04 May 2010

Game Time Part III: What Makes Long Games Long?

So what exactly is it that makes games longer and shorter? Here I employ an Ordinary Least Squares regression model to test the variables that influence game time. Some of these variables are obvious, some less so. Let's take a look at each one individually (tables below).

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. 

As noted above, games tend to be longer when they consist of more innings, more pitching changes, more runs, when more people show up to see them in person, when they occur on the weekend, and when they take place during the postseason. Games tend to be shorter when they include more at bats, more strikes, larger margins of victory, and when the home team wins.

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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