Does the crowd make a difference to the D-backs performance?

The first thoughts in this direction came after Saturday night's game, where a crowd of over 37,600 cheered on Barry Enright and the Diamondbacks at Chase, to a 3-1 victory over Ubaldo Jimenez and the Rockies. It reminded me of SnakePitFest v3.2, where a full house enjoyed a walk-off home-run by Chris Young, after which he said, "When you're out there in the field and you hear the screaming fans it definitely makes a difference for us. Pretty much the fans got us the win tonight." Is that the case? Do home teams in general - and Arizona in particular - play better when there are more people in the stands?

After the jump, we'll take a look to see if there's evidence for this.

At first glance, it would appear so. The three best-attended games of the year to date were Opening Day, the first game in the Yankees series, and Gonzo Retirement Night, and all three resulted in Diamondbacks victories. Expanding the parameters a little further, Arizona are 9-6 when there are more than 28,000 people in attendance, which is a pretty good rate, considering the team's record is 30-36 overall at home in 2010. However, if we look at the extreme other end of the spectrum, the Diamondbacks also appear to play well when largely untroubled by attendees - they have gone 8-8 with less than eighteen thousand in the stands.

More analysis is clearly needed. Next step: average attendance at Chase Field this year for losses: 24,661. For wins: 25,888. That suggests a slight tendency for the team to play better in front of more people. However, if you try to correlate runs scored and runs allowed against crowd numbers, you get the complete opposite result. Runs scored has a marginally negative correlation of -0.06 and runs allowed is fractionally positive (+0.09). That means, the Diamondbacks score less and allows more as the crowd goes up, though it's a pretty weak connection. 

One of the things to note is that not all large crowds are created equal. When Luis Gonzalez retired, just about everyone in the park was cheering for the Diamondbacks. On the other hand, while the number in attendance for the game against the Yankees was almost the same, the crowd was much more evenly-split, and any fan-related energy would seem to apply in the appropriate proportion. It also is likely the case that good teams are more likely to draw fans to Chase: while the Diamondbacks may play better, they could well also be facing better opposition. Again, the Yankees provide a good example of this.

But let's expand things: given the somewhat... "relaxed," shall we say, nature of the Phoenix fan, might we find more impact elsewhere, in cities better known for a rabid fanbase? As a measure of increased home performance, we take the winning percentage of a team there and subtract the winning percentage on the road. The difference which results ranges from zero - Tampa Bay have the same record at Tropicana and elsewhere - to .303, for Detroit, who are 43-24 at home and 20-39 on the road. We then match that against the average crowd for that team. The theory would be, a big home crowd should result in an improved home/road differential. Is that what we see?

Here are the results for all thirty major-league teams, through Tuesday night's games:

Tm	Hm W-L		W%	Rd W-L		W%	Diff	Att
ARI	30	36	.455	19	41	.317	.138	24,805
ATL	44	17	.721	29	36	.446	.275	30,407
BAL	27	38	.415	17	44	.279	.137	21,069
BOS	39	25	.609	33	29	.532	.077	37,630
CHC	28	38	.424	25	36	.410	.014	38,453
CHW	36	24	.600	32	33	.492	.108	26,891
CIN	36	26	.581	36	28	.563	.018	25,585
CLE	26	34	.433	24	41	.369	.064	17,726
COL	40	20	.667	25	40	.385	.282	35,206
DET	43	24	.642	20	39	.339	.303	30,803
FLA	31	31	.500	31	31	.500	.000	17,979
HOU	32	33	.492	24	36	.400	.092	28,288
KCR	29	33	.468	24	40	.375	.093	20,383
LAA	33	29	.532	29	36	.446	.086	40,008
LAD	39	27	.591	25	35	.417	.174	44,796
MIL	30	33	.476	29	33	.468	.008	34,746
MIN	40	22	.645	32	32	.500	.145	39,742
NYM	37	22	.627	26	40	.394	.233	33,024
NYY	42	22	.656	36	26	.581	.076	46,429
OAK	38	27	.585	24	35	.407	.178	17,890
PHI	42	24	.636	28	31	.475	.162	44,948
PIT	29	36	.446	13	48	.213	.233	20,185
SDP	37	22	.627	38	27	.585	.043	25,573
SEA	29	32	.475	20	44	.313	.163	27,076
SFG	39	23	.629	32	33	.492	.137	37,350
STL	41	23	.641	27	32	.458	.183	40,977
TBR	39	24	.619	39	24	.619	.000	22,781
TEX	41	23	.641	30	31	.492	.149	29,499
TOR	32	25	.561	33	35	.485	.076	19,664
WSN	31	29	.517	22	44	.333	.183	23,932

The correlation between differential and attendance is 0.140; present, but not huge. It seems to have more effect at the lower end of attendance. Of the bottom 13 teams in attendance, only three - the Pirates, Nationals and A's - have a differential more than ten points better than league average (.128); two are within ten points of it, and eight are 20+ points lower  However, there are exceptions: the Yankees, Angels and Cubs are all  well-attended, with differentials below average. I also correlated % of park capacity against the differential to see if it was better to have a small, full stadium, than a large, half-empty one. However, the correlation there was only 0.046, basically negligible.

Specifically with regard to the Diamondbacks, our home-road differential is marginally above average, despite the lackluster crowds at Chase this year. I thought I'd also crank the wayback machine up, and see what the numbers were for Arizona, for each year in franchise history. Did the crowds that packed the stadium in 1998, lured by the novelty of baseball, lead to an improved home-field advantage for the team? In two word: not much. Here's the same chart as above, done for each season of Diamondbacks history.

Year	Hm W-L		W%	Rd W-L		W%	Diff	Att
1998	34	47	.420	31	50	.383	.037	44,571
1999	52	29	.642	48	33	.593	.049	37,280
2000	47	34	.580	38	43	.469	.111	36,324
2001	48	33	.593	44	37	.543	.049	33,783
2002	55	26	.679	43	38	.531	.148	39,494
2003	45	36	.556	39	42	.481	.074	34,636
2004	29	52	.358	22	59	.272	.086	31,106
2005	36	45	.444	41	40	.506	-.062	25,425
2006	39	42	.481	37	44	.457	.025	25,823
2007	50	31	.617	40	41	.494	.123	28,707
2008	48	33	.593	34	47	.420	.173	30,987
2009	36	45	.444	34	47	.420	.025	26,281
2010	30	36	.455	19	41	.317	.138	24,805

There's pretty much no discernible trend here either. The correlation over the history of the Diamondbacks is 0.173, in line with the overall MLB number this season. Again, the lowest attendances - 2005, 2006 and 2009 - tend to equate in general with the lowest differentials, but there are exceptions, such as this season, where Arizona are performing much better at home [this year's differential is the second-highest in franchise history]. As in the majors overall, while there seems to be a slight connection, you'd be hard pushed to claim much predictive effect.

There is certainly a benefit to playing on your own turf. Over the 1,215 games played last season, the home team won 54.9%, very close to the numbers in the two years prior to that (55.6% and 54.2%). That only works out to about four games over the course of the season, perhaps not as much as you might expect. From what we've seen here, the home crowd - or, at least, their basic number - do not seem to be a significant part of that benefit, probably representing only a fraction of a win in a year. Maybe the silent majority at Chase are right to save their energy!