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It is by now well known that some version of the mis-called “Pythagorean” formula is a good reckoning of probable games won from runs scored and runs allowed in some number of games. That formula is—
—where n is a number that Bill James originally set at simply 2; but further investigation has shown that the best result comes from a value of 1.8455.
The average number of wins by the NL West division leader over the past 4 years is 97.5. Thus, the target we want to design our team for is 98 wins. So what R and OR numbers do we need? The MLB average team runs per season for the last two years (projecting 2026 runs per team from September 12th stats) is 728. We can start with a rough rule-of-thumb reckoning that 10 runs is about one win’s worth; so, to get from 81 wins to 98 wins would thus—again, as a broad-brush first estimate—take 17 wins, meaning a 170-run differential. If we want our team to have pitching and hitting carry equal loads, that means scoring 85 runs (170 divided by 2) above average and allowing 85 runs below average. And that means scoring 813 runs (728 + 85) and allowing 643 runs (728 - 85).
But! Those numbers derive from MLB-average play. To get the same win result in Oracle Park, we need to adjust both runs numbers down. The business of meaningful “park factors” is messy and fairly unreliable. There are numerous sources that purport to deliver Runs park factors. Here are a few for Oracle:
That’s not all of them, but suffices to give you the flavor.
(See also An Empirical Assessment of MLB Park Factors by Xavier Fünf)
I have used 0.94, which happens to be the average of the six shown above (though that’s not how I came to it). That converts the criteria to R = 764 and OR = 604, which we can round off to 765 R and 605 OR (and of course their average, 685 just about equals = 728 x 0.94 = 684).
Now, and vital, we need to understand what we have arrived at. The figures of 765 and 605 are guidelines. What we will be doing next is using those guidelines as indicators of which batters and pitchers we do or don’t want, based on their TOPs and TPPs (as appropriate). (The TOP or TPP for a man is, in effect, what a lineup or staff made up entirely of exact clones of him whould score or give up (respectively).
But, again, those are guidelines. And something to keep in mind is that you cannot get to a team TOP (or TPP, as the case may be) by just using a PA- or BFP-weighted sum of the individual players’ numbers. That is because, in general, the product of the averages is not equal to the average of the products.
To clarify what the mouthful means, look at this simple example:
5 x 7 = 35 9 x 3 = 27 ----------- 14 10 62 sums 7 5 31 averages
But 7 x 5 (the product of the averages) is 35, while 31 (not 35) is the average of the products!
And TOPs and TPPs are—like most good runs-scored equations—a multiplicative process (on-base probability times runner-advance probability).
That is not a criitical issue, as the point applies to both offense numbers and defense numbers, but it does mean one shouldn’t try to reckon real-world team numbers from a simple PA-weighted (or BFP-weighted) averaging of individual player numbers.
The bottom line, then, is that in looking at individual Giants players, we really, really want batters whose TOPs (in Oracle) are at least 760 and pitchers whose TPP (again, in Oracle) are no more than 600. If a significant part of their career numbers come from elsewhere than Oracle, we need to try making allowances for the park differences (not simple, and I won’t go into that topic here). Anyway, now onward.
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