The Gezer conundrum, again

My anonymous commentator is trying to understand the park effects at Gezer. Actually, so am I.

The problem in a nutshell is how to distinguish between the skill levels of the home teams at Gezer and the effects of the park itself. Gezer was home to Bet Shemesh and Modiin, the league's two biggest slugging teams. If you look at the home run totals at Gezer versus the other fields, you'll find a tremendous gap:



Teams at Gezer scored over 2.8 times as many home runs per game as teams playing at Yarkon, and about 2.7 times as many home runs per fly ball. Compared to Sportek, the ratios are 2.4 and 2.2. Overall, 117 of the IBL's 187 home runs, or 63%, were hit at Gezer, where just 39% of the games were played.

But the performance gap narrows substantially when we look at broader measures of offense, not just home runs:



Batters at Gezer actually reached base less often than those at Sportek, and not a whole lot more than those at Yarkon. The slugging gap is substantial, but not nearly as wide as the home run gap. This may reflect on the pitchers of Bet Shemesh and Modiin, which were among the league's best.

If we count times reached base on errors as hits - which for all intents and purposes they are - the gap narrows further:



Remember that error rates were highest at Yarkon and Sportek. Counting errors, it turns out that on-base rates were pretty similar across the fields, with Sportek leading. In slugging, which is less important to run scoring than getting on base, Gezer led Sportek by just 60 points (or 13%) and Yarkon by 110 (28%).

Translated into run scoring, in runs per game, plate appearance and 27 outs:



That's right. At Gezer, the average game scored just 12% more runs than at Yarkon and 10% more than at Sportek. Per plate appearance, that's 14% more than Yarkon and 8% more than Sportek; per out, 15% more than Yarkon and 7% more than Sportek.

If you followed my recent post about how runs are scored, you'll understand why. Getting on base is much more important than slugging. And there are plenty of ways to score other than home runs.


What about the park factor?

But that 12-15% run boost at Gezer is not Gezer's park factor for runs. How much of the run increase was due to the field at Gezer, and how much due to the high-slugging teams that played there?

To find that out, you have to compare how the same set of teams played at Gezer versus away from Gezer. That's what I ultimately did in this post, where I took all the teams that played each other at least twice both at Gezer and elsewhere (and likewise for the other parks). This gives us a close approximation of how the different parks affect the same player matchups.

And that's where I discovered that though Gezer produced a home run boost of 76% over Sportek and 176% over Yarkon, overall run production for the same team matchups was just 4.4% higher than at Yarkon, and was actually 2.5% lower than at Sportek.

Now, these figures may be substantially inaccurate. The sample size is very small, with just 122 games distributed among six teams and three fields. The "pros" estimate major-league park effects over at least three full seasons of 162-game play. All sorts of noise could be skewing these results: a few unrepresentative games, or an untimely injury, or the distribution of pitchers in the games being compared.

But it seems clear that most of the 12-15% difference in run production among the three venues (as opposed to home run hitting) can be attributed to the offensive power of the teams that played in them.

This is consistent with the per-team run production averages:



Look at Bet Shemesh and Modiin, which shared Gezer; Netanya and Tel Aviv, which shared Sportek; and Petach Tikva and Ra'anana, which shared Yarkon. Most of the apparent park factors for run production are in fact due to differences in team offensive ability.


The upshot

What does this mean for comparing player performance? That park factors have their main impact on individual components of performance, such as home runs or strikeout rates. When comparing them among players, we have to pay close attention to park effects. But when comparing overall run production, we can be sloppier, since the park differences are not great.

For precise comparisons, we should weight performances by their respective parks by adjusting the run production estimates on a per-park basis, and I hope to post park-adjusted tables for batting leaders soon. But whatever corrections are necessary will not change the overall offensive domination by the Bet Shemesh sluggers.


One last comment. The two run production estimators I'm currently using, Base Runs and custom IBL linear weights, when calibrated to match overall IBL run scoring are also quite accurate at estimating overall run production at Gezer. But they show similar biases for the other two fields, overestimating production at Sportek by about 3.7% and underestimating production at Yarkon by some 3%. This could be pure chance, if teams overall scored about 12 more runs than should be expected at Yarkon and about 12 fewer at Sportek. But it might indicate that the formulas aren't quite capturing all the aspects of run production at the two fields.

Perhaps run estimates based on these formulas should be scaled up or down 3% to calibrate them to the actual results at Sportek and Yarkon.

Surprise! Park factors are not what you expected!

I'd like to take a first stab at estimating IBL park factors.

For this first attempt, I'm going to average the performance of all six teams at each of the three fields.

I know I already explained why that's somewhat problematic: it overweights the home teams at each park, so that (for example) Gezer, home to the IBL's strongest batters (Bet Shemesh and Modiin) would have its park effects exaggerated in favor of batting, while Yarkon, home to the league's weakest teams (Petach Tikva and Raanana) would look too much like a pitcher's park.

To correct for this problem, I've decided to weight each team's record equally at each of the fields. That is, rather than tote up all the games played at each field and average the number of runs, hits, etc., I computed each team's individual performance at each field, and then averaged the team results weighting each team equally.

So even though Bet Shemesh played 24 games at Gezer and Modiin played 27, while Petach Tikva played only 9 there, I've treated them as equal for the purpose of averaging Gezer's performance levels. The same, of course, goes for Sportek and Yarkon.

This approach doesn't eliminate all forms of bias in the computation. For example, the home teams are still overrepresented in the average level of fielding faced at each park. But nothing we do will realistically eliminate all forms of bias, and I consider this approach to be a reasonable start.

The envelope, please:


Now, for the analysis. We've already seen the home run effects. Gezer produced 32% more home runs per game than the average field, while Yarkon produced 37% fewer. Overall, home runs were hit more than twice as often at Gezer as at Yarkon (relative factor: 2.08), and the difference from Sportek was nearly as large (1.82). Presumably, this is mainly due to the distances to the fences. Most of those Gezer home runs became fly outs at Yarkon.

So Gezer was a big hitters' park, right?

Not so fast.

What about triples?

Triples aren't that common to begin with. Only 19 were hit in the IBL season. Of those, 13 were at Yarkon, 6 at Sportek and 0 at Gezer. Shorter fences, not enough room to hit a triple.

How about base hits? Not much to say about them. Gezer was smack in the middle here, with a range of just 13% in hit rates between the three fields - probably too narrow to be meaningfully distinguished, given the sample size. Gezer was above average for doubles, with Yarkon below average, but again the range was not that great - 19%. Total bases from all hits - including those frequent Gezer homers - was just 7% above average at Gezer, with Yarkon 11% below average, a range of 21%.

Gezer also yielded more strikeouts and fewer walks than average. Overall, after home runs, the most telling column in the chart, and the most relevant to winning or losing games, is the one labelled R. Average runs per game, when weighting all six teams equally, varied within a range of 5% among the three parks. And Gezer was by no means the leader - it was just below average!

What can we learn from this? First, as usual, the data doesn't always support our intuitions about baseball. Second, a lot more goes into a baseball game than home run hitting. Third, if we were to assess IBL batters by adjusting their performances based on park factors, we'd see changes in home runs and triples, but batting and slugging averages wouldn't be affected much.

To confirm that suspicion, I calculated batting and slugging averages on the same basis as the park factors - averaging team results per field on an equal basis. (I don't have enough data tabulated yet to analyze on-base percentages.)

IBL 2007 batting and slugging averages by field, weighting teams equally at each field
Field	AVG	SLG
IBL	.270	.411
Gezer	.271	.435
Sportek	.284	.380
Yarkon	.251	.359

So how much does Gezer field inflate offense? Not as much as I expected, at least.