Tuesday, June 26, 2007

My Top 60 Starters, 41-50

50. Jack Powell (.508 NW%, 106 ARA, +14 WAA, +75 WAR)
49. Rube Waddell (.561, 125, +32, +74)
48. Dazzy Vance (.596, 125, +32, +74)
47. Don Drysdale (.535, 118, +29, +77)
46. Gus Wynn (.531, 106, +13, +77)
45. Luis Tiant (.559, 117, +29, +78)
44. Joe McGinnity (.603, 119, +29, +77)
43. Hal Newhouser (.565, 125, +35, +76)
42. Jim Bunning (.547, 115, +27, +79)
41. Billy Pierce (.534, 121, +32, +78)

POWELL: His career record was 245-256, but he pitched for bad (.462 Mate) teams. His neutralized record of 255-246 is good for +59 WCR, but he does much better in a run-based analysis, coming at +75. He has no peak to speak of, especially for a pitcher of his time, but has a lot of value against a low baseline over the course of almost 4400 innings.

WADDELL & VANCE: As you can see, these two are almost a perfect match, except Vance’s W-L record is more impressive and he was sane (and right-handed). They were both strikeout pitchers, but have wildly different career paths. Waddell was done by age 33 and dead by 36. Vance had cups of coffee at ages 24 and 27, but didn’t establish himself until age 31. In the end, the shooting star and the late bloomer had pretty much equal value.

DRYSDALE: I know that I will catch flak, if anyone cares, for putting Drysdale ahead of Koufax. But from a career comparison against a replacement baseline, it is tough to avoid, as Drysdale has twelve more WAR and is only four behind in WAA. There is absolutely no question that Koufax was the Dodgers’ ace, but four or five years don’t override the career. Neither lasted much past thirty, but Drysdale pitched 1000 more innings.

WYNN: The lowest-ranking 300 game winner, and perhaps sliding him past Drysdale was inappropriate, but certainly a fine pitcher.

NEWHOUSER: Some people take away credit because two of his best seasons came during the war. 1945 was his best, but actually 1946 was a little better then 1944. Anyway, the principle here is that a major league win is worth the same no matter what. Top five years of +49.8 WAR is a dead ringer for Koufax. In fact, he had a six year string from 1944-49 of 10.7, 12.8, 11, 7.5, 7.5, 7.8.

PIERCE: Pierce is the highest ranking pitcher on my list not in the Hall of Fame who is either 1) eligible or 2) not through to the Vets Committee yet. There are two eligible pitchers ahead of him who have not yet been inducted, but they are both still on the main ballot.

Tuesday, June 19, 2007

Homers in (Win) Context

As Barry Bonds closes in on Hank Aaron’s record, there will surely be a lot of discussion about which player’s accomplishments are more impressive, who is more worthy of the record, etc. From a sabermetric perspective, there are a number of different approaches available to shed light on the comparison. These generally attempt to evaluate not only the raw totals but the context in which they were achieved.

One of the most basic examples is the use of relative or adjusted statistics, comparing the frequency of home runs hit by a player to that of his league, and using this to give a plus/minus figure against the league average, or to restate that figure as a new raw number of homers expected in a different context. These results might be based on the difference or ratio of the player’s performance to that of his league.

Another approach along the same lines is to look at the number of standard deviations away from the mean the player’s performance is. This has the presumed effect of accounting for league quality, with the theory that a lower standard deviation means a higher-quality league.

One can also look at ranks or percentiles of performance within the league. Under this approach, leading the league in home runs is considered equally impressive to leading the league in a different year. The best of a given time are assumed to be equal to the best of another time.

There are also more complex approaches that attempt to project performance in a different context while maintaining the same run or win value of the player’s overall performance. Examples of these approaches include Bill James’ “Willie Davis Method” and Clay Davenport’s Davenport Translations.

All of these approaches have their pros and cons. Relative methods are easy to understand, but often give results that are outlandish (ex. Babe Ruth would hit 100+ home runs in a modern context if he bettered the league home run rate by the same ratio as he did in his great seasons). Rank and percentile methods assume that leading a deadball league with 11 homers is inherently equivalent to leading a modern league with 55 homers.

The standard deviation and translation methods have less obvious flaws. The biggest hurdle to the translation methods is complexity; the principles behind Davenport’s have been explained, but not the details. The Willie Davis method is based on a flawed run estimator (basic Runs Created), which makes all of the results somewhat circumspect.

My approach is similar in spirit to those, but cuts out a good deal of complexity with maybe a small loss in theoretical purity. It is hardly a unique or revolutionary approach, and for all I know may have been published by another analyst in nearly identical form, but if it has I do not recall seeing it. As I have explained in previous posts on other subjects, I begin my analysis of baseball performance with the premise that a major league win today is worth the same as a major league win in 1961 is worth the same as a major league win in 1927…you are of course free to disagree with this premise, but it is where I am coming from.

Saying that a win is a win is not immediately helpful when moving away from comparing estimated win contributions of players to comparing player performance in specific component categories, like home runs. However, in a linear weight construct, we can put a run or win value on each home run that the batter hits. By comparing the win value of player’s home runs, we can avoid making any assumptions about how difficult it was to hit home runs in the given contexts, and focus on what the home runs the player actually hit were actually worth in his own context.

After all, home runs are only valuable because they contribute to wins. Hitting 70 home runs, even in a modern high-scoring context, contributes more wins to a player’s team then hitting 10 home runs to lead the league in the dead ball era. It may have been “harder” to hit the ten homers, they may have stuck out more from the other players in that time in terms of standard deviations or differences in frequency, but that does not matter from a pure value perspective. All that matters is the number of wins each player contributed via the home run in his own time and place. And of course we also started with the premise that a major league win is of equal value regardless of the year in which it was achieved.

So how does this approach work? Let’s assume that the run value of a homer is always 1.4 runs. This is obviously not correct; the coefficient of a home run is variable, although it is not nearly as variable as that of some other events. You could of course use Base Runs or some other approach to find a unique coefficient for the HR in each context, but I am going to just use 1.4, while acknowledging that it is imprecise.

Let’s look at Roger Maris’ 1961 season. His 61 home runs are estimated to be worth 1.4*61 = 85.4 runs. We will assume that the runs per win factor is equal to the total number of runs per game in the league that season. This again is imprecise, but not to too great a degree, and it makes things very simple. In 1961 the AL average was 9.06 RPG. We can also account for how Maris’ home park changed the value of runs in terms of wins. I have the ’61 Yankee Stadium PF at .94. That means that the prevailing RPW in Maris’ context was PF*RPG or .94*9.06 = 8.52. Putting it all together, the win value of Maris’ home runs was 1.4*HR/(PF*RPG) or 1.4*61/(.94*9.06) or 85.4/8.52 = 10.02 wins.

We can keep Maris’ figure at 10.02, but homer-wins are not in a scale that we are familiar with, and we can easily convert this into a number of homers in an average major league context of 9 RPG. All we have to do is figure out how many homers one would need in a 9 RPG context to get 10.02 homer-wins. The answer is 10.02*9/1.4 = 64.4, or we can easily express that New HR = HR/(PF*RPG)*9, since we are assuming that the home run is worth 1.4 runs, always.

We can now figure equivalent win-value home runs for all players. Let’s look at a Gavvy Cravath, leading the NL in longballs with 19 in 1913. The NL RPG was 8.3, and Cravath’s park had a PF of 1.04. Cravath therefore had 19.8 adjusted home runs. Since this is kind of a frivolous stat, I’ll give these adjusted home runs a less serious name, Gavvys. I’m using Cravath here because he is an example that leading the lead in home runs did not have the same value in 1913 as it did in 1961. Hitting home runs in 1913 was, as always, beneficial to the team, but 19 homers just do not produce that many wins. Again, it is feasible that Cravath’s performance was more difficult to achieve or more impressive then Maris’. Whether it was or not is irrelevant when considering the win value they had.

I calculated Gavvys for all of the members of the 500 home run club (through 2006, considering only performance up to 2006. Each season was evaluated individually and the totals were summed for a career). Here is the list sorted by Gavvys:

No player’s home runs have had a higher win impact then Hank Aaron’s, and he has a wide enough margin that his “record” may sustain Bonds’ challenge. Ironically, Bonds has 755 Gavvys, matching Aaron’s real total. Only Foxx and Williams played in high enough scoring environments to see their modified figures drop below 500. Here is the list again, this time sorted by Gavvys minus home runs.

The overall trend is for Gavvys>homers, which is most likely because 4.5 is not the true long term mean; we could use 1 as the mean, or 1000, or leave them in terms of homer-wins, and the order of the career leader list would hold, so 4.5 works just fine.

In order to find the best single season Gavvy performance, I also looked at the 50 home run club. Obviously, these seasons will not represent all of the best single seasons in terms of Gavvys, but doubtlessly the record-holder will be found. And the 50 in a season club is a natural one to consider, just like the 500 in a career. The list is sorted by Gavvys, and “DIFF” again is Gavvys less actual home runs:

Bonds’ 2001 and McGwire’s 1998 still top the list, with Maris’ 1961 holding against all of the other times McGwire and Sosa beat the raw total. Ruth’s single season luster fades a bit as does his career total, while multiple seasons tumble out of the 50 HR club.

Take Gavvys for what they are worth--they only focus on one single event and attempt to restate it as a win-equivalent figure in a certain context. They are based on the assumptions I discussed earlier and they are by no means the be all and end all of accounting for context in determining the best home run hitters. I do believe that they represent an interesting way to evaluate home runs while keeping an eye on the ultimate goal of the game (winning), and evaluating them in that light.

Let me stress again that Gavvys are not a projection of how many home runs a player would have hit in a nine RPG context, and do not attempt to adjust for how difficult it was to hit home runs in the player’s environment (RPG coupled with PF is to some extent a proxy for this, but that is not how it is being used here). What they are is a number of home runs in a 9 RPG context that would be equal in win value to the win value of the player’s home runs in his actual context.

Tuesday, June 12, 2007

My Top 60 Starters, 51-60

Here is the first group of 10:
60. Dave Stieb (.561 NW%, 120 ARA, +28 WAA, +68 WAR)
59. Jack Quinn (.526, 109, +18, +73)
58. Addie Joss (.616, 133, +33, +65)
57. Sandy Koufax (.633, 130, +33, +65)
56. Tommy Bridges (.570, 122, +29, +68)
55. Urban Shocker (.609, 126, +31, +68)
54. Waite Hoyt (.531, 111, +22, +74)
53. Rick Reuschel (.547, 114, +23, +73)
52. Wilbur Cooper (.551, 115, +25, +73)
51. Babe Adams (.567, 121, +29, +71)

I’m not going to discuss each pitcher, but will comment on some.

STIEB: He’s not a guy that you think of as one of the greats, but he had one of the best peaks of roughly cotemporary pitchers (Gooden, Saberhagen, Cone). Again, in this area of the rankings there is not a lot of distinction between the pitchers, so being #60, there are a lot of others you can make a case for.

QUINN: Jack Quinn might be the least known pitcher with 247 wins. Adjusting to his teams, his neutral record is 244-221. His runs allowed stats look similar, so he’s a guy who doesn’t do that great against average but could be ranked several spots higher if you focus on WAR. He only had one 20 win season, with the Baltimore Feds in 1914, and bounced around, with two main stints with the Yankees and one with the Red Sox and the A’s.

JOSS & KOUFAX: Many people will be stunned to see Koufax so low, but by career value, you have to start raising the baseline from replacement in order to even get him on the list. Koufax and Joss do have the highest WAA for any pitchers in this group, and were certainly brilliant. Koufax had better W-L records, but they are almost dead ringers in the other categories. The reason I’ve put Koufax ahead is that he was pitching fifty years later.

However, Koufax’s peak value is perhaps not as astronomical as some believe it to be, depending on how it is defined. His best five seasons by WAA are 1962-66, by WAR 1961 and 1963-66. Only four of those were truly brilliant, those being 63-66. His WAR over his top five seasons was +50, fifteenth best of the pitchers I’ve looked at, but within two and a half wins are Carlton, Maddux, and Clemens, while Gibson and Seaver both rank slightly higher then him. The difference is that the others did not string their peaks together as Koufax did.

So if your definition of peak is “top 3 or 4 consecutive seasons”, then Koufax is the greatest modern peak pitcher. But if you use other definitions, he’s just one of the best. This is a great example of the issues I have with peak value.

REUSCHEL: Another modern pitcher who nobody expects to see here, but the guy was good. He’s probably underrated by traditionalists because they don’t account for the fact that he pitched in Wrigley Field from 1972-81 when the PF was hovering around 1.08. For his career, he pitched in a 1.05 PF park on average. His peak is nothing to write home about, but that doesn’t count for much here. I believe Bill James had him around eightieth.

Friday, June 01, 2007

Discounted Team Championships

Here I’m just going to have a little fun with the idea of “discounted team achievements” I discussed in this post. The basic thing you need to know is that I decided to deflate past achievements by 3% per year, compounding. So a game won three years ago is now, in today’s equivalent, 1/(1.03^3) = .915 wins.

Here we are going to examine Discounted Team Championships, where the championships are of the World Series variety. There is no credit given for a pennant, a playoff appearance, or a good regular season. The base year is 2006, so the Cardinals’ win is worth a full 1 championship. The White Sox’ occurred one year prior to the base year, so it is worth 1/1.03. The Red Sox’ 1/1.03^2, the Marlins 1/1.03^3, the Angels 1/1.03^4, and so on. Then we just sum these for all of the teams that have ever won the World Series, and we have the franchise total.

For simplicity’s sake, I have defined the franchise as the entity, regardless of where they played, so the Boston/Milwaukee/Atlanta Braves are all considered “ATL”, the old(est) Senators are the Twins, etc. So which franchises fans should, under this model, have the most satisfaction from all of their teams’ championships?

Not surprisingly, the Yankees are #1, and the Cardinals, the only other team with double-digit WS wins and the defending champs are #2. The #3 A’s may seem surprising, but remember that they have won four titles in the last thirty-five years, which means that any A’s fan from 45 up should have experienced a good share of WS wins. On the flip side, it is not surprising that the Indians and the Cubs bring up the rear, as they have had the longest droughts and each have only one additional title to go along with the most recent.

An interesting question is how long would the Yankees have to go without winning the World Series in order to fall behind the Cardinals on this list? Of course, the Cardinals standing will change over that period, as will all of the teams, some up and some down. But the point is not to compare the Yankees to the Cardinals; it is to say “How long would the Yankees have to go before their fans’ satisfaction would be lower then the next-best alternative as of 2006?”

The answer is 2038. Now if the Yankees go another 31 years without winning it all, there are going to be a lot of angry New Yorkers. Which is an opportunity to emphasize again that the 3% rate is a figure chosen because it made sense to me. It may only model the way I think; I certainly wouldn’t claim that it is “correct” in any sense, or that others should think this way. From the sports culture, it would seem that Yankees fans (and even their owner) have a much higher deflation rate. Maybe Yankees fans set the rate at 10%, while Cubbies fans are more patient and would set it at .05%. Of course all of these would vary among the individuals that make up those fan bases as well.

The Yankees would also lead the list today over the Cardinals had they not won a title since 1977. The five that they have won since then have only served to advance their lead over the Cards from 3.82 DTC from 21 real titles to their current 7.43/26.

The point, again, is that this is an exercise done in fun, not to make any hard conclusions about everything. It’s just a different way of thinking about comparing team histories while placing more emphasis on recent performance.

There have been 102 World Series, and the sum of the discounted titles is 31.96. With this, we can see that the ratio is 3.2 real titles/discounted titles. We can multiply each franchise’s DTC by 3.2 to put it on an equivalent scale to actual titles. That gives us this list:

We can use either the ratio of actual titles to DTC or the difference between the actual titles and the DTC equivalents to find the teams that have gotten the most bang for the buck for their titles. The difference is easier to process as a number, but it also favors larger numbers for teams with large number of titles. The Yankees have 2 less DTC equivalent titles then actual titles; they still have 24 DTC equivalent, which is not going to cause anyone to shed any tears for them. So by ratio:

Looking at this list, we can see that the most fortunate teams are recent winners of their only championship(s), which is not exactly a surprise, but it accounts for the Angels, Diamondbacks, Marlins, Blue Jays, Royals, and Phillies. On the flip side, we can see that the Cubs and the Giants have the greatest disconnect between what it says in the record book and the amount of satisfaction their current fans have received from it. My Indians also stand out; I hope to see this rectified some time in the near future.