Ever since Sean Smith made his historical WAR database public on his website BaseballProjection.com, we have been able to compare some of the games great all time players.  Take Willie Mays and Hank Aaron:

These are two of the greatest players in the in the history of the game.  Since 1955, which unfortunately is as far as Sean's database goes, they are in a virtual tie for the second best player of that era, racking up about 140 Wins Above Replacement apiece.  Only Barry Bonds has more, with a whopping 173.9 WAR.  However, as you can see from the above graph, they both did it in a different way.  Willie had the higher peak with five 10+ WAR seasons compared to none for Hank; however, Hank had a longer and more consistent career.  Obviously, it is impossible to measure greatness and  these two players are so legendary than any attempt to make any esoteric judgments about their ability seems foolish.  However these two greats represent a conundrum in player valuation.  Do we value a high peak or a long and consistent career?  Using the Pennants Added concept I will try to answer that question.     

The Pennants Added concept was first thought of by Bill James.  The idea behind it is that wins are just a means to a greater goal, which is winning the world series.  The most comprehensive study I've seen, at least in my opinion, was done by David Gassko in an article for The Hardball Times.  His method was basically figuring how many playoff appearances does a player add if he was put on an array of teams that mirrored the normal distribution of wins.  I will be recreating his method with a few tweaks of my own.  Then we can take it on an individual player level, specifically some of the games greats, and use it to objectively value their contributions.

In his article for THT, David use actual wins as a means to calculate Pennants Added; however, given that I am using it to value players using WAR, I don't think this is the right way to do so.   Actual wins that a player adds cannot be measured by any stat that we have.  Instead, WAR measures how many runs a player adds to his team, and those runs are then mathematically turned into wins based on the historical value of runs.  So when a player is worth 5 WAR, he raises his teams true talent level so that they can be expected to win 5 more games.  However, there are many factors that allow a team to under or over perform their true talent level:

So in order to make a stronger comparison with WAR, I will be using Pythagenpat Wins as a rough measure of a teams true talent level.

So the first step in creating a Pennants Added model is to figure out the distribution of talent in baseball.  To do this, I looked at every teams' Pythagenpat win totals since 1961 (when the league switched to a 162 game format) and mapped out a normal distribution:

Click to see a larger version.

Obviously, the average team has a true talent level of about 81 wins, with the worst being about 50 wins (like the 03 Tigers) and the best being about 110 wins (like the 01 Mariners).  I got a standard deviation of just over 10 wins, meaning that 68% of teams have a true talent level between 71 and 91 wins, and about 95% of teams will have a true talent level of between 61 and 101 wins.  That make the 03 Tigers all the more "impressive", as they were over 3 standard deviations from the mean, meaning that a team like that should only come around once every three centuries!  Anyway, the important thing to take away from that distribution is that it also shows the chances that a random player will be assigned to x win talent team.  That will be come up later. 

The next step in Pennants Added is, given the distribution of talent in baseball, figuring out the chances that an x win true talent team makes the playoffs.  We can do that by means of a logistic regression.  A logistic regression, in this case, would figure out the historical chances of a team making the playoffs given their Pythagenpat win total.  However, this is where we run into a problem.  The way the leagues have been structured has fluctuated over the past 50ish years:

10 Teams, 1 Playoff Spot: 1962-1968 AL and NL

12 Teams, 2 Playoff Spots: 1969-1976 AL, 1969-1992 NL

14 Teams, 2 Playoff Spots: 1993 NL, 1977-1993 AL

14 Teams, 4 Playoff Spots: 1996-1997 NL, 1996-2009 AL

16 Teams, 4 Playoff Spots: 1998-2009 NL

Therefore it becomes necessary to separate a teams chances of making the playoffs based on what league format they played in to properly assess playoff probability.   So I did 5 seperate regressions for each league state.  The results are best shown like this: 

As you can see, it is a lot easier to make the playoffs in the current league format.  A team with a true talent level of 90 wins has over a 50% chance of making the playoffs now compared to less than a 10% chance in 1966.  In fact, very mediocre teams, like the Dodgers last year or the Cardinals in 06, have been able to make the playoffs seemingly every year.

Anyway, now that we can know the chances of a random team having a true talent of x wins, and the probability that that team makes the playoffs, we can combine to two to create Pennants Added.

I'll show you with Albert Pujols.  Last season he put up ridiculous 8.9 WAR, yet for some reason wasn't the unanimous MVP.  whatever.  If you added his production to a team in the current NL format with a true talent level of 80 wins, then their playoff probability goes up by 41.2%.  However, the chances of a random team having a true talent level of 80 wins is just 3.7%.  So combining those two leads to .015 playoff appearances added.

Then you repeat that for every team from 1-162 that he could be on, and you get .276 playoff appearances added.  Then you divide that by how many teams from each league make the playoffs, in this case 4, and you get a final tally of... drumroll please... 0.069 Pennants Added.  Or in other words, he would have increased a random teams chances of going to the world series by about 7%.  That seems like it's a little harsh to Albert and it does raise an interesting point that I will get to in a bit.

First, let's go back to Willie Mays and Hank Aaron.  Given that they played in almost exactly the same time period, we can make an almost perfect comparison.  So I calculated the Pennants Added for each player, using whatever league format they played in that year:

That may not look like a big difference, however, given the 10,1 league format, it is equivilant to about an 11 WAR season.  That is pretty significant, and while it doesn't mean that Mays was any better than Aaron, he was most likely more valuable.

That above graph shows those two players' Pennants Added in the actual league format that they played in; however, if you put their production in the current NL format (16 teams, 4 playoff spots), it looks a lot different:  

In this case, Aaron comes out ever so slightly ahead.   

You'll probably notice a couple of things when you compare those two graphs.  1) a high peak appears to be lot more valuable back in the day in comparison to consistency than it is now, and 2) the value of players has dropped significantly.  Here is a better representation of what I am talking about:

As you can see the value of a player has dropped, a lot.  In 1965, a 9 WAR player would increase a random teams chances of going to the world series by over 20%.  Now, that same player, like Albert Pujols last year, adds less than 7%.

Also you can tell that the upward arc of those regression lines have become more flat in time.  A 10 WAR season in 1965 was worth more than two 5 WAR seasons; however, now they appear to be equal.  So it definitely appears that a player, especially a star, has become inherently less valuable over time.

The ideas in this post aren't very groundbreaking, but with the information gathered here, I am going to attempt to create a value metric for the hall of fame.  That will come in a couple of days.  Anyway, I hope you enjoyed reading this, and if not, you should at least enjoy the pretty looking graphs.