this cover? This is most important to Warner, who should have a great deal of RPA from the 99-01 seasons.

tunesmith said...

Fun idea! I'm a little confused why the Super Bowl doesn't count as 100% though? I mean, if you've won the game that is the Super Bowl, then that means you're 100% likely to have won the actual Super Bowl.

James said...

tunesmith, but if you don't make the Superbowl then you can't win it, and if you don't win in the divisional round then you can win in the championship round, etc.

Anonymous said...

It only covers 2000 onwards - so yes there is a problem for many QBs such as Warner, Favre etc.

The Super Bowl only counts as 50% because at the beginning of the game you already have a 50% chance of winning.

So by winning that game you have added 50% to get to a total of 100%.

Joe Harris

Anonymous said...

Much like the stats WPA/game and WPA / play, you should adjust this to a RPA added per, perhaps dividing by the sum total of all games played in, with each game appropriately modified by their leverage index (so playing in a super bowl is worth 128 times playing in a regular season game and so on). That would make this a more interesting stat, otherwise it just benefits QBs who have played in the most high leverage games (regardless of whether they got the team there or not), since a replacement QB has an above 0 expected WPA in any given game.

Anonymous said...

"perhaps dividing by the sum total of all games played in, with each game appropriately modified by their leverage index"

This would just result in WPA/Game - no?

I think you do raise two valid points though:

1) RPA could be adjusted so that it is "RPA added per". I would suggest dividing by the number of seasons.

2) Replacement level QBs do have above 0 WPA/game. So any QB who is either good, average or even slightly below average will benefit from more opportunities to accumulate RPA, regardless of whether they earned them.

In fact, one of my biggest problems with WPA as a stat for QBs is that replacement level has changed over time. These are the WPA/game stats for regular seasons from 2000 - 2011:

2000: 0.011
2001: 0.008
2002: 0.036
2003: 0.018
2004: 0.054
2005: 0.017
2006: 0.024
2007: 0.028
2008: 0.079
2009: 0.075
2010: 0.066
2011: 0.084

There is a big jump after 2007. So QBs playing after 2007 are going to have better WPA stats.

I am not sure whether this is because the model is not consistent across years or because coaches are now acting making different decisions (e.g. run/pass ratio). Probably a bit of both.

But this was only meant as a bit of fun, and I did not want to over-complicate matters by taking into account replacement level QB WPA.

mike s said...

This is really interesting. Another more complex thought/idea is in the regular season that "not all wins are created equal" and all the ramifications it has. And in the regular season to use "playoff probability added". The thing is, a 9-6 team for example might only get in with a win. To them any win probability added in that game will get 100% of it's value because a win is 100% responsible for the playoffs. When the team is 8-6 (assuming they HAVE to win out and if they do they are in for sure, and if they don't they are out for sure) a win would correspond to 50% of their playoff hopes, or all playoff probability added would be 50% of their normal WPA to compose of their PPA.
The reason this gets interesting is you If you could determine how much not using a play at all adds to it's effectiveness, you could determine strategically if it's worth not using the most effective play in one game, based upon calculating out the playoff percentages. Just like a pool hustler (billiards) when someone might intentionally throw a game at a $50 stake to try to win two more at $100 stake and double the amount they get, it might make sense tofor example, NOT use an onside kick early on in the season as a surprise, even though it is advantageous so that when the win is more meaningful and the play is more critical to your playoff chances, then you can consider a more optimal gameplan. So perhaps coaches are right being more conservative early in the year, because if they end up 3-10 no amount of wins will help and they can save the element of surprise for next year (if there is one for that coach) or if they are 13-0 and have clinched division and homefield advantage, they can save it for the playoffs, but if they are 7-6 or 8-5 or something, then they can consider using more optimal gameplan provided they don't have a crushing lead at halftime... This way they save the element of surprise advantage like Sean Peyton did in the superbowl when he needed to the most.
Of course if you get a bye week your superbowl chances are significantly better by at least one game, so you can quantify that advantage as well as getting into the playoffs and convert Playoff probability added to "superbowl probability added" depending on your odds of getting a first round bye or not.

Anonymous said...

oh, good point about already having a 50% chance of winning the game when it starts....
The other thing that should be possible is to try to "normalize" the data for opportunity.

So if a QB on a terrible team had perhaps a .10 WPA per game, but his team not including himself has a .40 WP or -.10 WPA, then the player is on a team that would need to be boosted by 5/4 to figure out his opportunity on an average team... So you could multiply his RP by 1.25 for regular season games to "normalize" the data, giving him a WP per game of .125 while QBs that benefit from a strong defense and offensive line would get cut down perhaps by 80% from .1 per game to .08. This way you don't unfairly cut down QBs on terrible teams that do FAR more to get their team in position to win a Superbowl and make the most of it when they are there. Afterall, this "RP" will greatly be skewed by QBs on VERY VERY GOOD teams that are just mildly have positive WPA in the playoffs and superbowl, and you should account for the chance their team gets of getting them there.

Anonymous said...

I think that is extremely unfair to look at "rings". Dan Marino didn't have a chance, and neither would many "great" QBs on that same team. But I do believe there is some serious validity in adding value based on how "clutch" someone is, or how "clutch" a coach is, even if there isn't significant evidence that it exists, it still is much more important than a regular season game if it determines your playoff fate, or if it is a playoff game, and the difficulty of winning is as hard as it ever will be. But you would HAVE to normalize it based upon the team and opportunity that they can be given. Daunte Culpepper is a bit surprising to do that well in this list because the defense was so horrendous the Vikings never really had a chance in that day and age of winning a superbowl. So mainly it was ALL on Daunte and the offense to do it. Yet he didn't have a great runningback, even though the offensive line and running game ranked near the top because Daunte often scrammbled for big gains. The fact that he still has a RP in the top 10 I think is extremely impressive, and perhaps more so than some above him on incredibly talented teams with excellent defenses. Tom Brady is no doubt an amazing QB, as is Eli Manning, but both of those teams have some serious weapons around them and great coaching staff and defenses. I think we tend to put the players that happen to get opportunity more because of the strong defenses in a higher regard, and perhaps unfairly so.

Anonymous said...

would be interesting to "normalize" the data by considering how his odds would change had he had an "average" defense and all QBs having an "average" defense and as a result the probability of GETTING to the playoffs would have to be adjusted. For example, if the probability of an average QB getting to the playoffs with that same defense is 30% rather than the theoretical 12/32 or 37.5%, you would need to boost the QBs RP by at least 25%. I think it could still be skewed towards QBs on superior teams perhaps even with this adjustment because what if due to randomness a player got there and happened to have a good game or two... Maybe Tom Brady in a different dimension never gets to the playoffs because he gets drafted by the Detroit Lions or Bengals or whatever team has been the most terrible and they don't manage the cap as well as the Patriots and he never has a chance. Even though hedrastically boosts the amount of wins per season from say a 3-13 team to 6-10 or 6-10 to 9--7 perhaps his team still doesn't make the playoffs and as a result, even though his regular season WPA is excellent, his RP would be nowhere near what it is. So although I agree the WPA is already goo dand I see what you are trying to do with the "superbowld rings" argument, I think it still should be normalized to boost QBs who are on bad teams and punish QBs on good teams. But I also think there are certain games in the regular season that are more important, and if a QB blows his chance of getting into the playoffs with low or negative WPA when it counts most (9-6 where a win gets them into the playoffs and a loss doesn't), that is nearly as significant as a playoff loss, and it needs to be reflected as well. We could create a "clutch index" that weights the important games more significantly and normalizes the data.

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