A Second Look at Luck

“Anyone who has never made a mistake has never tried anything new.”– Albert Einstein

As we’ve been reporting on our home page, the reviews of The Hardball Times Baseball Annual 2006 have been very good, and I’d like to take this opportunity to publicly praise Aaron Gleeman and Dave Studeman for the many hours they devoted to getting the book out the door.

But alas, despite their dedication they couldn’t prevent some of their writers’ mistakes from creeping into the book, not the least of which was yours truly. And so I’d also like to take this opportunity to make two corrections related to my article “Are You Feeling Lucky?” that were, in the literal translation of the Latin phrase mea culpa, or “through my own fault.”

For those who haven’t read the book (and shame on you if you haven’t ), the article is a continuation of sorts of a study Phil Birnbaum presented at last year’s SABR convention in Toronto. In that study Phil attempted to quantify the confluence of factors that might tell us which teams were the most fortunate in recent history. He used five factors in his analysis, which you can read about here.

In the article I used three of these when analyzing the 2005 season including:

A team scoring more runs than expected by its batting line

A team allowing fewer runs than expected by the opposition’s batting line

A team winning more games than expected by its ratio of runs scored to runs allowed

After discussing some of the reasons that teams might excel or fall short in each of these areas, including hitting with runners in scoring position, great performances by relievers, performance in one-run games and team scoring distribution (all of which, of course, are not totally luck but are influenced by it), I went on to perform the calculations for each factor and bring them together to come up with the total positive or negative number of runs for each team. I then applied this value to their actual win-loss record to try to project what each team’s record might have been had the “luck” been removed.

While my calculations for the third factor listed above do not have to be adjusted, those for the first two do.

First, those who looked at the lists of runs allowed for each team on page 137 may have noticed that the table indicates that the Mariners gave up 642 runs. They didn’t. They actually gave up 751 runs, a whopping error. You’ll also find errors for the Giants, Indians, Marlins, Mets and Nationals. Contrary to Einstein’s quote, this mistake didn’t occur from trying something new; it can be attributed to nothing more interesting than an Excel operator error.

The second mistake, however, is more instructive. I noted in the article that I used the BaseRuns (BsR) formula in order to estimate how many runs a team would be expected to score and how many the team would allow given both its batting line and its opponents’. In using BsR for the article I calculated a single B multiplier for the entire 2005 season. In thinking about it later what I should have done is calculate separate multipliers for the NL and AL. I have now done this, and the result is that NL teams are not as clustered towards the top of the lists on pages 135 and 136. In other words, NL teams don’t underperform their offensive BsR estimate and overperform their defensive BsR estimates as much as indicated in the tables.

These new calculations have been taken into account in order to re-create each team’s projected win-loss record with the “luck” extracted as shown below.

                  Actual                                    Projected
                   W    L    Pyth Pitching  Hitting  Total    W    L
Diamondbacks      77   85     113     -17        56    152   62  100
White Sox         99   63      78      42        11    132   86   76
Red Sox           95   67      50      15        -7     58   89   73
Padres            82   80      55     -12        14     56   76   86
Nationals         81   81      39      19        -3     55   76   86
Yankees           95   67      55     -16         8     47   90   72
Angels            95   67      16      50       -26     40   91   71
Giants            75   87      42     -12        -3     27   72   90
Marlins           83   79      36     -19         3     20   81   81
Cubs              79   83      -9     -11        38     18   77   85
Orioles           74   88      -1     -19        37     17   72   90
Indians           93   69     -32       4        39     11   92   70
Braves            90   72      -7      29       -17      5   89   73
Twins             83   79      -9       7         0     -2   83   79
Astros            89   73     -21      15         3     -4   89   73
Devil Rays        67   95      22     -43        15     -6   68   94
Reds              73   89     -25      19        -3    -10   74   88
Brewers           81   81     -31      12         2    -17   83   79
Phillies          88   74      -8      -5        -8    -22   90   72
Rockies           67   95     -28      15       -19    -32   70   92
Cardinals        100   62      16       2       -52    -34  103   59
Tigers            71   91     -38     -20        23    -35   74   88
Mets              83   79     -60      10        -2    -53   88   74
Rangers           79   83     -26     -33         3    -57   85   77
Dodgers           71   91     -28     -15       -14    -58   77   85
Pirates           67   95     -50     -18         6    -62   73   89
Blue Jays         80   82     -81      43       -26    -64   86   76
Mariners          69   93     -68      15       -21    -74   76   86
Athletics         88   74     -48      -2       -30    -81   96   66
Royals            56  106     -42     -19       -21    -82   64   98

While the order of the luckiest (at the top) to unluckiest (at the bottom) teams remains relatively constant, these corrections have changed some of the summary points I offered at the end of the original article.

For example, in the initial analysis the Indians and White Sox came out about even with the projected record for the Sox at 89-73, while for the Indians it was 88-74, thereby vindicating Sox fans everywhere who were offended by the implication made by some (like me) who considered their hot start in 2005 as driven mostly by good fortune. Correcting the Indians runs allowed the Tribe to move up to 92-70, while the Sox slid to 86-76. In another example, by correcting the Nationals’ runs allowed, they also don’t look as fortunate as they did initially, because now their projected record is 76-86 whereas before it was 69-93. Of course many things didn’t change, and the poor Royals, on top of all their other problems, were still eight wins “unlucky,” while the A’s could have won their division had things fallen their way and the Angels not been quite so fortunate.

As I said in the original article, the element of luck is signficant in baseball even over the course of an entire season. But far from disdaining the role of chance in the game, I think that’s one of the reasons we enjoy watching so much. You never know what’s going to happen because in the end, it really is a “game of inches.”