*Blogger's note: As it often happens with interesting research, it appears that someone was working along the same lines and published before I intended to. Russell Carleton at BPro just posted a piece on game time regressions. Now, I really don't know most of what he said because I don't have a subscription. Because of this, and because I'm guessing most of you don't have a BPro subscription either, I'm going to post my work anyway. Enjoy!*

**Time of Game**

Games with more

**innings**last longer to the tune of about 10 minutes and 13 seconds each. The same applies to individual

**pitches**(+0:26) and

**pitching changes**(+1:48). We can expect high offense games to take longer: controlling for the other variables, each

**run**adds 1:19. Close games take longer than blowouts: adding a run to the

**margin of victory**shaves 1:14. Of course, when the home team wins a non-walkoff, the game is a half inning shorter.

**Home wins**yield a savings of 3:13,

*ceteris paribus*.

Slightly less intuitive are the effects of batters faced and the time of the season during which games are played. In a world with no money and no television, playoff games would take just as long as any other game. However, in our society playoff games command higher TV ratings, more ad dollars and thus longer commercial breaks. All else being equal in 2009,

**LDS**games lasted an additional 39:41,

**LCS**games another 42:38, and

**World Series**games another 40:17.

Counterintuitively, additional

**at bats**appear to make games

*shorter*to the tune of 29 seconds each. How can additional batters faced shorten a game? Well, if every at bat took an equal amount of time, then of course at bats would have an undoubtedly positive effect. However, this is not the case: close games should have

*longer*at bats (more pick-off attempts, more conferences, etc...) than blowouts. Therefore, a close three-hour match will have longer at bats than a three-hour blowout. Of course, if time of game remains constant while the

*duration*of at bats increases, then the

*number*of at bats will decrease. The unexpectedly inverse correlation probably stems from this phenomenon.

Some variables I expected to influence the initial model turned out to be statistically insignificant. Games where a

**DH**bats were no longer or shorter than non-DH games, so there was nothing particularly unusual about games in AL parks in 2009.

**Weekend**games had no discernible effect (even though they're more likely to be televised nationally), nor did the number of

**strikes**thrown (which I expected would shorten the game). Despite the higher stakes of

**divisional matchups**, the effect of these games on game time was indiscernible from chance.

Finally, what I really wanted was a variable measuring "game importance," based on the assumption that pitchers would be more cautious, managers more involved, and network producers greedier in high-stakes games. These games might be elimination games, but they also may be divisional rivalries or interleague matchups. As a proxy, I substituted relative attendance, or

**attendance vs. stadium capacity**. I felt this was a long shot, but as it turns out relative attendance is both positively correlated and statistically significant. A game that is fully attended should last about 3 minutes and 4 seconds longer than one that is filled to 50% capacity.

**The BOS-NYY Factor**

At this point we have a good understanding of what makes long games long--the variables we've already discussed explain ~80% of the variation in game times during the 2009 season. But at the same time, we don't yet know if Yankee-Red Sox games are long because A) they tend to be outliers among the variables we've already discussed, or B) because there's something about Yankee-Red Sox games that makes them particularly long even when controlling for all of the above.

To find out, let's make a few changes to our model. First, let's introduce the Yankees and Red Sox as independent binary variables (also known as "dummy" variables) for games in which one of the two teams played. Second, let's isolate the effect of pitch counts by changing our dependent variable from "minutes played" to "minutes per 100 pitches" or MHP. In doing so we get some pretty interesting results.

Even when controlling for all the variables presented above, games involving either the Yanks or BoSox tend to last longer than others: Yankees games last an extra 12:09, while the Red Sox require an additional 6:20. Even when isolating the number of pitches thrown,

**Yankee**

**games**require an extra 3:35 to reach 100, while the

**Red Sox**take another 1:49. To put this in perspective, each inning adds just over 10 minutes to a game. According to this model,

*we can expect a Yankees-Red Sox matchup to nearly add the equivalent of two innings of playing time,*ceteris paribus.

Also notable--when isolating for pitch counts--is that many of the variables from the initial models remain significant, and some that were not significant become so.

**Weekend**games take longer to reach 100 pitches than non-weekend games, to the tune of about 19 seconds per 100 pitches. More

**strikes**means less time to reach the century mark, with each strike shaving off about 6 seconds.

**Designated hitters**and

**divisional matchups**remain insignificant.

Finally, when isolating for pitches thrown, the negative effects of

**at bats**and the positive effects of

**attendance**remain significant. It is interesting however, when the Yankees and Red Sox variables are included in the model, that the substantive effects of attendance decrease. In the full game time model, a shift from half-capacity to a sell-out cuts only 2:47 from a game (as opposed to 6:20). It appears that much of this effect is likely from games at Fenway that A) always push 100% capacity B) always involve the Red Sox.

**Conclusion**

Unfortunately, I did not have time to compile data on TV schedules, so I was not able to perfectly isolate the effect of commercial breaks for nationally broadcast games. However, weekend, playoff series and attendance variables should serve as decent proxies.

Games tend to be

*substantially*longer when they involve the Yankees and the Red Sox, even when controlling for all else. It appears that Joe West has a point--there is something peculiar about the way the Yankees and Red Sox play the game that makes their games longer than normal, and that effect can be especially bad when they play each other. But were the Yankees and Red Sox the worst offenders of 2009?

Tune in tomorrow for the answer!

**Game Time Series**

Part I: Introduction

Part II: Response to Joe West

Part III: What Makes Long Games Long?

Part IV: Head-to-Head Matchups

Tables

Independent Variable | Model 1 (Minutes) | Model 2 (Minutes) | Model 3 (Minutes) | Model 4 (MHP) | Model 5 (MHP) | Model 6 (MHP) |

Innings | 10.210 | 10.197 | 10.411 | 2.904 | 2.906 | 2.936 |

At Bats | -0.486 | -0.529 | -0.517 | -0.115 | -0.116 | -0.114 |

Pit. Changes | 1.794 | 1.790 | 2.061 | 0.456 | 0.462 | 0.515 |

Pitches | 0.433 | 0.410 | 0.388 | |||

Strikes | -0.055 | -0.099 | -0.099 | -0.105 | ||

Weekend | 0.724 | 0.316 | 0.311 | 0.428 | ||

LDS | 39.676 | 39.706 | 37.772 | 12.953 | 12.920 | 12.377 |

LCS | 42.629 | 42.963 | 38.969 | 13.082 | 13.046 | 11.831 |

WS | 40.287 | 40.412 | 30.943 | 13.284 | 13.255 | 10.448 |

DH | 0.447 | -0.057 | ||||

Division | 0.349 | 0.073 | ||||

Runs | 1.318 | 1.336 | 1.305 | 0.380 | 0.379 | 0.364 |

Run Diff. | -1.231 | -1.229 | -1.214 | -0.414 | -0.413 | -0.411 |

Home Win | -3.209 | -3.173 | -3.365 | -1.025 | -1.028 | -1.075 |

Attend % | 6.145 | 6.330 | 2.778 | 1.856 | 1.877 | 0.777 |

Red Sox | 6.328 | 1.815 | ||||

Yankees | 12.152 | 3.586 | ||||

Constant | -27.738 | -27.499 | -24.499 | 52.414 | 52.426 | 53.245 |

Adjusted R^2 | 0.796 | 0.796 | 0.811 | 0.278 | 0.278 | 0.319 |

Weakly significant (0.05 > p > 0.10) | ||||||

Not statistically significant (p > 0.10) | ||||||

n = 2448 |

Minutes (1) | Coefficient | Std. Error | P>t |

Innings | 10.210 | 0.518 | 0.000 |

At Bats | -0.486 | 0.076 | 0.000 |

Pit. Changes | 1.794 | 0.178 | 0.000 |

Pitches | 0.433 | 0.020 | 0.000 |

Strikes | -0.055 | 0.037 | 0.137 |

Weekend | 0.724 | 0.550 | 0.188 |

LDS | 39.676 | 3.524 | 0.000 |

LCS | 42.629 | 3.838 | 0.000 |

WS | 40.287 | 5.102 | 0.000 |

DH | 0.447 | 0.523 | 0.393 |

Division | 0.349 | 0.509 | 0.493 |

Runs | 1.318 | 0.085 | 0.000 |

Run Diff. | -1.231 | 0.109 | 0.000 |

Home Win | -3.209 | 0.543 | 0.000 |

Attend % | 6.145 | 1.113 | 0.000 |

Constant | -27.738 | 3.366 | 0.000 |

n = 2448 | |||

Adjusted R^2 = 0.7961 |

Minutes (2) | Coefficient | Std. Error | P>t |

Innings | 10.197 | 0.516 | 0.000 |

At Bats | -0.529 | 0.070 | 0.000 |

Pit. Changes | 1.790 | 0.174 | 0.000 |

Pitches | 0.410 | 0.012 | 0.000 |

LDS | 39.706 | 3.512 | 0.000 |

LCS | 42.963 | 3.811 | 0.000 |

WS | 40.412 | 5.093 | 0.000 |

Runs | 1.336 | 0.084 | 0.000 |

Run Diff. | -1.229 | 0.109 | 0.000 |

Home Win | -3.173 | 0.541 | 0.000 |

Attend % | 6.330 | 1.069 | 0.000 |

Constant | -27.499 | 3.344 | 0.000 |

n = 2448 | |||

Adjusted R^2 = 0.796 |

Minutes (3) | Coefficient | Std. Error | P>t |

Innings | 10.411 | 0.497 | 0.000 |

At Bats | -0.517 | 0.067 | 0.000 |

Pit. Changes | 2.061 | 0.168 | 0.000 |

Pitches | 0.388 | 0.011 | 0.000 |

LDS | 37.772 | 3.383 | 0.000 |

LCS | 38.969 | 3.692 | 0.000 |

WS | 30.943 | 4.974 | 0.000 |

Runs | 1.305 | 0.081 | 0.000 |

Run Diff. | -1.214 | 0.105 | 0.000 |

Home Win | -3.365 | 0.521 | 0.000 |

Attend % | 2.778 | 1.066 | 0.009 |

Red Sox | 6.328 | 0.992 | 0.000 |

Yankees | 12.152 | 0.971 | 0.000 |

Constant | -24.499 | 3.226 | 0.000 |

n = 2448 | |||

Adjusted R^2 = 0.811 |

MHP (4) | Coefficient | Std. Error | P>t |

Innings | 2.904 | 0.174 | 0.000 |

At Bats | -0.115 | 0.025 | 0.000 |

Pit. Changes | 0.456 | 0.057 | 0.000 |

Strikes | -0.099 | 0.007 | 0.000 |

Weekend | 0.316 | 0.186 | 0.089 |

LDS | 12.953 | 1.190 | 0.000 |

LCS | 13.082 | 1.293 | 0.000 |

WS | 13.284 | 1.722 | 0.000 |

DH | -0.057 | 0.176 | 0.743 |

Division | 0.073 | 0.172 | 0.669 |

Runs | 0.380 | 0.028 | 0.000 |

Run Diff. | -0.414 | 0.037 | 0.000 |

Home Win | -1.025 | 0.183 | 0.000 |

Attend % | 1.856 | 0.376 | 0.000 |

Constant | 52.414 | 1.137 | 0.000 |

n = 2448 | |||

Adjusted R^2 = 0.2779 |

MHP (5) | Coefficient | Std. Error | P>t |

Innings | 2.906 | 0.173 | 0.000 |

At Bats | -0.116 | 0.025 | 0.000 |

Pit. Changes | 0.462 | 0.056 | 0.000 |

Strikes | -0.099 | 0.007 | 0.000 |

Weekend | 0.311 | 0.185 | 0.093 |

LDS | 12.920 | 1.187 | 0.000 |

LCS | 13.046 | 1.290 | 0.000 |

WS | 13.255 | 1.721 | 0.000 |

Runs | 0.379 | 0.028 | 0.000 |

Run Diff. | -0.413 | 0.037 | 0.000 |

Home Win | -1.028 | 0.183 | 0.000 |

Attend % | 1.877 | 0.370 | 0.000 |

Constant | 52.426 | 1.128 | 0.000 |

n = 2448 | |||

Adjusted R^2 = 0.2784 |

MHP (6) | Coefficient | Std. Error | P>t |

Innings | 2.936 | 0.169 | 0.000 |

At Bats | -0.114 | 0.025 | 0.000 |

Pit. Changes | 0.515 | 0.054 | 0.000 |

Strikes | -0.105 | 0.007 | 0.000 |

Weekend | 0.428 | 0.180 | 0.018 |

LDS | 12.377 | 1.154 | 0.000 |

LCS | 11.831 | 1.261 | 0.000 |

WS | 10.448 | 1.696 | 0.000 |

Runs | 0.364 | 0.027 | 0.000 |

Run Diff. | -0.411 | 0.036 | 0.000 |

Home Win | -1.075 | 0.178 | 0.000 |

Attend % | 0.777 | 0.373 | 0.038 |

Red Sox | 1.815 | 0.338 | 0.000 |

Yankees | 3.586 | 0.330 | 0.000 |

Constant | 53.245 | 1.099 | 0.000 |

n = 2448 | |||

Adjusted R^2 = 0.3189 |

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