## Are Crucial Games Slower Than Trivial Ones?

Do teams slow down when there is more at stake?

A couple of trends indicate that they do. While there is no basic indicator of game "importance" (that I am aware of), we can infer importance by looking at a few other variables, such as attendance, the absolute quality (win percentage) of the two teams in the match-up and the relative quality (divisional rank, games back) of the two teams in the match-up.

Theoretically, unimportant games should draw fewer fans than important games; crucial games should see a higher sell-thru ratio (attendance / stadium capacity). Additionally, games with two winning teams should be more important than games with two losing teams.

A quick look at the chart above confirms (or fails to reject) the working hypothesis: there is a clear positive relationship between sell-thru and game pace (minutes played per hundred pitches thrown, or MCP). A chart below the jump shows a similar relationship between team quality (the sum of the two teams' win percentages) and pace.

Albeit, the lines don't fit too well to the data points in a simple bivariate relationship, nor is the slope particularly steep, but multivariate testing shows that the relationship is actually rather strong.

Above, we see the same relationship between team quality and pace. Note that both charts are significantly bracketed. The attendance chart ignores games prior to 4/15/10 to avoid including opening day games, which are usually well-attended but have little impact on playoff advancement. The team quality chart looks only at games after the all-star break, by which point the differences between team win percentages have largely stabilized. Both charts include only the regular season.

The real impact of these variables is more obvious when we plug them into a multivariate model that controls for more obvious variables, such as innings pitched, batters faced, pitches thrown, runs scored, run differential and bullpen calls (to name a few). For those of you who want to examine the full models, I've included the coefficient, standard error and significance data below. For the rest of you, allow me to summarize:

• During the regular season, a 50% increase in sell-thru correlates with a four minute increase in game duration and a 1.5 minute increase in game pace (MCP), ceteris paribus.
• During the regular season, a .500 increase in total team quality (sum of win percentages) yields a 4.5 minute increase in game duration, and a 0.9 minute increase in game pace, ceteris paribus.*
• During the regular season, a match-up between two first-place teams lasts nearly two minutes longer than a match-up between a first- and a fifth-place team, and would slow down by about 0.5 MCP.

*Note that duration and pace are calculated in two different models, with different variables and an all-other-variables-equal assumption, so duration calculations do not necessarily equal pace-by-pitches-thrown numbers.

To confirm the working hypothesis one must to investigate more deeply, with additional years of data and better variables. However, until we develop the equivalent of leverage index for games during a season, these numbers do suggest that, controlling for all else, crucial games take longer to complete than trivial ones.

 Duration Models (Time in Minutes) Regular Season + Postseason Regular Season Only Model 1 Model 2 Model 3 Model 4 Coef. SE Coef. SE Coef. SE Coef. SE Innings Pitched -0.2630 0.4803 -0.2019 0.4777 Batters Faced 0.5586 0.0704 0.5269 0.0521 0.5572 0.0701 0.4218 0.0108 Pitches Thrown 0.4314 0.0164 0.4272 0.0108 0.4211 0.0165 2.3735 0.1328 Strikes Thrown -0.0100 0.0257 -0.0011 0.0258 Runs Scored -0.1446 0.0788 -0.1153 0.0607 -0.1364 0.0783 -0.1088 0.0602 Run Differential -0.9612 0.0846 -0.9538 0.0841 -0.9621 0.0842 -0.9667 0.0835 Pitching Changes 2.3654 0.1361 2.3735 0.1355 2.4117 0.1368 -0.1088 0.0602 Weekend Game 0.0127 0.4189 0.0064 0.4188 AL Home Game 0.6962 0.3974 0.6912 0.3959 0.6113 0.4070 Division Matchup 0.1887 0.3909 0.2516 0.3880 Games Back (Sum) -0.0498 0.0251 -0.0445 0.0248 Games Back (Difference) -0.0497 0.0293 -0.0500 0.0293 WPCT (Sum) 9.2687 1.6947 9.1255 1.6887 WPCT (Difference) -3.2155 1.8162 -3.3193 1.8138 Division Rank (Sum) 0.2358 0.1338 0.2035 0.1311 Division Rank (Difference) -0.4569 0.1837 -0.4742 0.1830 Division Series 17.8651 2.4919 17.6780 2.4787 Championship Series 23.7970 2.7702 23.7094 2.7616 World Series 19.3449 4.2704 19.1094 4.2580 Attendance Sell-thru 8.6490 0.8263 8.6427 0.8068 8.2196 0.8694 8.0164 0.8347 Constant -4.9721 2.5337 -5.7310 2.1765 -14.3652 3.4163 -14.3961 3.1378 N 2456 2456 2424 2424 R^2 0.8768 0.8768 0.8787 0.8786 Adjusted R^2 0.8761 0.8763 0.8779 0.8780 Significant at p <= 0.05 Significant at p <= 0.10 Not significant at p <= 0.10

 Pace Models (Minutes per 100 Pitches) Regular Season + Postseason Regular Season Only Model 1 Model 2 Model 3 Model 4 Coef. SE Coef. SE Coef. SE Coef. SE Innings Pitched 0.4401 0.1729 0.3045 0.1354 0.4712 0.1732 0.4726 0.1729 Batters Faced 0.0595 0.0241 0.0795 0.0190 0.0546 0.0241 0.0551 0.0240 Strikes Thrown -0.0728 0.0063 -0.0732 0.0063 -0.0734 0.0063 -0.0735 0.0063 Runs Scored 0.0357 0.0288 0.0402 0.0288 0.0409 0.0287 Run Differential -0.3239 0.0313 -0.3138 0.0298 -0.3266 0.0314 -0.3272 0.0312 Pitching Changes 0.7328 0.0494 0.7288 0.0480 0.7393 0.0498 0.7361 0.0485 Weekend Game -0.0135 0.1554 -0.0137 0.1563 AL Home Game 0.1267 0.1471 0.0506 0.1515 Division Matchup 0.0016 0.1450 0.0151 0.1448 Games Back (Sum) -0.0117 0.0093 -0.0113 0.0092 Games Back (Difference) -0.0129 0.0109 -0.0130 0.0109 WPCT (Sum) 1.7513 0.6317 1.7975 0.4886 WPCT (Difference) -1.2007 0.6781 -1.2129 0.6757 Division Rank (Sum) -0.0043 0.0499 Division Rank (Difference) -0.1268 0.0686 -0.1285 0.0683 Division Series 6.7366 0.9234 6.7595 0.9197 Championship Series 7.5680 1.0276 7.5683 1.0244 World Series 7.6920 1.5831 7.7705 1.5803 Attendance Sell-thru 2.9861 0.3065 2.9505 0.2967 2.8492 0.3245 2.8335 0.3079 Constant 59.2250 0.9389 59.3462 0.9314 57.8401 1.2756 57.7749 1.0392 N 2456 2456 2424 2424 R^2 0.2641 0.2634 0.2311 0.2310 Adjusted R^2 0.2602 0.2607 0.2259 0.2272 Significant at p <= 0.05 Significant at p <= 0.10 Not significant at p <= 0.10

Data from BaseballReference.com

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