### Monday, July 28, 2003

What is BAP?

Right now, many of the bases gained and lost in a baseball game are not being recorded. Others are being recorded, but they aren't being included in any of the percentages developed to evaluate teams or players. The purpose of BAP is to evaluate baseball teams and players with one measurement by including bases and outs gained and lost by every act on the baseball field, including:

Hits

Outs

Walks

Hit Batsmen

Sacrifices

Sacrifice Flies

Fielder's Choice

Double Plays

Stolen Bases

Fielder's Indifference

Wild Pitches

Passed Balls

Balks

Errors

Base Running

The formula used by BAP to accomplish this reads as follows:

BAP = # of bases advanced / # of plate appearances

where bases advanced equals total bases + walks + HBP + EXTRA BASES GAINED - bases gained by a baserunner lost.

There are some definitions that need to be explained in regards to the formula. Extra Bases Gained includes any bases gained in any activity that is not already included in the formula. Those activities would include:

Sacrifices

Sacrifice Flies

Fielder's Choice

Double Plays

Stolen Bases

Fielder's Indifference

Wild Pitches

Passed Balls

Balks

Errors

Base Running

Extra Bases gained by base runners are recorded whenever a baserunner advances more bases than the number of bases recorded on a hit, including moving two bases or more on a single, or three bases on a double.

Bases Gained By a Base Runner Lost includes all bases gained by that baserunner already, including any bases gained by sacrifices and sacrifice flies that moved that runner forward. For instance, say a player walked, went to third on a single, and was thrown out at home on an attempted sacrifice fly. It would be (-2) EBs, one for the base gained on the walk, and another for the Extra Base gained going from first to third on the single. But if the player who was thrown out at home was on third because he had tripled, that would be (-3 ) EBs, because the out negates the three bases he had already been credited for.

Here are a couple of examples of BAP at work. The innings are taken from game logs at ESPN:

SAN DIEGO 5TH

-G Stephenson relieved J Fassero.

-Bottom of the 5th inning

-R Vazquez walked. (0 EBs)

-G Matthews Jr singled to center, R Vazquez to second. (0 EBs)

-M Loretta hit by pitch, R Vazquez to third, G Matthews Jr to second. (0 EBs)

-R Klesko hit sacrifice fly to center, R Vazquez scored, G Matthews Jr to third. (2 EBs)

-R White grounded into fielder's choice to third, G Matthews Jr scored, M Loretta out at second. (1 EB)

-B Buchanan struck out looking.(0 EBs)

The Padres gain two Extra Bases on Klesko's Fly, because two runners moved up one base without a hit. On Rondell White's grounder, they gain a base when Matthews moves up a base without a hit. White replaces Loretta at first, so there are no bases won or lost there. The total Padres score for the inning is 3 EBs.

-Top of the 4th inning

-A Nunez grounded out to first.

-J Suppan singled to left.

-J Kendall singled to left, J Suppan to second.

-J Wilson flied out to deep right, J Suppan to third.

-B Giles doubled to right center, J Suppan and J Kendall scored, B Giles tagged out at third attempting to advance on throw.

The Pirates get an Extra Base when Suppan moves to third on the flyball. On the next play, there's an EB when Kendall scores from first on a Giles' double, because he has advanced three bases on a two-base hit. But when Giles is thrown out at third, he costs the team 2 EBs for losing the double. The total Pirates EB score for the inning is 0.

BAP For Individual Players

In order to come up with a BAP score for individual players, we need to figure out just who should get credit for bases gained in all of the acts that gain Extra Bases. Let's go through those one by one:

Sacrifices - Credit for the Extra Base will go to the hitter. If it is a squeeze play, credit will be divided evenly between the batter and the runner.

Sacrifice Flies - If a runner goes from first to second or second to third, he will get credit for it. If the SF scores a run, credit will be divided evenly between the runner and the batter.

Fielder's Choice - Any base gained during a fielder's choice will be divide evenly between the runner and Team Bases.

Double Plays - The lost base will be charged to the hitter on a grounder, to the baserunner on any type of attempted SF, and as a Team Base on a liner to an infielder.

Stolen Bases - Credit goes to the runner.

Fielder's Indifference - Credit goes to the runner.

Wild Pitches - Team Base. No player gets credit for the first base. The runner wil be charged with a lost base if he is thrown out. The runner will get credit for any additional bases after the first one.

Passed Balls - Same as Wild Pitches

Errors - Same as Wild Pitches

Base Running - The runner will get credit for any bases beyond the number of bases of the hit that has caused him to run. Example - 2 bases on a single is 1 EB.

There is one inherent problem in BAP for individual players. A player's opportunities to advance on the bases are directly related to the performance of players hitting around him. It might be better to get a look at a player's base running ability independent of his hitting ability, in which case we could use a formula such as this:

(# of times a player advances from first to third on a single) + (# of times a player advances from second to home on a single) + (# of times a player advances from first to home on a double) + ( # of times a player scores from third on a flyout or a grounder that does not become a doubleplay) + (0.5 x # of times a player scores from third on a fielder's choice) + (all other Extra Bases) - (base running outs) divided by Opportunities, where Opportunities = (# of times a player is on first when a non-infield single is hit, and no other baserunner is blocking him) + (# of times a player is on second when a non-infield single is hit) + (# of times a player is on first when a double is hit) + ( # of times a player is on third and there is a flyball out, or a groundout) + (all base running outs).

There are ways to gain Extra Bases in this formula that are outside of the Opportunities listed, such as stealing bases. In those cases, because they are either very rare or because they are already independent of what the player's teammates are doing, we consider those to be bonus opportunities that the player has created for himself, and the player is only charged for them if he is thrown out.

Right now, many of the bases gained and lost in a baseball game are not being recorded. Others are being recorded, but they aren't being included in any of the percentages developed to evaluate teams or players. The purpose of BAP is to evaluate baseball teams and players with one measurement by including bases and outs gained and lost by every act on the baseball field, including:

Hits

Outs

Walks

Hit Batsmen

Sacrifices

Sacrifice Flies

Fielder's Choice

Double Plays

Stolen Bases

Fielder's Indifference

Wild Pitches

Passed Balls

Balks

Errors

Base Running

The formula used by BAP to accomplish this reads as follows:

BAP = # of bases advanced / # of plate appearances

where bases advanced equals total bases + walks + HBP + EXTRA BASES GAINED - bases gained by a baserunner lost.

There are some definitions that need to be explained in regards to the formula. Extra Bases Gained includes any bases gained in any activity that is not already included in the formula. Those activities would include:

Sacrifices

Sacrifice Flies

Fielder's Choice

Double Plays

Stolen Bases

Fielder's Indifference

Wild Pitches

Passed Balls

Balks

Errors

Base Running

Extra Bases gained by base runners are recorded whenever a baserunner advances more bases than the number of bases recorded on a hit, including moving two bases or more on a single, or three bases on a double.

Bases Gained By a Base Runner Lost includes all bases gained by that baserunner already, including any bases gained by sacrifices and sacrifice flies that moved that runner forward. For instance, say a player walked, went to third on a single, and was thrown out at home on an attempted sacrifice fly. It would be (-2) EBs, one for the base gained on the walk, and another for the Extra Base gained going from first to third on the single. But if the player who was thrown out at home was on third because he had tripled, that would be (-3 ) EBs, because the out negates the three bases he had already been credited for.

Here are a couple of examples of BAP at work. The innings are taken from game logs at ESPN:

SAN DIEGO 5TH

-G Stephenson relieved J Fassero.

-Bottom of the 5th inning

-R Vazquez walked. (0 EBs)

-G Matthews Jr singled to center, R Vazquez to second. (0 EBs)

-M Loretta hit by pitch, R Vazquez to third, G Matthews Jr to second. (0 EBs)

-R Klesko hit sacrifice fly to center, R Vazquez scored, G Matthews Jr to third. (2 EBs)

-R White grounded into fielder's choice to third, G Matthews Jr scored, M Loretta out at second. (1 EB)

-B Buchanan struck out looking.(0 EBs)

The Padres gain two Extra Bases on Klesko's Fly, because two runners moved up one base without a hit. On Rondell White's grounder, they gain a base when Matthews moves up a base without a hit. White replaces Loretta at first, so there are no bases won or lost there. The total Padres score for the inning is 3 EBs.

-Top of the 4th inning

-A Nunez grounded out to first.

-J Suppan singled to left.

-J Kendall singled to left, J Suppan to second.

-J Wilson flied out to deep right, J Suppan to third.

-B Giles doubled to right center, J Suppan and J Kendall scored, B Giles tagged out at third attempting to advance on throw.

The Pirates get an Extra Base when Suppan moves to third on the flyball. On the next play, there's an EB when Kendall scores from first on a Giles' double, because he has advanced three bases on a two-base hit. But when Giles is thrown out at third, he costs the team 2 EBs for losing the double. The total Pirates EB score for the inning is 0.

BAP For Individual Players

In order to come up with a BAP score for individual players, we need to figure out just who should get credit for bases gained in all of the acts that gain Extra Bases. Let's go through those one by one:

Sacrifices - Credit for the Extra Base will go to the hitter. If it is a squeeze play, credit will be divided evenly between the batter and the runner.

Sacrifice Flies - If a runner goes from first to second or second to third, he will get credit for it. If the SF scores a run, credit will be divided evenly between the runner and the batter.

Fielder's Choice - Any base gained during a fielder's choice will be divide evenly between the runner and Team Bases.

Double Plays - The lost base will be charged to the hitter on a grounder, to the baserunner on any type of attempted SF, and as a Team Base on a liner to an infielder.

Stolen Bases - Credit goes to the runner.

Fielder's Indifference - Credit goes to the runner.

Wild Pitches - Team Base. No player gets credit for the first base. The runner wil be charged with a lost base if he is thrown out. The runner will get credit for any additional bases after the first one.

Passed Balls - Same as Wild Pitches

Errors - Same as Wild Pitches

Base Running - The runner will get credit for any bases beyond the number of bases of the hit that has caused him to run. Example - 2 bases on a single is 1 EB.

There is one inherent problem in BAP for individual players. A player's opportunities to advance on the bases are directly related to the performance of players hitting around him. It might be better to get a look at a player's base running ability independent of his hitting ability, in which case we could use a formula such as this:

(# of times a player advances from first to third on a single) + (# of times a player advances from second to home on a single) + (# of times a player advances from first to home on a double) + ( # of times a player scores from third on a flyout or a grounder that does not become a doubleplay) + (0.5 x # of times a player scores from third on a fielder's choice) + (all other Extra Bases) - (base running outs) divided by Opportunities, where Opportunities = (# of times a player is on first when a non-infield single is hit, and no other baserunner is blocking him) + (# of times a player is on second when a non-infield single is hit) + (# of times a player is on first when a double is hit) + ( # of times a player is on third and there is a flyball out, or a groundout) + (all base running outs).

There are ways to gain Extra Bases in this formula that are outside of the Opportunities listed, such as stealing bases. In those cases, because they are either very rare or because they are already independent of what the player's teammates are doing, we consider those to be bonus opportunities that the player has created for himself, and the player is only charged for them if he is thrown out.